Introduction to Behavioral Economics by Just

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Introduction to Behavioral Economics by Just is the textbook authored by David R. Just, Cornell University, and published in 2014 by John Wiley & Sons, Inc.

  • Absolute magnitude effect is the observation that people tend to require proportionally less compensation to delay larger amounts of consumption. This leads to an observation of higher empirical discount factors when larger amounts are in play and behavior that is much closer to rational exponential discounting. One explanation for this effect is found in asymmetric elasticity condition employing a prospect-theory value function.
  • Absolute risk aversion is a measure, based on expected utility theory, of how willing someone is to take on a dollar of risk. Absolute risk aversion measures the relative curvature of the utility function and can be written as RA = −u″ u′, where u is the utility of wealth function. The larger the value, the less willing one is to take on a given risk.
  • Acquisition utility is the utility obtained from consumption of the good minus the utility lost from giving away an amount of wealth equal to the cost of consumption. In this book this is often referred to as the utility of consumption.
  • Additive model of intertemporal choice supposes that one's utility function of consumption in this period, c1, and consumption next period, c2, can be represented by U c1, c2 =u c1 +δu c2, where δ represents a discount factor.
  • Allais' paradox is a violation of the independence axiom generated by manipulating a common outcome between two gamble choices. Independence implies that any two gambles that include probability p of outcome x should lead to the same choice no matter what x is chosen. Typically this paradox is observed when the choice between a pair of gambles where x= 0 is compared to the choice between a pair in which x>0.
  • α-maxmin expected utility theory is a model of ambiguity aversion. Let p be the set of possible probability distributions over outcomes. Further, let p p be such that maxxE U x p= p ≤ maxxE U x p p , for all p p . Also, let p p be such that maxxEUx p=p ≥ maxxEUx p p , for all p p . Then a person behaving according to α-maxmin expected utility theory will behave so as to solve maxxαE U x p= p +αEUx p= p . The coefficient α is a measure of ambiguity aversion. A person is considered ambiguity averse if α> 1 2 and ambiguity loving if α < 1 2
  • Altruistic refers to preferences such that decision makers are willing to reduce their own consumption in order to increase to consumption of at least one other person.
  • Ambiguity is a situation in which either decision makers face unknown probabilities associated with outcomes resulting from their choices, or they are not aware of the possible outcomes.
  • Ambiguity aversion is a tendency to choose gambles with explicitly stated probabilities over those that involve ambiguity (probabilities are not known) even if this could result in loss of utility.
  • Anchoring and adjusting is a heuristic process for forming beliefs in which the decision maker takes some convenient value as an anchor and then makes adjustments from this value to determine the final answer. Often the anchor is some unrelated number that happens to be presented at the time of decision. Generally this anchor then affects the outcome belief despite being unrelated to the decision at hand.
  • Asymmetric elasticity condition requires that the utility of losses is more elastic than utility of gains. Let z2 >z1 >0. Then we can express this requirement in terms of arc elasticities as − z1 +z2 v −z1 −v −z2 z2 −z1 v −z1 +v −z2 > z1 +z2 v z2 −v z1 z2 −z1 v z1 +v z2 , or for any z> 0 in terms of exact elasticities as − zv′ −z v −z > zv′ z v z . This is closely related to the notion of strong loss aversion. Asymmetric elasticity is one explanation for the gain–loss asymmetry in intertemporal choice.
  • Availability heuristic leads one to estimate the probability of an event by how easily one can recall or construct an event in one's mind. Thus, events that might have been more publicized or more extreme can be judged to be more probable than they truly are.
  • Backward induction is method of solving for the optimal behavior of an intertemporal decision maker with sophisticated preferences. To employ this method, you begin by solving for the optimal behavior in the last period of the decision problem, then solve for behavior in the second-to-last period assuming optimal behavior in the last, and so on. This method is also often used in game theory to solve for subgame perfect Nash equilibrium (SPNE).
  • Base rate neglect is the tendency to ignore or severely discount prior information about the frequency of an event when judging the probability of that event. In the terms of Bayes' rule, the prior information is underemphasized and the likelihood information is overemphasized.
  • Bayesian Nash equilibrium is the Nash equilibrium concept employed in games involving uncertain payoffs. This is in reference to the requirement that each player must have beliefs regarding the strategies and playoffs of all other players that is consistent with their strategies in the equilibrium. In this game we require that each player has the same prior beliefs regarding the distribution of valuations and that each anticipates the correct strategy of others given their valuation. At each information set, beliefs are updated according to Bayes' rule, a statistical tool for updating probabilities based on information available.
  • Behavioral anomaly is defined as behavior that differs from the predictions of the rational choice model. The term anomaly generally suggests that the behavior is rare, though still potentially important.
  • Behavioral choice model is a model designed to describe observed choices without necessarily explaining the motivations or considerations of the decision maker when making the decision.
  • Behavioral economics is the study of how observed human behavior affects the allocation of scarce resources. This field of economics incorporates the tools from psychology and sociology into more traditional economic theory.
  • Behavioral model see behavioral choice model.
  • Betweenness is an axiom often used in place of the independence axiom. If A B, and C is a compound gamble that yields A with probability p and some gamble B with probability 1 −p , then betweenness implies that A C B. Betweenness implies that all indifference curves must be straight lines, though they may differ in slope.
  • Bliss point is the lowest amount of consumption above which the consumer no longer desires to consume no matter what the price. This is the maximum point on the utility of consumption curve considering the consumption of all other goods to be fixed.
  • Bounded rationality is the notion that people behave rationally given the constraints on information, cognitive resources, and time.
  • Bracketing refers to how choices are grouped in the process of decision making. Broadly bracketed decisions take many simultaneous choices into account at once. Narrowly bracketed decisions may ignore the effect of one decision on the other choices facing the consumer.
  • Calibration refers to one's ability to accurately relate probabilistic information. One is well calibrated if, when one forecasts that an event will happen with probability x, the event happens about x percent of the time.
  • Cancellation is one component of the editing phase of prospect theory. In cancellation, components that are common to the gambles being considered are eliminated before the choice is made.
  • Certainty effect is the general tendency of decision makers to prefer outcomes with certainty beyond what is implied by expected utility theory. Uncertain outcomes face an additional penalty beyond the loss of probability associated with them.
  • Certainty equivalent is the amount of money with certainty that players would receive in place of a gamble that would leave them with the same level of utility.
  • Cheap talk refers to nonbinding discussions or commitments between players in a game.
  • Coding is one activity engaged in by decision makers in the editing phase of prospect theory decision making under risk. The decision maker codes each outcome as a gain or a loss.
  • Coefficient of ambiguity aversion is a measure of ambiguity aversion resulting from the α-maximin expected utility model of decision under ambiguity. The higher the value of α, the more ambiguity averse the person. The person is considered ambiguity averse if α > 1 2, and ambiguity loving if α < 1 2 . The coefficient of ambiguity aversion must be contained in the unit interval.
  • Cold state refers to a state in which visceral factors (such as hunger, anger, or arousal) are latent. In this state, people might have a difficult time anticipating their preferences at some future date when these visceral factors become active.
  • Combination is one activity in the editing phase of prospect theory. In combination, probabilities associated with identical outcomes are combined before the decision is made.
  • Commitment mechanisms allow decision makers to impose penalties on their future self if they deviate from their planned activities.
  • Committed decision maker is one who can enforce her consumption plans on her future self no matter what her future preferences.
  • Common difference effect is the observation that period-by-period discount factors applied to future consumption appear to change depending upon how far in the future the events will take place. Let δ be the period by period discount factor. The fully additive model of time discounting imposes that people will be indifferent between consuming c at time t and c′ at time t′ if U c = δt′ −t U c′ , where the discount only depends on the interval between t and t′ and not the starting time. However, research has found that empirical discounts tend to be much deeper in the near future than in the distant future.
  • Common outcome effect is a violation of the independence axiom. See Allais' paradox for a description.
  • Common ratio effect is a violation of the independence axiom generated by offering a choice between a pair of gambles, and then a choice between two compound lotteries in which the decision maker has a fixed probability of obtaining the original gambles, and a remaining probability of obtaining a payoff of $0. The violation typically occurs when the probability of $0 added to each gamble is relatively high and the gambles are of a $-bet and P-bet form.
  • Common-value auction is an auction for an item that has the same value to each bidder bidding in the auction, though this value is unknown and uncertain.
  • Complete preferences implies that for any two potential choices people either prefer the first, prefer the second, or are indifferent between the two. This is a general requirement for rational decision theory.
  • Compound gamble is a gamble that consists of the combination of two separate gambles.
  • Conditional probability function is a function p A B that measures the probability of event A given that event B has occurred or will occur.
  • Confidence interval is an interval that represents the most probable location of an unknown parameter. Let θ be an unknown parameter and θ be an estimate of the unknown parameter. Then, the x percent confidence interval is a confidence interval θ −l, θ + u , such that P θ − l < θ = 100− x 200, and P θ + u> θ = 100− x 200.
  • Confirmation bias is a general tendency commonly displayed either to seek information that is likely to confirm one's currently held beliefs or to interpret vague information as being generally supportive of one's currently held beliefs.
  • Confirmatory information is information that could potentially conform to one's currently held belief but that cannot possibly (or is at least unlikely to) contradict one's currently held belief.
  • Confirming forecast is an information forecast that almost always results in information that is congruent with current beliefs.
  • Conjunction effect is the tendency to judge the probability of two events A and B occurring jointly to be larger than the probability of event A, where B is a representative event and A is an unrepresentative event.
  • Conservatism is the tendency to discount or ignore new information and continue to hold on to prior beliefs. This is the opposite of base rate neglect.
  • Constant additive loss aversion describes a set of reference structures that satisfy constant loss aversion and for which vr x = n i=1 Ri xi .
  • Constant loss aversion describes a set of reference structures that assume that the utility of gains and losses differs by a multiplicative constant. A reference structure is displaying constant loss aversion if the preferences can be represented as a utility function of the form vr x = U R1 x1 , , Rn xn , with Ri xi = ui xi −ui ri if xi ≥ ri ui xi − ui ri λi if xi < ri. Here u is an increasing function, and λi is a positive constant representing the degree of loss aversion.
  • Constant sensitivity is an assumption under loss aversion that people display constant marginal utility for gains and constant marginal pain from losses.
  • Consumption smoothing refers to the behavior of rational consumers facing an intertemporal choice problem. Because discounting from period to period has small effects, rational decision makers will consume nearly equal, though declining, amounts each period. Plotting the consumption profile over time should result in a relatively smooth curve with no spikes or jumps.
  • Consumption utility see acquisition utility
  • Continuity axiom is one of the foundational axioms of expected utility theory. Continuity requires that if A B C then there is exactly one value r such that rA+ 1−r C B). Further, for any p> r, pA + 1 −p C B, and for any q < r, B qA+ 1− q C.
  • Contrapositive statements are logical statements implied by a proposition. For example, the proposition "if P then Q" results in the contrapositive statement, "if not Q then not P."
  • Crowding-out effect occurs when a government subsidy of a public good results in a dollar-for-dollar decrease in private contributions to the provision of that public good.
  • Cruel refers to a motivation to harm another person at the expense of the actor. cumulative prospect theory is a version of prospect theory of decision making in which the probability weighting function is a rank-dependent probability weighting function. This eliminates the possibility of intransitive preferences over gambles.
  • Curse of knowledge occurs when people possess some unique knowledge and cannot fully anticipate how others without this knowledge will behave. The person acts as if others also possess this same knowledge.
  • Cursed equilibrium is a generalization of the Bayesian Nash equilibrium where people believe with positive probability that others randomly select their actions from a distribution irrespective of any private information they might have and with the remaining probability that actions are strategic. The equilibrium requires that each person is maximizing his expected payout of the game given the distribution of actions by others and the strategies employed by others. In this case, people fail to take others' actions as a signal of any private information held by other players.
  • Default option is the option that is automatically selected when the decision maker expresses no explicit choice.
  • Default option bias is a decision maker's tendency to select the default option.
  • Delay–speedup asymmetry is the observation that people must be compensated much more to undergo a delay in consumption than they would be willing to pay to speed up consumption by the same amount of time. This framing effect clearly violates the fully additive model of intertemporal choice.
  • Dependent refers to random variables for which the outcomes are related. Knowing the outcome of one will provide you information about the outcome of the other.
  • Detection of dominance is one activity in the editing phase of prospect theory. In this activity the decision maker examines the gambles available to determine whether one of the options is first-order stochastically dominated by another gamble. If a gamble is determined to be dominated, it is eliminated from consideration.
  • Dictator game is a game with two players in which one player, the dictator, is given money to be shared between both players. The dictator decides how the money is to be divided, and then the second player receives her portion.
  • Diminishing sensitivity is an assumption under loss aversion that people display diminishing marginal utility from gains and diminishing marginal pain from losses. Thus, one becomes less sensitive to changes in wealth or consumption as one moves farther from the reference point.
  • Directly revealed preferred is the relationship of the state s1 to s2 if s1 is chosen when s2 is in the set of available choices.
  • Disconfirmatory information is information that is likely to (or at least that could possibly) contradict currently held beliefs.
  • Discount factor is the coefficient applied in each time period to utility of consumption to represent the consumer's preference for current over future consumption. Thus, if U c is the instantaneous utility of consumption, consuming c in the future, t periods from now, would yield δt U c in present calculated utility.
  • Disposition effect is the tendency of investors to sell gaining investments rather than losing investments in order to avoid realizing losses.
  • Diversification bias is the tendency to choose a consumption bundle for the future that includes a wide variety of items and then to wish one had less variety when the time arrives for consumption.
  • $-bet is a bet that in comparison to other choices has a larger potential payoff but a smaller probability of obtaining that payoff.
  • Dominance is the state in which, if whenever there exists some period t with benefits of performing and action vt > 0 and costs ct = 0, the person will not choose to complete the task in any period t′ with ct′ > 0 and vt′ = 0.
  • Dominant strategy is a strategy that results in a superior payout no matter what the actions of other players.
  • Double-entry accounting is a system of accounting whereby every transaction is entered as a gain in one ledger and a loss in another ledger. For example, purchasing an item is listed as a loss of money in the acquisitions ledger, and the value of the good acquired is listed as a gain in the inventory ledger.
  • Dual entitlement refers to the rules of fairness that consumers and employees enforce on firms regarding fair prices and wages. For example, consumers consider it tolerable to increase prices when the cost to the firms has increased, allowing the firms to maintain profits. It is not acceptable to increase prices simply owing to a shift in demand.
  • Dutch auction is an auction mechanism that begins by the auctioneer calling out a high price, and then decreasing the price by small increments until one bidder is willing to buy.
  • Editing is a component of prospect theory decision making in which people simplify their decision. This can include rounding probabilities and outcomes, eliminating similar components of each choice, and coding outcomes as either gains or losses.
  • Ellsberg paradox results when people are asked to choose between two urns filled with red and black balls from which to draw a ball. Urn 1 contains only red and black balls in an unknown ratio. Urn 2 contains 50 percent red balls and 50 percent black balls. When asked which to draw from when a red ball will result in a prize, people tend to choose urn 2. When asked to choose when a black ball will result in a prize, they also choose urn 2. In both cases, people tend to choose the urn with specified probabilities rather than the ambiguous outcome, violating subjective expected utility theory. This paradox results from ambiguity aversion.
  • Empirical discount factor is the discount factor calculated by asking a person to name an amount of money in one time period and another amount of money in another time period such that the person is indifferent between the two. Let z1 be the amount in time t1, and z2 the amount in time t2. Then the empirical discount factor can be calculated as δ, such that z1 = δ t2 −t1 z2. This differs from the discount factor that would represent the person's preferences because it omits the utility function, instead assuming each dollar is valued equally.
  • Endowment effect is the phenomenon whereby people are willing to pay substantially less money to obtain an item than they are willing to accept to give the item up if given to them.
  • English auction is an auction in which the auctioneer begins by calling out a small price and continues to raise the price by increments until only one bidder continues to be willing to pay the called price.
  • Excess sexual cannibalism refers to the practice among some female fishing spiders of killing and eating all potential mates, thus ensuring they never pass their genes on to the next generation.
  • Expectation is the mean of a random variable. If the distribution of a random variable x can be represented as p x , the expectation is given by E x = xp x x. Alternatively, if the variable is continuously distributed with probability density f x , the expectation is given by E x = xxf x dx.
  • Expected utility theory is a theory of decision under risk that supposes people behave so as to maximize the expected utility of wealth. Expected utility theory is a rational model, built on three rational axioms of behavior under risk. These axioms include independence, continuity, and transitivity.
  • Exponential time discounting is a model that assumes that people maximize U c1, c2, = T i=1 δi−1u ci , where ci is consumption in period i, u c is the instantaneous utility of consumption, and δ is the discount factor applied to each period. This model is considered the only rational model of intertemporal choice because it is necessary to imply time-consistent preferences. In continuous time, the utility function can be stated as max c t Uct = 0 δt uct dt, where t represents time measured continuously.
  • External validity is the ability to use a study to predict behavior in a broader setting. Secondary data analysis generally results in more external validity than an experimental study.
  • Fairness refers to a motivation to help those who are intending to be kind and to hurt those who are intending to be cruel.
  • False consensus is a tendency to believe that others hold beliefs and preferences that are similar to their own.
  • First-price auction is an auction in which the highest bidder wins the auction and pays his bid for the item.
  • Fixed cost is the fixed investment required by a firm to produce. In general economic decisions, fixed costs are the portion of costs that do not depend on the amount produced or consumed.
  • Flat-rate bias is a behavioral preference that people display to buy services based on flat-rate pricing rather than linear pricing even when they can obtain the same level of use more cheaply using linear pricing.
  • Flat-rate pricing is a pricing scheme that charges a fixed rate for access to a good and no additional fees no matter how much is consumed.
  • Framing refers to the external cues surrounding the description of a decision. Often the wording of a decision problem influences the decision that is made by signaling the decision maker to classify outcomes as gains or losses.
  • Framing effect refers to the impact of wording on a decision. Often identical choices can be worded to focus decision makers on losses associated with choices or to focus them on gains associated with choices. The framing effect is the change in decision-making behavior that results from this shift in focus.
  • Free-rider problem refers to the problem that in a free market, people are unwilling to contribute an amount equal to the value they obtain from a public good. This leads to underprovision of the public goods.
  • Fully cursed equilibrium is an alternative to the Bayesian Nash equilibrium where people believe that others randomly select their actions from a distribution irrespective of any private information they have. The equilibrium requires that each person is maximizing her expected payout of the game given the distribution of actions by others and the strategies employed by others. In this case, people fail to take others' actions as a signal of any private information held by other players.
  • Fungible means that an item can be transferred easily between uses. A dollar in an account is fungible if it can be easily transferred to other accounts or spent as any other dollar might be spent.
  • Gain–loss asymmetry is the observation that people tend to discount the utility of future losses less than the utility of future gains. Thus, delayed gains require much greater compensation to induce indifference than equivalently delayed losses. This phenomenon can be modeled by using a prospect theoretic value function that satisfies the asymmetric elasticity condition.
  • Gambler's fallacy is the tendency to believe, after observing a series of realizations of a random variable of the same value, that the probability of realizations of other values of the random variable becomes more probable.
  • Game is a collection of available actions for all players, and a set of payoffs, with one potentially random value of payoff corresponding to each possible collection of actions by all players. A game generally involves situations in which one player's actions can affect the payouts of other players.
  • Generalized axiom of revealed preference states that if s1 is indirectly revealed preferred to s2, then s2 is not strictly directly revealed preferred to s1.
  • Hedonic editing refers to a process of integrating loss events and segregating gain events to maximize the enjoyment of a series of events. There is some evidence that decision makers do not engage in hedonic editing.
  • Hedonic framing refers to the wording of decision options to integrate or segregate events so as to make one or a set of options more or less attractive. For example, a marketer can integrate a series of losses while segregating a series of gains to make a purchase more attractive.
  • Heuristic is a simple decision rule or rule of thumb that may be used to approximate rational optimization when decision resources are limited.
  • Hindsight bias occurs when people evaluate past decisions as if they possessed a foreknowledge of the results of the various decisions. People act as if it were obvious which decision would produce the best result.
  • Hot–cold empathy gap refers to projection bias by people in either hot or cold states (e.g., states in which visceral factors such as hunger are either active or latent).
  • Hot hand is the illusion that a series of realizations of independent random variables of the same value constitutes a streak indicating that the realizations are positively correlated.
  • Hot state refers to a state in which visceral factors (such as hunger, anger, or arousal) are active. In this state, people have difficulty anticipating their preferences at some future date when these visceral factors will be satisfied and thus latent.
  • Hyperbolic discounting replaces the discount factor δt in the exponential utility model with the hyperbolic discount factor, h t = 1+ αt − β α , where β, α > 0 are parameters and t is the amount of time that will have passed by the instance of consumption. The function generally represents deep discounting of near-future events relative to distant future events. The hyperbolic discount factor induces time-inconsistent preferences. Thus, people who display hyperbolic discounting often do not execute the consumption plans that they use to calculate current optimal consumption.
  • Hypothesis-based filtering is actively seeking information that is likely to confirm a currently held belief while scrutinizing information that disconfirms a currently held belief.
  • Illusion of control is the tendency to believe that one has some control over the outcome of completely random events.
  • Immediate cost actions are actions that incur a cost in the period in which they are completed and rewards that accrue in future periods.
  • Immediate reward actions are actions that induce an immediate reward in the period in which the action is completed and costs that accrue in future periods.
  • Impure altruism in considering contributions to a public good refers to the private motive to contribute to a public good in order feel the satisfaction of having contributed.
  • Income expansion path is the set of points that represent the optimal consumption bundle as the budget is varied.
  • Incremental bidding behavior occurs when a bidder in an auction initially bids below their valuation of a good and increases their bid in increments in response to other bidders.
  • Independence implies that two random variables are not related to one another. Thus knowing the outcome of one does not provide further information about the outcome of the other. If two events are independent, then the probability of both occurring is the product of the probabilities of each event, or if events A and B are independent, then P A B = P A P B .
  • Independence axiom is one of the foundational axioms of expected utility theory. Independence requires that if A B, then pA+ 1− p C pB+ 1− p C). This axiom implies that indifference curves are straight and parallel lines in the Marschak–Machina triangle.
  • Independence of irrelevant alternatives. A decision maker obeys independence of irrelevant alternatives if whenever the decision maker chooses t′ t, when given the choice of when to complete a task embodied by the potential rewards v = v1, v2, , vt−1, vt, vt+1 , vT , and costs c = c1, c2, , ct−1, ct, ct+1, , cT , the decision maker also chooses t′ when given the choices embodied in v = v1, v2, , vt−1, vt+1 , vT , c= c1, c2, , ct−1, ct+1, , cT .
  • Indirect utility function is the maximized value of the utility function as a function of wealth and prices.
  • Indirectly revealed preferred. If s1 is directly revealed preferred to s2, and s2 is directly revealed preferred to s3, . . . to sT −1, and sT −1 is directly revealed preferred to sT , then s1 is indirectly revealed preferred to sT .
  • Induced value refers to the amount a bidder may win in an experimental auction. This amount is assigned by the researcher and may differ between participants in the auction.
  • Inequality averse refers to a person's motivation to avoid outcomes in which some people receive lower payouts than others.
  • Inference refers to the information we discern from the data we are able to observe.
  • Infinite planning horizon refers to intertemporal-choice problems involving an unending planning horizon. In discrete time problems, consumption must be planned for time periods t = 0, . In continuous time problems, the consumption must be planned over t = 0, .
  • Instantaneous utility function in a multiperiod consumption problem refers to a function that represents the current utility of consumption in a particular time period. Most models of intertemporal choice suppose that the instantaneous utility function is identical for each time period, but that utility of future consumption is multiplied by a discount factor to represent the fact that current consumption is preferred to future consumption.
  • Integrated events are considered together when evaluating their joint utility. Thus, if two integrated events resulted in monetary outcomes x and y, they would result in a value of v x+ y . See also segregated events.
  • Intermediate loss aversion requires that for any c> 0 the prospect theoretic value function satisfies v c < − v − c .
  • Internal validity is the ability to show causality in a study. Generally, experimental design is necessary to obtain internal validity.
  • Kind refers to an actor's motivation to help another person at the expense of the actor.
  • Kindness function measures how cruel or kind someone is intending to be as a function of her beliefs about other players' strategies and her own chosen strategy. A positive value indicates kindness and a negative value indicates cruelty. This function becomes part of the utility function together with material payoffs in a kindness equilibrium.
  • Knightian risk refers to a situation in which the outcome is not known with certainty but in which the decision maker knows all the possible outcomes and the probabilities associated with each.
  • Knightian uncertainty is a situation in which decision makers know all possible outcomes and the probabilities associated with each outcome given each possible decision they may make.
  • Law of large numbers can be stated as follows: let xi n i=1 be a sequence of independent random variable, each identically distributed with mean μ and variance σ2. Then, for any ε> 0, limn P μ− μ < ε =1, where P represents the probability function.
  • Law of small numbers is a tendency to wrongly believe that small samples of data have very similar properties to the population from which the sample is drawn. Belief in the law of small numbers leads people to jump to conclusions.
  • Likelihood is a conditional probability function P A B in Bayes' rule, where we are interested in learning about P B A . The likelihood function represents the new information in the Bayes' learning problem.
  • Linear pricing is a pricing scheme that charges a fixed marginal price for consumption of a good.
  • Loss aversion is the notion that people experience significantly greater marginal pain from losses than marginal benefit from gains of the same size.
  • Loss aversion in consumption space is typified by indifference curves that discontinuously change slope as they cross a reference point, requiring greater amounts of any item considered a gain to compensate a unit of loss in another item. Formally, let x and y be any two consumption bundles, with xi > yi and yj > xj. Further, let r and s be any two reference points, with xi ≥ ri > si, si =yi, and rj = sj. A reference structure displays loss aversion if for any consumption bundles and reference points satisfying these conditions, x ry whenever x sy
  • Marschak–Machina triangle is a graphic representation of gambles with three possible outcomes. The triangle is a right triangle, with the right angle placed in the southwestern corner. Probabilities of the lowest possible outcome are represented along the horizontal axis of the triangle, and probabilities of the highest possible outcome are represented along the vertical axis. This graph is generally used to plot gambles and indifference curves representing risk preferences.
  • Material outcomes refer to the standard payoffs from a game, often thought of in dollar or utility terms.
  • Maxmin expected utility theory is a model of ambiguity aversion. Let p be the set of possible probability distributions over outcomes. Then someone behaving according to maxmin expected utility theory will behave as if the value of each choice is given by minp p maxx EUx p . In essence, the person assumes the worst possible probabilities that could describe each choice are the true probabilities.
  • Melioration is the tendency of people to make decisions that maximize current utility and to ignore the future consequences of these actions.
  • Mental accounting is a model of consumer decision making whereby the person evaluates all events as gains or losses in a prospect theory value function, uses a mental double-entry accounting ledger to keep track of transactions, and creates separate mental budgets for various categories of purchases. Although this heuristic bars the possibility of maximizing overall utility, it can result from decision makers' attempts to simplify the cognitive effort of optimization.
  • Money pump is created when one displays intransitive preferences among three or more gambles. In this case, the person would be willing to pay to trade gamble A for B, B for C, and C for A. You could infinitely cycle the person between gambles, taking more money from him for each trade.
  • Moral hazard occurs when someone can take actions that are not fully observed by others but that affect the welfare of both the actor and others.
  • Naïfs are decision makers who have preferences embodied in the quasi-hyperbolic discounting model and who do not recognize that their preferences are time inconsistent. They thus plan to behave so as to maximize their discounted utility in the first period; however, they do not necessarily execute this plan in future periods.
  • Naïve decision maker see naïf.
  • Nash equilibrium, intuitively, is a set of strategies, one for each player, such that each player is maximizing their payoff given the strategies of all others involved. Let πi si S −i be the payoff received by player i for playing strategy si, when all other players are playing strategies represented by the symbol S −i. The Nash equilibrium is a collection of strategies S = s1, , sn , such that for each player i, πi si S −i ≥ πi si′ S −i , where S= si S −i.
  • Negatively correlated random variables are two variables x and y such that observing higher values of x increases the probability of observing lower values of y. More formally, E x− E x E y −E y < 0.
  • Node is a decision faced by a player in a game. A node is characterized by the information available to the player as well as the actions available to the player.
  • Nonexcludable means that it is not possible to bar someone from consuming the good. One good example of a nonexcludable good is national defense.
  • Nonrival means one person consuming the good does not prevent others from consuming the good also and does not diminish his utility of consumption.
  • Normal distribution is a common distribution commonly referred to as a bell curve. The normal distribution is completely determined by its mean and variance. The probability density of the normal distribution is given by f x =exp − x− μ 2 2σ2 2πσ2, where μ is the mean of x and σ2 is the variance of x. Generally the probability that x falls in the interval μ− 2σ, μ+2σ is approximately 0.95.
  • One-tailed test is a statistical test of an initial hypothesis that can be represented as an inequality. Thus, if one were to test the hypothesis that θ < θ0, where θ is the unknown parameter and θ0 is the hypothesized value, one would use a one-tailed test.
  • Opportunism is self-interest unconstrained by moral considerations.
  • Optimistic overconfidence is displayed when one holds beliefs that the state of the world is more favorable for one than it truly is.
  • Order axiom is one of the foundational axioms of expected utility theory. Order is satisfied if is complete and transitive. Completeness implies that if A and B are any two gambles, then either A B, B A, or A B. Additionally, transitivity implies that if A, B, and C are any three gambles, and A B and B C then A C.
  • Other-regarding preference refers to preferences such that one's own utility depends on the utility or actions of others.
  • Overconfidence of one's own knowledge is displayed when she assesses the probability she is correct as x, when in fact she is correct less than x percent of the time.
  • Overconfident is a general underestimation of the amount of risk faced in a specific context. This can arise because of overconfidence in one's own knowledge regarding the context or because one holds beliefs that fail to acknowledge the possibility of unfavorable states of the world.
  • P-bet is a bet that in comparison to other choices has a smaller potential payoff but a larger probability of obtaining that payoff.
  • Pareto optimal refers to an outcome in which no player can be made better off without making at least one player worse off.
  • Partial naïf is a decision maker who anticipates the behavior of a sophisticate with parameter β. However, in any period he actually makes decisions discounting the future according to β < β. Thus the partial naïf might not execute plans in the future but might still engage commitment devices.
  • Payment decoupling occurs when the consumer ceases to consider the purchase price in the cost of consumption because the purchase and use of a good are separated by substantial passage of time.
  • Payment depreciation is the phenomenon of consumers gradually discounting the memory of payment over time when considering future consumption or investment.
  • Peanuts effect is the tendency people have to treat decisions involving small amounts of money as inconsequential in aggregate because they are inconsequential individually.
  • Positional externalities refers to a reduction in utility that occurs for others when one decision maker consumes goods that increase her status or position in the group.
  • Positively correlated random variables are two variables x and y such that observing higher values of x increases the probability of observing higher values of y. More formally, E x− E x E y− E y > 0.
  • Precision is the ability to predict events using probabilities that are close to either 1 or 0. A weather forecast with 98 percent chance of rain is precise.
  • Preference reversal is set of observed choices that violates either transitivity or order. One may choose a when a and b are available, b when b and c are available, and c when a and c are available—a violation of transitivity. More simply, one may choose x when x and y are available and in another choice, select y when x and y are available—a violation of the order axiom.
  • Present-biased preference refers to a condition in which when someone considers a trade-off in consumption between two future periods, the individual gives increasingly more weight to utility in the earlier period as those periods draw closer to the present.
  • Primacy is displayed when initial information is more prominent in beliefs than subsequent information.
  • Prior refers to the unconditional probability density in the Bayes' learning problem. This represents the initial beliefs about how likely event B is when learning about P B A .
  • Probability of an event is the relative proportion of times that the event would occur if an experiment could be repeated under identical conditions an infinite number of times.
  • Probability density function is a function describing the relative likelihood of outcomes of a random variable. Thus, if f x is a probability density, the function will be higher where the random variable x is more likely to be realized. The probability of x falling in any interval x, x is given by x x f x dx.
  • Probability weighting supposes that people maximize n i=1 π pi U xi , where pi is the probability of outcome xi occurring. The function π is a probability weighting function that is everywhere increasing. Evidence from laboratory experiments suggest that π p >p for small values of p, while π p < p for large values of p. Thus people overweight small probabilities and underweight large probabilities. This function might explain some behaviors that violate the independence axiom.
  • Procedurally rational model is a model that describes a rational procedure that is used to arrive at a decision given potential misperception or a lack of cognitive resources. The decision is not necessarily rational given the human limitations implied, though it is reasoned. A procedurally rational model tries to explain why someone makes a particular choice given his perception of the decision structure.
  • Projection bias refers to peoples' inability to predict their own preferences when a different state of the world prevails. People tend to believe that their current preferences will persist even when very different circumstances prevail.
  • Prorating refers to the tendency of people to consider future payments for a good in relation to the number and value of future uses of the good. Payments on a good with no future use episodes will feel more painful than those with some expected future use.
  • Prospect theory is a theory of behavior that explains loss-averse behavior using a concave utility function over gains and a convex utility function over losses. In particular, prospect theory supposes that people classify outcomes as either gains or losses and evaluate gains and losses using different utility functions, experience a greater marginal pain for a given monetary loss than pleasure for the same monetary gain so long as the given monetary amount is relatively small, and experience diminishing marginal pain from losses. When used as a model of risky choice, prospect theory dictates that decision makers engage in three distinct tasks: prospect editing, probability weighting, and evaluating outcomes via the loss-averse value function. People displaying loss aversion take severe risks or other steps to avoid losses.
  • Psychological equilibrium is a set of strategies and beliefs, one strategy and one set of beliefs for each player, such that all beliefs are accurate representations of the actual strategies employed, and each player is maximizing her payout given the strategies of all other players.
  • Psychological games are games in which the payouts to one or more players depend on the higher-order beliefs of players regarding the strategies of the players involved. Higher-order beliefs refer to, for example, player 1's belief regarding player 2's beliefs regarding player 1's strategy, and so on.
  • Public goods are goods that are nonrival and nonexcludable in consumption.
  • Quasi-hyperbolic discounting is a model of intertemporal choice in which the decision maker maximizes U c1, c2, =βu c1 + T i=2 βδi−2u ci , where β < δ, where ci is consumption in period i, u c is the instantaneous utility of consumption, and β and δ are discount factors. This is an approximation of the hyperbolic discount function that produces time-inconsistent preferences.
  • Rational choice model supposes that people find the best possible choice for their wellbeing. Often rational choice models impose full information, a well-defined set of preferences, and infinite ability to reason. Behavioral economics builds on the rational choice model with an aim of incorporating more human decision qualities.
  • Recency is displayed when recent information is more prominent in beliefs than initial information.
  • Reciprocity is an in-kind response to the actions of others. Much like fairness, reciprocity leads people to reward kind behavior or punish mean behavior. In this book, reciprocity is defined so that intent to be kind or malicious is not as important as impact of the action taken by another when considering how to reciprocate.
  • Recursive optimization problem is a way to represent an intertemporal choice problem as a recursive series of maximization problems. Thus the standard intertemporal choice problem can be written recursively as maxct < wt u ct + δmaxct +1 < wt +1 u ct +1 + δ2maxct + 2 < wt + 2 u ct +2 + where the consumer maximizes utility of consumption in each period assuming they will also maximize their utility in each subsequent period.
  • Reference point is a comparison point used in making decisions. Often outcomes above a reference point are considered a gain, and an outcome below a reference point is considered a loss. Alternatively, facing a cost above the reference point can result in a loss of transaction utility, and paying less that the reference cost results in positive transaction utility.
  • Reference point in consumption space is a consumption bundle to which all other bundles are compared. If a bundle contains more of good i than the reference point, then that bundle is considered a gain in dimension i. If a bundle contains less of good i than the reference point, then that bundle is considered a loss in dimension i.
  • Reference state is an externally determined factor (or set of factors) that results in a rational preference relation. Thus, when the reference state is held constant, the decision maker makes decisions that satisfy completeness and transitivity. However, if the reference state is allowed to change, preferences can violate transitivity.
  • Reference structure is a set preference relations that each satisfy rationality, indexed by a reference state.
  • Reference transaction refers to a transaction price and quantity that is used as a reference to determine the fair division of surplus between a buyer and a seller. A seller may raise prices and still be considered fair if the rise in price results from a corresponding rise in costs.
  • Reflection effect is observed when a decision maker presented two gambles with only positive outcomes chooses one gamble, and when facing the same gambles, only with outcomes replaced with the same magnitude, but negative values, chooses the other gamble. Risk preferences for gains are exactly opposite of those over losses.
  • Regret aversion is satisfied if for any outcomes x> y> z, it must be that U z, x < U y, x + U z, y , where U a, b is the utility of obtaining a when an alternative choice would have resulted in b. This property represents the negative feelings of regret when obtaining a lower outcome than what would have been possible with a different choice.
  • Regret theory is a procedurally rational model of choice under uncertainty in which the person obtains utility U a, b , where a is the object obtained and an alternative choice would have resulted in b. This theory embodies feelings of regret resulting from outcomes that are worse than would have obtained with different choices.
  • Relative risk aversion is a measure, based on expected utility theory, of how willing someone is to take on a gamble putting a given fraction of her wealth at risk. Relative risk aversion measures the relative curvature of the utility function and can be written as RR = −u″w u′, where u is the utility of wealth function, and w is a measure of wealth. The larger the value of relative risk aversion, the less willing one is to put her wealth at risk.
  • Representativeness heuristic is the tendency to judge the probability of an event based on how representative the observable data are of the event in question.
  • Revealed preference refers to people revealing their preferences when a choice is made among some set of choices.
  • Reversion to mean is displayed by random variables whereby after a particularly high (or low) realization of the random variable x, there is high probability that the next independent realization will be lower (or higher). For example, the child of a tall parent, given the family history, is likely to have a shorter child.
  • Risk is a situation in which decision must be made before one can know the payoffs of the alternative choices with certainty. However, the decision maker does know the options available, the possible outcomes associated with each choice, and the probabilities associated with each outcome given each possible choice.
  • Risk averse means that people would prefer the expected value of a gamble with certainty to taking the said gamble.
  • Risk aversion refers to a person's preference to avoid risk. In general a person is risk averse if he is willing to forgo a risk with expected payout x for some amount of money less than x.
  • Risk loving means that an person would prefer to take a gamble than to receive the expected value of the gamble with certainty.
  • Risk neutral refers to a person's indifference to risk. A risk-neutral decision maker behaves so as to maximize the expected value of her payout. The person is indifferent between taking a gamble and receiving the expected value of the gamble with certainty.
  • Risk premium is the amount one is willing to give up in expected value to obtain a payoff with certainty. This is the difference between the expected value of a gamble and the certainty equivalent of that gamble.
  • Salience is a state of prominence in decision making.
  • Second-price auction is an auction in which the highest bidder wins the auction and pays a price equal to the second-highest bid.
  • Segmentation independence is the rational decision-making property that decisions made sequentially are identical to decisions made simultaneously if the choices available are otherwise identical and if the decision maker is aware of all available choices in each case.
  • Segregated events are considered separately when evaluating their joint utility. Thus, if two segregated events resulted in monetary outcomes x and y, they would result in a value of v x +v y . See also integrated events.
  • Segregation is one activity in the editing phase of prospect theory. In segregation, outcomes that occur with certainty are segregated from risky outcomes for the purpose of evaluation.
  • Self-serving bias is a general tendency of people to overestimate their ability to perform a specific task or to overestimate their ex post contribution to a task. In some circumstances it can also refer to people's tendency to evaluate what is fair or equitable in a way that favors their own position.
  • Significantly different at the α level means that the probability that an unknown parameter is different from an observed value given the observed data is smaller than α.
  • Similarity is a theory of decision under risk that supposes that people rely on rules of thumb to make risky choices when the choices are reasonably similar. If the gambles have similar outcomes, then the decision maker relies on the probabilities associated with those outcomes. If the probabilities are similar, then the decision maker makes the choice based upon the outcomes associated with the probabilities. Such general rules could explain the types of preference cycling observed in laboratory experiments.
  • Simple projection bias is a model of projection bias that supposes people making a current decision for consumption to be realized in a future state s maximize u c, s s′ = 1−α u c, s + αu c, s′ , where u c, s is the utility of consuming c in the future state s, u c, s′ is the utility of consuming sin the current state s′, and α 0, 1 is a simple weighting of the two utility functions.
  • Simplification is one activity in the editing phase of prospect theory. In simplification, the decision maker rounds dollar amounts and probabilities to round numbers. Similar outcomes will be combined.
  • Skew symmetric is satisfied by the function U , if for all outcomes x, y, U x, y = − U y, x and U x, x = 0. This is a general property of regret-theory utility functions.
  • Social capital is a term originating in sociology that refers to the durable social relationships one has and can draw upon as resources for goods—tangible, emotional, or informational.
  • Social norm. A behavior one engages in because one wishes to comply with the behavior of others. This social norm might or might not be enforced by the threat of punishment or penalty.
  • Social preferences are preferences that depend on the well-being or actions of others.
  • Sophisticated decision maker see sophisticates.
  • Sophisticates are decision makers with preferences embodied in the quasi-hyperbolic discounting model, who recognize that their time preferences are inconsistent. They thus anticipate how their future self will behave and respond accordingly. This can lead sophisticates to seek a commitment device to impose their current preferences on their future self. Their future self might seek to defeat such a commitment device.
  • Spiteful is behaving in a way that makes others worse off at the expense of the actor.
  • Standard normal distribution is a normal distribution with a mean of 0 and variance of 1. Thus, the probability that a standard normal variable falls between − 2 and 2 is approximately 0.95.
  • [[Stationarity requires that the magnitude of discounting utility between time periods depends only the amount of time between the two periods considered. The fully additive model of time discounting imposes that decision maker is indifferent between consuming c at time t and c′ at time t′ if U c = δt′ −t U c′ , where the discount only depends on the interval between t and t′ and not the starting time.
  • Status quo bias is a tendency by a consumer to continue with current consumption decisions even when new attractive opportunities arise.
  • Stochastic dominance rank orders two gambles. Let gambles A and B have possible outcomes x1, , xn, such that xi < xi+1. Further, let gamble A have associated probabilities p1, , pn and gamble B have associate probabilities q1, , qn. Gamble A stochastically dominates gamble B if for all i=1, , n, i j=1 pi ≤ i j=1 qi. If gamble A stochastically dominates gamble B, then A is always preferred under expected utility theory.
  • Strategy is a collection of the actions a player will take at each possible node of a game should that node be reached.
  • Strictly revealed preferred. An allocation w = w1, w2 is strictly revealed preferred to w′= w′ 1, w′ 2 if it is directly revealed preferred and if p1w′ 1 +p2w′ 2 < p1w1 + p2w2.
  • Strong axiom of revealed preference. If s1 is indirectly revealed preferred to s2, then s2 is not directly revealed preferred to s1.
  • Strong loss aversion is displayed by a value function if for any two positive numbers z1 and z2 with z1 < z2 it is always the case that vg z2 −vg z1 < vl z2 −vl z1 . This requires that a loss function always has a greater slope than the gain function a given distance from the reference point.
  • Subadditivity occurs when the sum of probability weights over all possible outcomes is less than 1. This has been used as one explanation for the certainty effect, because it implies a penalty associated with uncertain outcomes relative to outcomes with certainty (which always have perceived probability 1).
  • Subgame-perfect Nash equilibrium of a game is a set of strategies that constitute a Nash equilibrium in every subgame.
  • Subjective expected utility theory is a theory of how people make decisions under ambiguity. In subjective expected utility theory, the decision maker hypothesizes a single probability distribution of outcomes associated with each action and then maximizes expected utility theory based upon this probability distribution.
  • Subproportional requires that the value function increases in elasticity as the absolute value of consumption increases. Let z2 > z1 > 0, and let 0 < Δ < z1. Then we can express this requirement in terms of arc elasticities as 2z2 + Δ v z2 + Δ −v z2 Δ v z2 + Δ +v z2 > 2z1 + Δ v z1 + Δ −v z1 Δ v z1 + Δ +v z1 and − 2z2 + Δ v −z2 + Δ −v −z2 Δ v −z2 + Δ +v −z2 > − 2z1 + Δ v −z1 + Δ −v −z1 Δ v −z1 + Δ +v −z1 or in terms of exact elasticities as z2v′ z2 v z2 > z1v′ z1 v z1 and − z2v′ −z2 v −z2 > − z1v′ −z1 v −z1 . A subproportional value function displays smaller relative differences in utility between relatively large outcomes compared to the difference in utility of two relatively small outcomes of the same proportions. Another way to state this requirement is that whenever z2 >z1 >0, and α> 1, v z2 v αz2 < v z1 v αz1 , hence the name subproportionality.
  • Sunk cost is investment in a project that cannot be avoided nor recovered.
  • Sunk cost fallacy is displayed when sunk costs influence decisions to continue a project. Here people might try to recover sunk costs by engaging in a losing project.
  • Superadditivity occurs when the sum of probability weights over all possible outcomes is greater than 1. This can lead to preferences for stochastically dominated outcomes.
  • Support is a range of possible values for a random variable.
  • Time-inconsistent preferences occur when people make decisions for their future selves that they later regret. This is generally due to people not being able to anticipate their preferences in some future state.
  • Transaction utility is enjoyment or pleasure consumers derive from feeling they have received a good deal on a purchase or paid a relatively low price for the level of consumption.
  • Transactions costs are time or resources that must be spent to effect a transaction. These costs benefit neither of the primary parties of the transaction directly.
  • Transitive preferences imply that if bundle a is preferred to bundle b, and bundle b is preferred to bundle c, then bundle c cannot be preferred to bundle a. Transitivity is a general requirement of rational decision theory.
  • Transparency refers to the clarity with which a gamble is presented. People violate expected utility much more often when gambles are presented in a way that obscures stochastic dominance or other relationships between gambles. Transparent gambles tend to lead to more consistently rational behavior.
  • Transparent means that people can easily discern their payout from each possible action without making complicated calculations or guesses.
  • Trust refers to a person's willingness to place others in a position to make decisions that could either help or harm the person.
  • Trust game refers to a game in which a sender is endowed with money that she may send to a second player, called a receiver. Any money sent is tripled. The receiver then decides how much of this money to return to the sender. The sender must trust the receiver in order to send money. The receiver is said to reciprocate if she returns more money than was sent.
  • Two-part tariff is a pricing scheme that charges a fixed access fee for consumption in addition to a fixed marginal price for consumption.
  • Two-tailed test is a statistical test of an initial hypothesis that can be represented as an equality. Thus, if one were to test the hypothesis that θ =θ0, where θ is the unknown parameter and θ0 is the hypothesized value, one would use a two tailed test.
  • Ultimatum game is a game in which player 1 proposes a division of a money reward between both players. Player 2 can then either accept the split, resulting in that split being realized, or reject the proposal, resulting in a zero payout to both players.
  • Uncertainty is a situation in which the decision maker faces either unknown probabilities associated with outcomes resulting from her choices or is not aware of the possible outcomes. This is often referred to as ambiguity.
  • Unraveling effect refers to the inability of rational agents to cooperate in a sequential move game such as the take-it-or-leave-it game in order to obtain larger payoffs for both players. In each stage of the game, players choose larger immediate payoffs rather than turning control of the game to the other player.
  • Utility of wealth is a function describing the consumer's preferences over levels of wealth. This function is used in expected utility theory to describe risk preferences. People who display diminishing marginal utility of wealth (a concave function of wealth) behave risk averse, and those with increasing marginal utility of wealth (a convex function of wealth) behave risk loving.
  • Variance is a measure of the dispersion of a random variable. The variance is larger if there is a greater probability of the random variable falling farther away from the mean. Variance can be defined as σ2 =E x −E x 2 .
  • Vickrey auction is a second-price sealed-bid auction. No bidders may know what others will bid before submitting their own bid. The highest bidder wins the auction and pays a price equal to the second-highest bid.
  • Visceral factors are emotions, physical appetites, or other physical factors that can be aroused. Visceral factors (such as hunger or anger) can fluctuate, but they influence individual preferences.
  • Warm glow refers to a feeling of satisfaction obtained from knowing one has contributed to a public good.
  • Weak axiom of revealed preference. If s1 is directly revealed preferred to s2 then s2 is not directly revealed preferred to s1.
  • Weighted expected utility theory supposes that one's preferences can be represented by maximizing the function U = n i=1 piu xi n i=1 piv xi . This function allows for indifference curves that are straight lines but that fan out across the Marschak–Machina triangle.
  • Windfall gain is any unexpected income, though usually referring to large income events.
  • Winner's curse is the tendency for the highest bidder in a common-value auction to have bid more than he anticipated relative to the actual value of the item. The highest bidder is the most likely to have bid more than the value of the item, leading to an unanticipated lower expected payout or even a negative expected payout.
  • χ-cursed equilibrium of a game is given by the set of strategies such that each player maximizes their own expected payout assuming probability χ that all other players' actions are not related to their underlying estimate of valuation, and 1 −χ probability is assigned to the event that all other players are fully strategic in responding to their estimate of valuation.
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