Abstract We examine the risky choices of contestants in the popular TV game show "Deal or No Deal" and related classroom experiments. Contrary to the traditional view of expected utility theory, the choices can be explained in large part by previous outcomes experienced during the game. Risk aversion decreases after earlier expectations have been shattered by unfavorable outcomes or surpassed by favorable outcomes. Our results point to reference-dependent choice theories such as prospect theory, and suggest that path-dependence is relevant, even when the choice problems are simple and well-defined, and when large real monetary amounts are at stake.

The motivation of decision makers who care for emotions, reciprocity, or social conformity may depend directly on beliefs (about choices, beliefs, or information). Geanakoplos, Pearce & Stacchetti (Games and Economic Behavior, 1989) point out that traditional game theory is ill-equipped to address such matters, and they pioneer a new framework which does. However, their toolbox — psychological game theory — incorporates several restrictions that rule out plausible forms of belief-dependent motivation. Building on recent work on dynamic interactive epistemology, we propose a more general framework. Updated higher-order beliefs, beliefs of others, and plans of action may influence motivation, and we can capture dynamic psychological effects (such as sequential reciprocity, psychological forward induction, regret, and anxiety) that were previously ruled out. We develop solution concepts, provide examples, and explore properties.

We review the experimental evidence on risk aversion in controlled laboratory settings. We review the strengths and weaknesses of alternative elicitation procedures, the strengths and weaknesses of alternative estimation procedures, and finally the effect of controlling for risk attitudes on inferences in experiments. Attitudes to risk are one of the primitives of economics. Individual preferences over risky prospects are taken as given and subjective in all standard economic theory. Turning to the characterization of risk in applied work, however, one observes many restrictive assumptions being used. In many cases individuals are simply assumed to be risk neutral;1 or perhaps to have the same constant absolute or relative aversion to risk.2 Assumptions buy tractability, of course, but at a cost. How plausible are the restrictive assumptions about risk attitudes that are popularly used? If they are not plausible, perhaps there is some way in which one can characterize the distribution of risk attitudes so that it can be used to analyze the implications of relaxing these assumptions. If so, such characterizations will condition inferences about choice behavior under uncertainty, bidding in auctions, and behavior in games.

We consider a decisionmaker who "narrowly brackets", i.e. evaluates her decisions separately. Generalizing an example by Tversky and Kahneman (1981) we show that if the decisionmaker does not have constant-absolute-risk-averse preferences, there exists a simple pair of independent binary decisions where she will make a first-order stochastically dominated combination of choices. We also characterize, as a function of preferences, a lower bound on the monetary cost that can be incurred due to a single mistake of this kind. Empirically, we conduct a real-stakes laboratory

We model the behavior of agents who care about receiving what they feel they deserve in a two-player rank-order tournament. Perceived entitlements are sensitive to how hard an agent has worked relative to her rival, and agents are loss averse around their meritocratically determined endogenous reference points. In a fair tournament sufficiently large desert concerns drive identical agents to push their effort levels apart in order to end up closer to their reference points on average. In an unfair tournament, where one agent is advantaged, the equilibrium is symmetric in the absence of desert, but asymmetric in the presence of desert. We find that desert concerns can undermine the standard conclusion that competition for a fixed supply of status is socially wasteful and explain why, when the distribution of output noise is fat-tailed, an employer might use a rank-order incentive scheme.

In this work we introduce a class of measures for evaluating the quality of financial positions based on their ability to achieve desired financial goals. In the spirit of Simon [34], we call these measures satisficing measures and show that they are dual to classes of risk measures. This approach has the advantage that aspiration levels, either competing benchmarks or fixed targets, are often much more natural to specify than risk tolerance parameters. In addition, we propose a class of satisficing measures that reward diversification. Finding optimal portfolios for such satisficing measures is computationally tractable. Moreover, this class of satisficing measures has an ambiguity interpretation in terms of robust guarantees on the expected performance as the underlying distribution deviates from the investor’s reference distribution. Finally, we show some promising results for our approach compared to traditional methods in a real-world portfolio problem against a competing benchmark.

This paper introduces a decision-theoretic model of beliefs that allows for the possibility that what a person believes to be true is affected by what that person wants to be true. The substantive assumptions are (i) that distortion requires uncertainty, and that only payoffs over uncertain events matter, and (ii) that belief distortion over an event has to do with what a person has to gain or lose from the event being true. Using these assumptions I derive a simple formula with only one free parameter, which is positive for optimists and negative for pessimists. The key comparative statics are that belief distortion is greater in situation that are important and are where there is a great deal of uncertainty. The representation has the same structure as Bayes Rule, with payoffs playing the same role as normatively relevant information. A key implication is that news that affects the expected payoff consequences of an event may alter beliefs, even when it provides no relevant information about its likelihood.

A large literature is concerned with analysis and empirical application of theories of decision making for environments with risky outcomes. Expected value theory has been known for centuries to be subject to critique by St. Petersburg paradox arguments. More recently, theories of risk aversion have been critiqued with calibration arguments applied to concave utility of payoffs. This paper extends the calibration critique to decision theories that represent risk aversion with transformation of probabilities, and thereby makes clear that questioning the plausibility of theories of risk aversion is not synonymous with questioning the plausibility of decreasing marginal utility of money. Testable calibration propositions are derived that apply to dual expected utility theory as well as expected utility theory, cumulative prospect theory, and rank dependent utility theory. Heretofore, calibration critiques of theories of risk aversion have been based on thought experiments. This paper reports real experiments that provide data on the empirical relevance of the calibration critique to evaluating the plausibility of theories of risk aversion. The paper also discusses implications of the data for prospect theory with (editing of) variable reference payoffs and for some recent additions to specialized literature on risky decisions. In addition, the paper reports an experiment with a finite St. Petersburg bet that adds to data inconsistent with risk neutrality.

This paper shows that subjective expected utility can be obtained using primitives that are much poorer than a preference relation on the set of acts. Our primitives only involve the fact that an act is judged either “attractive” or “unattractive”. We give conditions implying that there are a utility function on the set of consequences and a probability distribution on the set of states such that attractive acts have a subjective expected utility above some threshold. The numerical representation that is obtained has strong

Abstract Although many empirical investigations have documented reference-dependent preferences, most studies of reference dependence have considered only status quo reference points. In a large-scale field study of marathon runners, we test whether goals, a non-status quo reference point, act similarly to status quo reference points. We find that satisfaction as a function of relative performance (the difference between a runner's time goal and her finishing time) exhibits loss aversion and diminishing sensitivity, consistent with the Prospect Theory value function. Unlike the Prospect Theory value function, however, we also find a discontinuity (or jump) at the reference point. We further find that loss aversion is moderated by goal importance, that multiple reference points simultaneously impact runner satisfaction, and that loss aversion is overestimated in predictions of satisfaction, but still present in actual experienced satisfaction.