Risk Aversion and Incentive Effects

A menu of paired lottery choices is structured so that the crossover point to the high-risk lottery can be used to infer the degree of risk aversion. With "normal" laboratory payoffs of several dollars, most subjects are risk averse and few are risk loving. Scaling up all payoffs by factors of twenty, fifty, and ninety makes little difference when the high payoffs are hypothetical. In contrast, subjects become sharply more risk averse when the high payoffs are actually paid in cash. A hybrid "power/expo" utility function with increasing relative and decreasing absolute risk aversion nicely replicates the data patterns over this range of payoffs from several dollars to several hundred dollars

An experimental study of costly coordination

This paper reports data for coordination game experiments with random matching. The experimental design is based on changes in an effort-cost parameter, which do not alter the set of Nash equilibria nor do they alter the predictions of adjustment theories based on imitation or best response dynamics. As expected, however, increasing the effort cost lowers effort levels. Maximization of a stochastic potential function, a concept that generalizes risk dominance to continuous games, predicts this reduction in efforts. An error parameter estimated from initial two-person, minimum-effort games is used to predict behavior in other three-person coordination games

An explanation of anomalous behavior in models of political participation

This paper characterizes behavior with “noisy” decision making for models of political interaction characterized by simultaneous binary decisions. Applications include: voting participation games, candidate entry, the volunteer's dilemma, and collective action problems with a contribution threshold. A simple graphical device is used to derive comparative statics and other theoretical properties of a “quantal response” equilibrium, and the resulting predictions are compared with Nash equilibria that arise in the limiting case of no noise. Many anomalous data patterns in laboratory experiments based on these games can be explained in this manner

An Explanation of Anomalous Behavior in Binary-Choice Games: Entry, Voting, Public Goods, and the Volunteers' Dilemma

This paper characterizes behavior with "noisy" decision making for a general class of N-person, binary-choice games. Applications include: participation games, voting, market entry, binary step-level public goods games, the volunteer's dilemma, the El Farol problem, etc. A simple graphical device is used to derive comparative statics and other theoretical properties of a "quantal response" equilibrium, and the resulting predictions are compared with Nash equilibria that arise in the limiting case of no noise. Many anomalous data patterns in laboratory experiments based on these games can be explained in this manner.participation games, entry, voting, step-level public goods games, volunteers' dilemma, quantal response equilibrium, El Farol problem, bounded rationality.

Ten Little Treasures of Game Theory and Ten Intuitive Contradictions

This paper reports laboratory data for a series of two-person games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment for which behavior conforms quite nicely to the predictions of the Nash equilibrium or relevant refinement. In each case we change a key payoff parameter in a manner that does not alter the equilibrium predictions, but this theoretically neutral payoff change has a major (often dramatic) effect on observed behavior. These contradictions are generally consistent with simple economic intuition and with a model of iterated noisy introspection for one-shot games.Nash equilibrium, noncooperative games, experiments, bounded rationality, introspection

A Model of Noisy Introspection

This paper presents a theoretical model of noisy introspection designed to explain behavior in games played only once. The equilibrium determines layers of beliefs about others' beliefs about ..., etc., but allows for surprises by relaxing the equilibrium requirement that belief distributions coincide with decision distributions. The paper contains a convergence proof and reports estimated introspection and error parameters for data from 37 one-shot matrix games. The accuracy of the model is compared with that of two alternative approaches: the Nash equilibrium and the logit quantal response equilibrium.game theory, introspection, Nash equilibrium, experiments.

Further Reflections on Prospect Theory

This paper reports a new experimental test of prospect theoryâ??s reflection effect. We conduct a sequence of experiments that allow us to directly compare choices under reflected gains and losses where real and hypothetical payoffs range from several dollars to over $100. Lotteries with positive payoffs are transformed into lotteries over losses by reflecting all payoffs around zero. When we use hypothetical payments, more than half of the subjects who are risk averse for gains turn out to be risk seeking for losses. This "reflection effect" is diminished considerably with cash payoffs, where the modal choice pattern is to exhibit risk aversion for both gains and losses. However, we do observe a significant difference in risk attitudes between losses (where most subjects are approximately risk neutral) and gains (where most subjects are risk averse). Reflection rates are further reduced when payoffs are scaled up by a factor of 15 (for both real and hypothetical payoffs).

Asymmetric Inequality Aversion and Noisy Behavior in Alternating-Offer Bargaining Games

In two-stage bargaining games with alternating offers, the amount of the pie that remains after a rejection is what the first player should offer to the second player, since the second player can capture this remainder in the final (ultimatum) stage. Fairness considerations will reduce the correlation between first-stage offers and the size of the remaining pie, but randomness in behavior will have the same "flattening" effect. This paper reports an experiment designed to separate these considerations, by introducing asymmetric fixed money payments to each player. These endowments do not affect the perfect positive correlation between initial Nash offers and the remaining pie, but are selected to induce a perfectly negative relationship between the remaining pie size and the first-stage offer that would equalize final earnings of the two players. This negative relationship is apparent in the data, which suggests the importance of fairness considerations. A theoretical model of asymmetric inequality aversion and stochastic choice is used to provide maximum likelihood estimates of utility and logit error parameters. The parameters representing "envy," "guilt," and logit errors are all significant, and the resulting model produces the observed negative relationship between initial offers and residual pie size.bargaining, ultimatum game, bounded rationality, logit equilibrium, fairness, equity aversion, endowment effects, envy, guilt

An Experimental Study of Costly Coordination

This paper reports data for coordination game experiments with random matching. The experimental design is based on changes in an effort-cost parameter, which do not alter the set of Nash equilibria, nor do they alter the predictions of dynamic adjustment theories based on imitation or best responses to others' decisions. As would be expected, however, increases in effort cost result in reduced effort levels. Average behavior in the final periods is consistent with a one-parameter stochastic generalization of the Nash equilibrium that is calculated by maximizing a "stochastic potential function." The noise parameter estimated from the initial two-person, minimum-effort games is used to predict behavior in subsequent experiments with three-person games, using both minimum and medium-effort payoff structures.coordination games, laboratory experiments, stochastic potential, logit equilibrium, bounded rationality, minimum effort game, median effort game