Payoff levels, loss avoidance, and equilibrium selection in the Stag Hunt: an experimental study

Game theorists typically assume that changing a game’s payoff levels—by adding the same constant to, or subtracting it from, all payoffs—should not affect behavior. While this invariance is an implication of the theory when payoffs mirror expected utilities, it is an empirical question when the “payoffs” are actually money amounts. In particular, if individuals treat monetary gains and losses differently, then payoff–level changes may matter when they result in positive payoffs becoming negative, or vice versa. We report the results of a human–subjects experiment designed to test for two types of loss avoidance: certain–loss avoidance (avoiding a strategy leading to a sure loss, in favor of an alternative that might lead to a gain) and possible–loss avoidance (avoiding a strategy leading to a possible loss, in favor of an alternative that leads to a sure gain). Subjects in the experiment play three versions of Stag Hunt, which are identical up to the level of payoffs, under a variety of treatments. We find differences in behavior across the three versions of Stag Hunt; these differences are hard to detect in the first round of play, but grow over time. When significant, the differences we find are in the direction predicted by certain– and possible–loss avoidance. Our results carry implications for games with multiple equilibria, and for theories that attempt to select among equilibria in such games.

Consumer Behaviour in a Social Context: Implications for Environmental Policy

In this paper we summarise some of our recent work on consumer behaviour, drawing on recent developments in behavioural economics, in which consumers are embedded in a social context, so their behaviour is shaped by their interactions with other consumers. For the purpose of this paper we also allow consumption to cause environmental damage. Analysing the social context of consumption naturally lends itself to the use of game theoretic tools, and indicates that we seek to develop links between economics and sociology rather than economics and psychology, which has been the more predominant field for work in behavioural economics. We shall be concerned with three sets of issues: conspicuous consumption, consumption norms and altruistic behaviour. Our aim is to show that building links between sociological and economic approaches to the study of consumer behaviour can lead to significant and surprising implications for conventional economic policy prescriptions, especially with respect to environmental policy.

Experimental evidence of a sunk–cost paradox: a study of pricing behavior in Bertrand–Edgeworth duopoly

A well–known implication of microeconomic theory is that sunk costs should have no effect on decision making. We test this hypothesis with a human–subjects experiment. Students recruited from graduate business courses, with an average of over six years of work experience, played the role of firms in a repeated price–setting duopoly game in which both firms had identical capacity constraints and costs, including a sunk cost that varied across experimental sessions over six different values. We find, contrary to the prediction of microeconomic theory, that subjects’ pricing decisions show sizable differences across treatments. The effect of the sunk cost is non–monotonic: as it increases from low to medium levels, average prices decrease, but as it increases from medium to high levels, average prices increase. These effects are not apparent initially, but develop quickly and persist throughout the game. Cachon and Camerer’s (1996) loss avoidance is consistent with both effects, while cost–based pricing predicts only the latter effect, and is inconsistent with the former.

Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

Optimism and commitment: An elementary theory of bargaining and war

We propose an elementary theory of wars fought by fully rational contenders. Two parties play a Markov game that combines stages of bargaining with stages where one side has the ability to impose surrender on the other. Under uncertainty and incomplete information, in the unique equilibrium of the game, long confrontations occur: war arises when reality disappoints initial (rational) optimism, and it persist longer when both agents are optimists but reality proves both wrong. Bargaining proposals that are rejected initially might eventually be accepted after several periods of confrontation. We provide an explicit computation of the equilibrium, evaluating the probability of war, and its expected losses as a function of i) the costs of confrontation, ii) the asymmetry of the split imposed under surrender, and iii) the strengths of contenders at attack and defense. Changes in these parameters display non-monotonic effects.

Correlated equilibria, good and bad: an experimental study

We report results from an experiment that explores the empirical validity of correlated equilibrium, an important generalization of the Nash equilibrium concept. Specifically, we seek to understand the conditions under which subjects playing the game of Chicken will condition their behavior on private, third–party recommendations drawn from known distributions. In a “good–recommendations” treatment, the distribution we use is a correlated equilibrium with payoffs better than any symmetric payoff in the convex hull of Nash equilibrium payoff vectors. In a “bad–recommendations” treatment, the distribution is a correlated equilibrium with payoffs worse than any Nash equilibrium payoff vector. In a “Nash–recommendations” treatment, the distribution is a convex combination of Nash equilibrium outcomes (which is also a correlated equilibrium), and in a fourth “very–good–recommendations” treatment, the distribution yields high payoffs, but is not a correlated equilibrium. We compare behavior in all of these treatments to the case where subjects do not receive recommendations. We find that when recommendations are not given to subjects, behavior is very close to mixed–strategy Nash equilibrium play. When recommendations are given, behavior does differ from mixed–strategy Nash equilibrium, with the nature of the differ- ences varying according to the treatment. Our main finding is that subjects will follow third–party recommendations only if those recommendations derive from a correlated equilibrium, and further, if that correlated equilibrium is payoff–enhancing relative to the available Nash equilibria.

How private is private information? The ability to spot deception in an economic game

We provide experimental evidence on the ability to detect deceit in a buyer-seller game with asymmetric information. Sellers have private information about the buyer's valuation of a good and sometimes have incentives to mislead buyers. We examine if buyers can spot deception in face-to-face encounters. We vary (1) whether or not the buyer can interrogate the seller, and (2) the contextual richness of the situation. We find that the buyers' prediction accuracy is above chance levels, and that interrogation and contextual richness are important factors determining the accuracy. These results show that there are circumstances in which part of the information asymmetry is eliminated by people's ability to spot deception.