Game theory and reciprocity in some extensive form experimental games

We examine decision making in two-person extensive form game trees using nine treatments that vary matching protocol, payoffs, and payoff information. Our objective is to establish replicable principles of cooperative versus noncooperative behavior that involve the use of signaling, reciprocity, and backward induction strategies, depending on the availability of dominated direct punishing strategies and the probability of repeated interaction with the same partner. Contrary to the predictions of game theory, we find substantial support for cooperation under complete information even in various single-play treatments.

Nonatomic games on Loeb spaces

In the setting of noncooperative game theory, strategic negligibility of individual agents, or diffuseness of information, has been modeled as a nonatomic measure space, typically the unit interval endowed with Lebesgue measure. However, recent work has shown that with uncountable action sets, for example the unit interval, there do not exist pure-strategy Nash equilibria in such nonatomic games. In this brief announcement, we show that there is a perfectly satisfactory existence theory for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces, hyperfinite Loeb spaces. We also emphasize other desirable properties of games on hyperfinite Loeb spaces, and present a synthetic treatment, embracing both large games as well as those with incomplete information.

Stochastic game theory: For playing games, not just for doing theory

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.