McKelvey 631627 This project continues research on a class of statistical models of equilibrium behavior in games called Quantal Response Equilibria (QRE). Besides providing new insights into behavior in games, this approach provides a potentially useful tool for the econometrics of game theory. Under this renewal grant, the investigators: 1) further develop and extend the theory in a number of different directions; 2) investigate its implications for several applications, including bargaining, public good provision, spatial competition, and oligopolistic competition; and 3) continue experimental work in game theory, as it relates to the QRE model. The basic idea of this theory is that, from the point of view of an outsider, each player's behavior is subject to statistical variation. Regardless of the source of such variation, this variation will generally have systematic effects in equilibrium, even if the sources of the variation are non-systematic. This induces systematic changes in the responses of the other players. The basic hypothesis about the statistical process governing individual behavior is that, given a set of alternative choices, individuals choose probabilistically, choosing better alternatives more often than worse alternatives. In a game, the available choices to a player are give by his or her strategy set. The expect utility of each strategy for a player is determined by the probability distribution of the strategies of the other players of the game. The choice probability function in the model is called a Quantal Response Function and is assumed to be continuous and positively responsive to the expected payoff of each strategy. A Quantal Response Equilibrium is a fixed point of the quantal response function, just as a Nash Equilibrium is a fixed point of the best response correspondence. The Nash equilibrium model thus corresponds to an extreme limiting case of this model, in which the probability of choosing an optimal alternative is equal to one. To appl y this to specific games, the investigators use a particular class of response functions associated with the logit model of choice. Each individual is assumed to have the same logit response parameter (which indexes how close it is to the standard best response model). Under the previous grant the investigators established a number of properties of the logit equilibrium correspondence, illustrate these properties in some special games, and analyze the data from simple experimental 2-person games. The analysis of the experimental games consists of fitting the data for these different experiments to the logit model, by obtaining maximum-likelihood estimates of the logit parameters. Under this grant, the investigators extend the estimation models to allow for heterogeneity and learning, and also to test the logit specification against alternative parametric quantal response models. ??
