Evolutive equilibrium selection II: quantal response mechanisms

In this paper we develop a model of Evolutive Quantal Response (EQR) mechanisms, and contrast the outcomes with the Quantal Response Equilibria (QRE) as developed by McKelvey and Palfrey(1995). A clear distinction between the two approaches can be noted; EQR is based on a dynamic formulation of individual choice in the context of evolutionary game theory in which games are played repeatedly in populations, and the aim is to determine both the micro-configuration of strategy choices across the population, and the dynamics of the population frequencies of the strategies played. Quantal Response Equilibria focuses on the more traditional aspects of non-co-operative game theory, i.e. on equilibrium in beliefs regarding strategies.We focus attention on an analytical approach which enables closed form solutions to be constructed. We consider the case of all symmetric binary choice games, which will include analysis of all well known generic games in this context, such as Prisoner's dilemma, Stag-Hunt and Pure 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.

The Effect of Hysteresis on Equilibrium Selection in Coordination Games

One of the fundamental problems in both economics and organization is to understand how individuals coordinate. The widely used minimum-effort coordination game has been used as a simplifed model to better understand this problem. This paper first presents some theoretical results that give conditions under which the minimum-effort coordination game exhibits hysteresis. Using these theoretical results, some experimental hypotheses are developed and then confirmed using human subjects in the laboratory. The main insight is that play in a given game is heavily dependent on the history of parameters leading up to that game. For example, the experiments show when cost c = 0:5 in the minimum-effort coordination game, there is signifcantly more high effort if the cost has increased to c = 0:5 compared to when the cost has decreased to c = 0:5. One implication of this is that a temporary change in parameters may be able move the economic system from a bad equilibrium to a good equilibrium.Hysteresis, Minimum-effort Coordination Game, Logit Equilibrium, Experimental Economics, Equilibrium Selection

A unified approach to comparative statics puzzles in experiments

Many experimental studies implement two versions of one game for which agents’ behavior is fundamentally different even though the Nash prediction is the same. This paper provides a novel explanation of such findings. Starting from the observation that many of the games under consideration satisfy the strategic-complementarity property, I obtain predictions for the direction of adjustment in response to parameter changes which do not require calculation of the equilibrium. I show that these predictions explain the experimental evidence very well. Further, I provide a behavioral justification of the approach, and I explore the relation to alternative explanations based on equilibrium selection theories and the quantal response equilibrium.experimental economics, game theory, Nash equilibrium, embedding method

Self-tuning experience weighted attraction learning in games

Self-tuning experience weighted attraction (EWA) is a one-parameter theory of learning in games. It addresses a criticism that an earlier model (EWA) has too many parameters, by fixing some parameters at plausible values and replacing others with functions of experience so that they no longer need to be estimated. Consequently, it is econometrically simpler than the popular weighted fictitious play and reinforcement learning models. The functions of experience which replace free parameters “self-tune” over time, adjusting in a way that selects a sensible learning rule to capture subjects’ choice dynamics. For instance, the self-tuning EWA model can turn from a weighted fictitious play into an averaging reinforcement learning as subjects equilibrate and learn to ignore inferior foregone payoffs. The theory was tested on seven different games, and compared to the earlier parametric EWA model and a one-parameter stochastic equilibrium theory (QRE). Self-tuning EWA does as well as EWA in predicting behavior in new games, even though it has fewer parameters, and fits reliably better than the QRE equilibrium benchmark

Progress in Behavioral Game Theory

Is game theory meant to describe actual choices by people and institutions or not? It is remarkable how much game theory has been done while largely ignoring this question. The seminal book by von Neumann and Morgenstern, The Theory of Games and Economic Behavior, was clearly about how rational players would play against others they knew were rational. In more recent work, game theorists are not always explicit about what they aim to describe or advise. At one extreme, highly mathematical analyses have proposed rationality requirements that people and firms are probably not smart enough to satisfy in everyday decisions. At the other extreme, adaptive and evolutionary approaches use very simple models-mostly developed to describe nonhuman animals-in which players may not realize they are playing a game at all. When game theory does aim to describe behavior, it often proceeds with a disturbingly low ratio of careful observation to theorizing

Lost in Translation? Basis Utility and Proportionality in Games

Cooperative and noncooperative games have no representation of players's basis utilities. Basis utility is the natural reference point on a player's utility scale that enables the determination the marginal utility of any payoff or allocation. A player's basis utility can be determined by an observer and other players under standard rationality assumptions. Basis utility allows interpersonal comparison of proportional utility gains relative to the disagreement outcome. Proportional pure bargaining is the unique solution satisfying efficiency, symmetry, affine transformation invariance and monotonicity in pure bargaining games with basis utility. Characterization of the Nash (1950) bargaining solution requires the assumption of the irrelevance of basis utility in games with basis utility. All existing cooperative solution functions become translation invariant once proper account is taken of basis utility. The noncooperative rationality of these results is demonstrated with a proportional bargaining based on Gul (1988). Further noncooperative application is demonstrated by showing that quantal response equilibria with multiplicative error structures (Goeree, Holt and Palfrey (2004)) become translation invariant with specification of basis utility.Basis utility, equal split, Kalai-Smorodinsky solution, Nash bargaining, quantal response equilibria, proportional bargaining, translation invariance.