This paper describes three new developments in game theory that relax the classical assumptions of perfect rationality and perfect foresight. These approaches to noisy introspection (prior to play), learning (from previous plays), and equilibrium (after a large number of plays) provide complementary perspectives for explaining actual behavior in a wide variety of games

The quantal response equilibrium (QRE) notion of Richard D. McKelvey and Thomas R. Palfrey (1995) has recently attracted considerable attention, due in part to its widely documented ability to rationalize observed behavior in games played by experimental subjects. However, even with strong apriorirestrictions on unobservables, QRE imposes no falsifiable restrictions: it can rationalize any distribution of behavior in any normal form game. After demonstrating this, we discuss several approaches to testing QRE under additional maintained assumptions. (JEL C72, C52, C90) The quantal response equilibrium (QRE) notion of McKelvey and Palfrey (1995) can be viewed as an extension of standard random utility models of discrete (“quantal”) choice to strategic settings, or as a generalization of Nash equilibrium that allows noisy optimizing behavior while maintaining the internal consistency of rational expectations. Formally, QRE is based on the introduction of random perturbations to the payoffs associated with each action a player can take. 1 Realizations of these perturbations affect which action is the best response to the equilibrium distribution of opponents ’ behavior. 1We give a more complete discussion in the following section. The literature has considered generalizations of the QRE to extensive form games (McKelvey and Palfrey (1998)) and games with continuous strategy

Abstract. This paper presents a theoretical model of noisy introspection designed to explain behavior in games played only once. The model 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. Noise is injected into iterated conjectures about others ’ decisions and beliefs, which causes the predictions to differ from those of deterministic models of iterated thinking, e.g. rationalizability. The paper contains a convergence proof that implies existence and uniqueness of the outcome of the iterated thought process. In addition, estimated introspection and noise parameters for data from 37 one-shot matrix games are reported. The accuracy of the model is compared with that of several alternatives.

A growing body of literature in networked systems research relies on game theory and mechanism design to model and address the potential lack of cooperation between self-interested users. Most game-theoretic models applied to system research only describe competitive equilibria in terms of pure Nash equilibria, that is, a situation where the strategy of each user is deterministic, and is her best response to the strategies of all the other users. However, the assumptions necessary for a pure Nash equilibrium to hold may be too stringent for practical systems. Using three case studies on network formation, computer security, and TCP congestion control, we outline the limits of game-theoretic models relying on Nash equilibria, and we argue that considering competitive equilibria of a more general form helps in assessing the accuracy of a game theoretic model, and can even help in reconciling predictions from game-theoretic models with empirically observed behavior.

The mechanism design problem in economics is about designing rules of interaction for market games so they yield a globally desirable result in the face of self-interested agents. This problem, which is of importance for ecommerce since much ecommerce is carried out through auctions, can be extremely complex. Traditionally, economists have tried using game theory and other formal methods to construct suitable mechanism rules. However, analytical methods typically oversimplify the problem and so the resulting rules are not necessarily robust. In this paper, we report on an alternative approach which we hope will eventually yield more robust solutions. Our methodology views mechanism design as a multi-objective optimisation problem and addresses the problem using genetic programming.

Lecture audiences and students were asked to respond to virtual decision and game situations at gametheory.tau.ac.il. Several thousand observations were collected and the response time for each answer was recorded. There were significant differences in response time across responses. It is suggested that choices made instinctively, that is, on the basis of an emotional response, require less response time than choices that require the use of cognitive reasoning. There is growing interest among economists in the bounds on the rationality of economic agents. Economists are increasingly abandoning the Ôeconomic manÕ paradigm and instead are using models that reflect what they consider to be more realistic descriptions of the way in which human beings make decisions. One can identify three approaches in the literature to Ôopening the black boxÕ of decision making. Bounded Rationality This approach is based on casual observations of the way in which people make decisions (and primarily of our own decision-making processes). These are used to construct abstract models which are intended to increase our understanding of the effect of certain decision-procedural elements on the outcome of an economic interaction

It is standard in multiagent settings to assume that agents will adopt Nash equilibrium strategies. However, studies in experimental economics demonstrate that Nash equilibrium is a poor description of human players ’ actual behaviour. In this study, we consider a wide range of widely-studied models from behavioural game theory. For what we believe is the first time, we evaluate each of these models in a meta-analysis, taking as our data set large-scale and publicly-available experimental data from the literature. We then propose a modified model that we believe is more suitable for practical prediction of human behaviour. ii Table of Contents Abstract................................... ii

The authors assume that individuals adapt rationally to a utility function given constraints imposed by their cognitive architecture and the local task environment. This assumption underlies a new approach to modeling and understanding cognition—cognitively bounded rational analysis—that sharpens the predictive acuity of general, integrated theories of cognition and action. Such theories provide the necessary computational means to explain the flexible nature of human behavior but in doing so introduce extreme degrees of freedom in accounting for data. The new approach narrows the space of predicted behaviors through analysis of the payoff achieved by alternative strategies, rather than through fitting strategies and theoretical parameters to data. It extends and complements established approaches, including computational cognitive architectures, rational analysis, optimal motor control, bounded rationality, and signal detection theory. The authors illustrate the approach with a reanalysis of an existing account of psychological refractory period (PRP) dual-task performance and the development and analysis of a new theory of ordered dual-task responses. These analyses yield several novel results, including a new understanding of the role of strategic variation in existing accounts of PRP and the first predictive, quantitative account showing how the details of ordered dual-task phenomena emerge from the rational control of a cognitive system subject to the combined constraints of internal variance, motor interference, and a response selection bottleneck.

The structural Quantal Response Equilibrium (QRE) generalizes the Nash equilibrium by augmenting payoffs with random elements that are not removed in some limit. This approach has been widely used both as a theoretical framework to study comparative statics of games and as an econometric framework to analyze experimental and field data. The framework of structural QRE is flexible: it can be applied to arbitrary finite games and incorporate very general error structures. Restrictions on the error structure are needed, however, to place testable restrictions on the data (Haile et al., 2004). This paper proposes a reducedform approach, based on quantal response functions that replace the best-response functions underlying the Nash equilibrium. We define a regular QRE as a fixed point of quantal response functions that satisfies four axioms: continuity, interiority, responsiveness, and monotonicity. We show that these conditions are not vacuous and demonstrate with an example that they imply economically sensible restrictions on data consistent with laboratory observations. The reduced-form approach allows for a richer set of regular quantal response functions, which has proven useful for estimation purposes.

This article is concerned with the implications of the surprisingly different experimental practices in economics and in areas of psychology relevant to both economists and psychologists, such as behavioral decision making. We consider four features of experimentation in economics, namely, script enactment, repeated trials, performance-based monetary payments, and the proscription against deception, and compare them to experimental practices in psychology, primarily in the area of behavioral decision making. Whereas economists bring a precisely defined ìscriptî to experiments for