A systematic theory is introduced that describes stochastic effects in game theory. In a biological context, such effects are relevant for the evolution of finite populations with frequency-dependent selection. They are characterized by quantum Nash equilibria, a generalization of the well-known Nash equilibrium points in classical game theory. The implications of this theory for biological sys...

A computer simulation runs a model generating a phenomenon under investigation. For the simulation to be explanatory, the model has to be explanatory. The model must be isomorphic to the natural system that realizes the phenomenon. This paper elaborates the method of assessing a simulation's explanatory power. Then it illustrates the method by applying it to two simulations in game theory. The ...

Contents Preface vii Chapter 1. Backward Induction 3 1.1. Tony's accident 3 1.2. Games in extensive form with complete information 5 1.3.

This paper introduces a model of 'theory of mind', namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a 'game theory of mind'. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions an...

In applied game theory the motivation of players is a key element. It is encoded in the payoffs of the game form and often based on utility functions. But there are cases were formal descriptions in the form of a utility function do not exist. In this paper we introduce a representation of games where players’ goals are modeled based on so-called higher-order functions. Our representation provi...

ing interaction among rational and self-interested agents. The field took on its modern form in the 1940s and 1950s (von Neumann and Morgenstern 1947; Nash 1950, Kuhn 1953), with even earlier antecedents (such as Zermelo 1913 and von Neumann 1928). Although it has had occasional and significant overlap with computer science over the years, game theory received most of its early study by economi...

the differential information literature in economics and game theory? Why has the those posteriors are derived by updating the common prior. Perhaps the most world can be generated by conditioning by Bayes rule. If there are many. Find a weak perfect bayesian equilibrium (strategies and beliefs) where the be arbitrary (and thus don't have to be according to Bayesian updating) but I am under Bro...

An extremely simplified version of poker is completely solved from a game theoretic standpoint. The actual properties of the optimal solution are then compared to various common notions about game theory and bluffing in poker. No specialized mathematical knowledge is needed to understand this material.

This chapter summarizes two main views on norms and games as emerging in literature on game theory, social science, philosophy and artificial intelligence. The first view originates in the field of mechanism design or implementation theory and characterizes norms as mechanisms enforcing desirable social properties in classes of games. According to the second view, originating from work in the s...