Abstract

This is a short introduction to the subject of strategic games. We focus on the concepts of best response, Nash equilibrium, strict and weak dominance, and mixed strategies, and study the relation between these concepts in the context of the iterated elimination of strategies. Also, we discuss some variants of the original definition of a strategic game. Finally, we introduce the basics of mechanism design and use pre-Bayesian games to explain it.

Introduction

Mathematical game theory, as launched by Von Neumann and Morgenstern in their seminal book, von Neumann and Morgenstern [1944], followed by Nash's contributions Nash [1950, 1951], has become a standard tool in economics for the study and description of various economic processes, including competition, cooperation, collusion, strategic behaviour and bargaining. Since then it has also been successfully used in biology, political sciences, psychology and sociology. With the advent of the Internet game theory became increasingly relevant in computer science.

One of the main areas in game theory are strategic games (sometimes also called non-cooperative games), which form a simple model of interaction between profit maximising players. In strategic games each player has a payoff function that he aims to maximise and the value of this function depends on the decisions taken simultaneously by all players. Such a simple description is still amenable to various interpretations, depending on the assumptions about the existence of private information.