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A Primer on Strategic Games
Krzysztof R. Apt
CWI and University of Amsterdam
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.
1.1 Introduction
Mathematical game theory, as launched by Von Neumann and Morgenstern in
their seminal topic, 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 competi-
tion, 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 . The purpose of this
primer is to provide a simple introduction to the most common concepts used
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