Game Theory: An open access textbook with 165 solved exercises

[Pallas_Boreas]

Introduction

The discipline of game theory was pioneered in the early 20th century by mathematicians Morgenstern's The breakthrough book, Ernst Theory came Zermelo with of games (1913) John and and von economic John Neumann von behavior, Neumann and published  (1928). Oscar in 1944. This was followed by important work by John Nash (1950-51) and Lloyd Shapley (1953). Game theory had a major influence on the development of several branches of economics (industrial organization, international trade, labor economics, macroeconomics, etc.). Over time the impact of game theory extended to other branches of the social sciences (political science, international relations, philosophy, sociology, anthropology, etc.) as well as to fields outside the social sciences, such as biology, computer science, logic, etc. In 1994 the Nobel prize in economics was given to three game theorists, John Nash, John Harsanyi and Reinhardt Selten, for their theoretical work in game theory which was very influential in economics. At the same time, the US Federal Communications Commission was using game theory to help it design a $7-billion auction of the radio spectrum for personal communication services (naturally, the bidders used game theory too!). The Nobel prize in economics was awarded to game theorists three more times: in 2006 to Robert Aumann and Thomas Schelling, in 2007 to Leonid Hurwicz, Eric Maskin and Roger Myerson and in 2010 to Lloyd Shapley and Alvin Roth.

Game theory provides a formal language for the representation and analysis of interactive situations, that is, situations where several "entities", called players, take actions that affect each other. The nature of the players varies depending on the context in which the game theoretic language is invoked: in evolutionary biology (see, for example, John Maynard Smith, 1982) players are non-thinking living organisms; in computer science (see, for example, Shoham-Leyton-Brown, 2008) players are artificial agents; in behavioral game theory (see, for example, Camerer, 2003) players are "ordinary" human beings, etc. Traditionally, however, game theory has focused on interaction among intelligent, sophisticated and rational individuals. For example, Aumann describes game theory as follows:

"Briefly put, game and economic theory are concerned with the interactive behavior of Homo rationalis - rational man. Homo rationalis is the species that always acts both purposefully and logically, has well-defined goals, is motivated solely by the desire to approach these goals as closely as possible, and has the calculating ability required to do so." (Aumann, 1985, p. 35.)

This book is concerned with the traditional interpretation of game theory.

Game theory is divided into two main branches. The first is cooperative game theory, which assumes that the players can communicate, form coalitions and sign binding agreements. Cooperative game theory has been used, for example, to analyze voting behavior and other issues in political science and related fields. We will deal exclusively with the other main branch, namely non-cooperative game theory. Non-cooperative game theory models situations where the players are either unable to communicate or are able to communicate but cannot sign binding contracts. An example of the latter situation is the interaction among firms in an industry in an environment where antitrust laws make it illegal for firms to reach agreements concerning prices or production quotas or other forms of collusive behavior.