Basic Solution Concepts and Computational Issues

We consider some classical games and show how they can arise in the context of the Internet. We also introduce some of the basic solution concepts of game theory for studying such games, and some computational issues that arise for these concepts. Games, Old and New The Foreword talks about the usefulness of game theory in situations arising on the Internet. We start the present chapter by giving some classical games and showing how they can arise in the context of the Internet. At first, we appeal to the reader's intuitive notion of a “game”; this notion is formally defined in Section 1.2. For a more in-depth discussion of game theory we refer the readers to books on game theory such as Fudenberg and Tirole (1991), Mas-Colell, Whinston, and Green (1995), or Osborne and Rubinstein (1994). The Prisoner's Dilemma Game theory aims to model situations in which multiple participants interact or affect each other's outcomes. We start by describing what is perhaps the most well-known and well-studied game. Example 1.1 (Prisoners' dilemma) Two prisoners are on trial for a crime and each one faces a choice of confessing to the crime or remaining silent. If they both remain silent, the authorities will not be able to prove charges against them and they will both serve a short prison term, say 2 years, for minor offenses.