Game Theory for Internetworking

Chapter 1 Principles of Game Theory Game theory is a mathematical theory, a discipline, that even a reader with scarce mathematical basis can adopt to analyse every day life problems: simple classical games, but also social behaviours, financial trends or telecommunication systems. In this chapter we depict principles of game theory, voluntarily avoiding math- ematical formalisms and historical facts for the sake of seamlessness. Our first references are, for an Italian reader, the book from Fioravante Patrone [1] and, for an English reader, the book from Osborne [2]. Game theory can intervene in all those situations in which more than one decision-makers have to plan their optimal strategy to solve a problem. Hence, it does not intervene in those situations with a single decision-maker, ground for operations research. In the following, before diving into the ways in which a player’s strategy is to be built and modelled, we highlight principles, concepts and assumptions of game theory, starting from the characterization of the decision-maker. 1.1 The decision-maker, i.e. the player The reader may think that life is a sentence to forced works, full of duties and difficulties. Others may, instead, think that life is a game, and that a person in charge of a decision, the decision-maker, is a player, as the game theory predicates. Not whatever player: an intelligent and rational player1. 1.1.1 Intelligence The starting hypothesis of game theory is that the player is infinitely intelligent, in the sense that he has infinite ability of deduction, computation and analysis. Besides being not really true for humans, it is a strong hypothesis especially for wide games, such as the chess, since just the simple enumeration of all the possible strategies may take a lot of resources. However, the vast majority of the problems 1From now on, we will refer to the decision-maker or to the player with the third male person for simplicity. 1