Rules of play: the starting point matters

Abstract

Introduction Classical game theory, as developed by von Neumann and Morgenstern (1944; 3rd edn, 1953), distinguishes between the extensive form of a game and the normal (or strategic) form . The extensive form is represented by a game tree, in which the players make sequential choices, not necessarily knowing all the prior choices of the other players. The normal form is represented by a payoff matrix , in which players independently choose strategies , or complete plans that specify what they will do in every contingency – that is, for each known choice of all the other players. TOM makes use of both forms. A payoff matrix defines the game configuration , which gives the basic structure of payoffs. An example of such a structure is shown in figure 1.1, which I identify as game 56. Note that Row ( R ) has two strategies, s 1 , and s 2 , and Column ( C ) also has two strategies, t 1 and t 2 , making this a 2 × 2 game (i.e., a game in which there are two players, each with two strategies). These strategies may be thought of as alternative courses of action that the players might choose, such as to cooperate or not to cooperate.