Introduction

In chapter 1 I illustrated, using just one game, a startling difference between the predictions of the standard theory (i.e., based on Nash equilibria) and TOM. Whereas TOM predicts one of three possible NMEs in game 56, depending on the initial state, the standard theory picks out only one of these NMEs as the (Nash) equilibrium. But if the players anticipate the NMEs in a prior “anticipation game,” the one that is also the Nash equilibrium will be chosen, as I shall show later. However, this may not always be the case, which gives rise to an “anticipation problem.”

I begin the analysis in this chapter with one of these games, which is a game of total conflict: what is the best (4) outcome for one player is worst (1) for the other, and what is next best (3) for one is next worst (2) for the other. This is game 11 and is shown in figure 2.1. To characterize these states verbally, let 4 indicate that a player “wins,” 3 that it is “advantaged”; not shown, 2 means that it is “disadvantaged,” and 1 that it “loses.”

Observe that the sum of the ranks for the players in each state in game 11 is 5. If these ranks were cardinal utilities, then game 11 would be a constant-sum game, wherein the constant is 5.