Deception in 2 × 2 Games

Abstract

Deception, which involves the conscious misrepresentation by Deceiver of his preferences to Deceived in a game of incomplete information, is analyzed in 2 × 2 games in which the preferences of players are strictly ordered. The 78 distinct 2 × 2 games are divided into three mutually exclusive classes: 1. Deception-proof (27 percent): Not susceptible to deception by either player. 2. Deception-stable (51 percent): While susceptible to deception by at least one player, neither player can ensure himself of a better outcome through deception. 3. Deception-vulnerable (tacit) (22 percent): At least one player can ensure himself of a better outcome only through deception. In addition, a fourth class of games (35 percent of total). which cuts across classes 2 and 3 above, are shown to be vulnerable to Deceiver who “reveals” himself in the play of a game. Several theorems that characterize and interrelate the four classes and eleven finer categories of 2 × 2 games are proved. The theory is applied to the analysis of the Cuban missile crisis, in which it is suggested that the United States might, paradoxically, have benefited from being deceived by the Soviet Union.