Towards a theory of deception

Deceiving an opponent about one own’s cognitive abilities cannot be captured by standard approaches in which players understand the strategy of their opponent perfectly well. We introduce a framework with boundedly rational players to explain deception. Following Jehiel (2003) we assume that players partition the decision nodes of their opponents into analogy classes, and form expectations only about the average reaction function of their opponent over the various nodes of analogy classes; we further differentiate cognitive types according to whether or not the player can distinguish between the types of the opponent. An equilibrium concept is proposed for such environments. Deception arises in our setup because the updating of beliefs is made as if each cognitive type behaved in the same way in the various nodes of an analogy class, thus allowing rational players to induce the wrong belief that they are less sophisticated than they really are (by adopting a behavior that is typical of the average behavior of a less sophisticated type). We illustrate the phenomenon through a variety of applications, first in a zero-sum game, then in a simple concession game. We also show the implication of the approach in a monitoring game and in a negotiation about the pay rise between an employer and employee