The deception of the Greeks: generalizing the information structure of extensive form games

The standard model of an extensive form game rules out an important phenomenon in situations of strategic interaction: deception. Using examples from the world of ancient Greece and from modern-day Wall Street, we show how the model can be generalized to incorporate this phenomenon. Deception takes place when the action observed by a player is different from the action actually taken. The standard model does allow imperfect information (modeled by nonsingleton information sets), but not deception: the actual action taken is never ruled out. Our extension of extensive form games relaxes the assumption that the information sets partition the set of nodes, so that the set of nodes considered possible after a certain action is taken might not include the actual node. We discuss the implications of this relaxation, and show that in certain games deception is inconsistent with common knowledge of rationality even along the backward induction path. “You are to hear now how the Greeks tricked us. From this one proof of their perfidy you may 1 Deception in games understand them all ” (Aeneas). Although the Trojan war pre-dates the formal study of games by almost three thousand years, the Greek generals clearly possessed a sound understanding of the basic principles of game theory