The paper addresses a paradoxical game-theoretic example which is closely related to the coordinated attack problem. Two players have to play one of two possible coordination games. Only one of them receives information about the coordination game to be played. It is shown that the situation with "almost common knowledge" is very different from when the coordination game played is common knowledge.

This paper explores how the requirement that the implementation of contracts be renegotiation-proof affects the set of contracts that can be implemented in a seller--buyer scenario in which the information regarding the agents' valuations is nonverifiable. This paper explicitly adds a time dimension to an implementation problem and introduces a natural criterion of renegotiation-proofness for the case of time-consuming renegotiation. The main insight gained is that the addition of the time dimension enlarges significantly the set of contracts that can be implemented in a renegotiation-proof manner.

We study interactive situations in which players are boundedly rational. Each player, rather than optimizing given a belief about the other players' behavior, as in the theory of Nash equilibrium, uses the following choice procedure. She first associates one consequence with each of her actions by sampling (literally or virtually) each of her actions once. Then she chooses the action that has the best consequence. We define a notion of equilibrium for such situations and study its properties.

We propose a new abstract definition of equilibrium in the spirit of competitive equilibrium: a profile of alternatives and a public ordering (expressing prestige, price, or a social norm) such that each agent prefers his assigned alternative to all lower-ranked ones. The equilibrium operates in an abstract setting built upon a concept of convexity borrowed from convex geometry. We apply the concept to a variety of convex economies and relate it to Pareto optimality. The “magic” of linear equilibrium prices is put into perspective by establishing an analogy between linear functions in the standard convexity and “primitive orderings” in the abstract convexity.

We study experimentally a new two-player game: each player requests an amount between 11 and 20 shekels. He receives the requested amount and if he requests exactly one shekel less than the other player, he receives an additional 20 shekels. Level-k reasoning is appealing due to the natural starting point (requesting 20) and the straightforward best-response operation. Nevertheless, almost all subjects exhibit at most three levels of reasoning. Two variants of the game demonstrate that the depth of reasoning is not increased by enhancing the attractiveness of the level-0 strategy or by reducing the cost of undercutting the other player.