Common knowledge of payoff uncertainty in games

Extensive Games and Common Knowledge

The usual justification foc Nash equilibrium behavior involves (at least implicitly) the assumption that it is common knowledge among the playecs both that the Nash equilibrium in question will be played by all and that all playecs ace expected utility maximizers. We show that in a large class of extensive form games, the assumption that rationality is common knowledge cannot be maintained thro...

Common Knowledge in Simultaneous-Move Games

Incentive Stackelberg Mean-Payoff Games

We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that a strategy profile is a Nash equilibrium if no player can improve his payoff by changing his strategy unilaterally. In the setting of incentive and leader eq...

Synchronic Information, Knowledge and Common Knowledge in Extensive Games

The language of extensive games is complex and rich. It allows one to express such notions as the order of moves, the information a player has when it is her turn to move, etc. It is not, however, a sufficiently rich language in the sense that there are meaningful and natural statements that one can make (about a given extensive game) whose truth cannot be decided without making the language ri...

Simple Stochastic Games, Parity Games, Mean Payoff Games and Discounted Payoff Games Are All LP-Type Problems1

We show that a Simple Stochastic Game (SSG) can be formulated as an LP-type problem. Using this formulation, and the known algorithm of Sharir and Welzl [SW] for LP-type problems, we obtain the first strongly subexponential solution for SSGs (a strongly subexponential algorithm has only been known for binary SSGs [L]). Using known reductions between various games, we achieve the first strongly ...