Two-player games on graphs provide the theoretical framework for many important problems such as reactive synthesis. While the traditional study of two-player zero-sum games has been extended to multi-player games with several notions of equilibria, they are decidable only for perfect-information games, whereas several applications require imperfect-information games. In this paper we propose a...

Patrolling games are partially observable games played by two players, the defender and the attacker. The defender aims for detecting intrusions into vulnerable targets by following randomized routes among them, the attacker strives to maximize the probability of a successful (undetected) intrusion. We show how to translate patrolling games into turn-based perfect information stochastic games w...

We present a simple proof of existence of subgame perfect equilibria in games with perfect information.

Games with imperfect information are an interesting and important class of games. They include most card games (e.g., bridge and poker) as well as many economic and political models. Here we investigate algorithms for finding the simplest form of a solution (a pure-strategy equilibrium point) to imperfect information games expressed in their extensive (game tree) form. We introduce to the artif...

The Global Newton Method for games in normal form and in extensive form is shown to have a natural extension to computing Markov-perfect equilibria of stochastic games. GLOBAL NEWTON METHOD FOR STOCHASTIC GAMES SRIHARI GOVINDAN AND ROBERT WILSON Abstract. The Global Newton Method for games in normal form and in extensive form is shown to have a natural extension to computing Markov-perfect equi...

Finite perfect information extensive (FPIE) games are quite well-understood: backward induction yields all of the pure strategy subgame perfect equilibria of such games. Iterative elimination of weakly dominated strategies (IEWDS), which can be hazardous in general games due to orderdependence of outcomes, can be much better behaved. In fact, for a large class of FPIE games, the outcomes of IEW...

1. Extensive form games with perfect information 3 1.1. Chess 3 1.2. Definition of extensive form games with perfect information 4 1.3. The ultimatum game 5 1.4. Equilibria 5 1.5. The centipede game 6 1.6. Subgames and subgame perfect equilibria 6 1.7. Backward induction, Kuhn’s Theorem and a proof of Zermelo’s Theorem 7 2. Strategic form games 10 2.1. Definition 10 2.2. Nash equilibria 10 2.3....