On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games
نویسندگان
چکیده
We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. secure equilibria) are guaranteed to exist in the multiplayer (resp. two-player) case. The existence of secure equilibria in the multiplayer case remained and is still an open problem. In this paper, we focus our study on the concept of subgame perfect equilibrium, a refinement of Nash equilibrium well-suited in the framework of games played on graphs. We also introduce the new concept of subgame perfect secure equilibrium. We prove the existence of subgame perfect equilibria (resp. subgame perfect secure equilibria) in multiplayer (resp. two-player) quantitative reachability games. Moreover, we provide an algorithm deciding the existence of secure equilibria in the multiplayer case.
منابع مشابه
Subgame Perfection for Equilibria in Quantitative Reachability Games
We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. secure equilibria) are guaranteed to exist in the multiplayer (resp. two-player) case. The existence of secure equilibria ...
متن کاملWeak Subgame Perfect Equilibria and their Application to Quantitative Reachability
We study n-player turn-based games played on a finite directed graph. For each play, the players have to pay a cost that they want to minimize. Instead of the well-known notion of Nash equilibrium (NE), we focus on the notion of subgame perfect equilibrium (SPE), a refinement of NE well-suited in the framework of games played on graphs. We also study natural variants of SPE, named weak (resp. v...
متن کاملStochastic evolutionary stability in extensive form games of perfect information
Nöldeke and Samuelson (1993) investigate a stochastic evolutionary model for extensive form games and show that even for games of perfect information with a unique subgame perfect equilibrium, non-subgame perfect equilibrium-strategies may well survive in the long run even when mutation rates tend to zero. In a different model of evolution in the agent normal form of these games Hart (2002) sho...
متن کاملVERY PRELIMINARY VERSION COMMENTS WELCOME A Notion of Subgame Perfect Nash Equilibrium under Knightian Uncertainty by
We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two wel...
متن کاملSubgame Perfect Equilibria and Communication in Stage Games
Any stage-game with in nite choice sets can be approximated by nite games obtained as increasingly ner discretizations of the in nite game. The subgame perfect equilibrium outcomes of the nite games converge to a limit distribution. We prove that (i) if the limit distribution is feasible in the limit game, then it is also a subgame perfect equilibrium outcome of the limit game; and (ii) if the ...
متن کامل