Brihaye, Thomas and Bruyère, Véronique and De Pril, Julie and Gimbert, Hugo - On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games

lmcs:790 - Logical Methods in Computer Science, February 28, 2013, Volume 9, Issue 1
On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games

Authors: Brihaye, Thomas and Bruyère, Véronique and De Pril, Julie and Gimbert, Hugo

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.


Source : oai:arXiv.org:1205.6346
DOI : 10.2168/LMCS-9(1:7)2013
Volume: Volume 9, Issue 1
Published on: February 28, 2013
Submitted on: May 31, 2012
Keywords: Computer Science - Computer Science and Game Theory,Computer Science - Logic in Computer Science,D.2.4


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