On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games
On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games
复制标题
论定量可达博弈中的（子博弈完美）安全均衡
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
H. Gimbert
中科院分区：
文献类型：
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作者：
Thomas Brihaye;V. Bruyère;Julie De Pril;H. Gimbert
我们研究了有限图上可达目标的回合制定量多人非零和博弈。在这样的博弈中，每个参与者的目标都是尽快达到自己的目标状态集。以前对这个模型的研究表明，纳什均衡（分别为）。安全均衡）被保证存在于多人游戏中（相应地，两个玩家）的情况下。多人游戏中安全均衡的存在仍然存在，并且仍然是一个悬而未决的问题。在本文中，我们专注于我们的研究的概念，子博弈完美均衡，完善的纳什均衡非常适合在框架内的游戏玩图。我们还引入了子博弈完美安全均衡的新概念。我们证明了子博弈完美均衡的存在性（分别为）。子博弈完美安全均衡）在多人游戏（分别）。两人）定量可达性游戏。此外，我们提供了一个算法，确定存在的安全平衡的多人情况下。
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.