加权对策中的安全均衡

V. Bruyère, N. Meunier, Jean-François Raskin
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引用次数: 28

摘要

我们考虑在加权图上进行的两方非零和无限持续博弈。我们将Chatterjee等人引入的安全均衡的概念从布尔设置扩展到这个定量设置。对于布尔设置,我们的安全均衡概念是对经典纳什均衡概念的改进。我们证明了安全均衡总是存在于一大类加权对策中,这些对策包括诸如sup, inf, lim sup, lim inf,平均收益和折现和等常见测度。此外,我们还证明了可以用很少的内存合成有限内存策略概要。我们还证明了安全均衡的约束存在问题对于sup,∞,lim sup, lim inf和平均收益措施是可决定的。我们的解决方案依赖于零和定量游戏的新结果,词典目标本身就很有趣。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Secure equilibria in weighted games
We consider two-player non zero-sum infinite duration games played on weighted graphs. We extend the notion of secure equilibrium introduced by Chatterjee et al., from the Boolean setting to this quantitative setting. As for the Boolean setting, our notion of secure equilibrium refines the classical notion of Nash equilibrium. We prove that secure equilibria always exist in a large class of weighted games which includes common measures like sup, inf, lim sup, lim inf, mean-payoff, and discounted sum. Moreover we show that one can synthesize finite-memory strategy profiles with few memory. We also prove that the constrained existence problem for secure equilibria is decidable for sup, inf, lim sup, lim inf and mean-payoff measures. Our solutions rely on new results for zero-sum quantitative games with lexicographic objectives that are interesting on their own right.
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