图博弈的设计与模态逻辑的发展

Interaction Between Graph Game Design and Modal Logics

图博弈是一种主体间互动的场景,可以使用模态逻辑的语言描述。模态词用来描述博弈玩家的行为,博弈的均衡和玩家的必胜策略则通常用模态逻辑的公式刻画,这些公式具有特定的模式。取决于博弈目标的设定、对玩家互动机制的设计,图博弈有着各种不同的版本。与之对应,模态逻辑的语言不断发展和扩展,新的逻辑系统也呈现不同的性质。逻辑学一方面作为分析现有图博弈的一种方法,另一方面,逻辑学也是设计新博弈的灵感来源。图博弈与逻辑学之间的相互渗透为研究博弈提供了新的视角,也是对博弈论和计算理论方法的重要补充。

Graph games are interactive scenarios with a wide range of applications. This article discusses old and new graph games in tandem with matching logics,and identifies general questions behind this match. Throughout the article,we pursue two strands: logic as a way of analyzing existing games,and logic as an inspiration for designing new games. Our aim is modest: we propose a style of thinking that complements existing game theoretic and computational ones,and we also raise questions,make observations,and suggest research directions. Technical results are left for future work.