对抗性团队游戏的公共信息表示
Public Information Representation for Adversarial Team Games
摘要：
对抗性团队游戏的特殊性在于游戏过程中团队成员获得的信息不对称，这使得即使在零和收益的情况下也很难计算均衡。文献中的算法采用策略空间的隐式表示，主要采用线性规划和列生成技术来逐步扩大策略空间。这样的表示阻止了标准工具的采用，如抽象生成，博弈求解和子博弈求解，这些工具在解决巨大的现实世界中的两人零和博弈时至关重要。从这些作品中，我们回答了是否有任何合适的游戏表示，使这些工具的采用的问题。特别是，我们的算法转换成一个经典的两人零和游戏的对手的顺序团队游戏。在这个转换的博弈中，团队被转换成一个协调者，他只知道整个团队共同的信息，并为玩家规定任何可能的私人状态的行动。有趣的是，我们表明，我们的游戏比原来的扩展形式的游戏更有表现力，因为任何状态/动作抽象的扩展形式的游戏可以被我们的表示捕捉，而反过来并不成立。由于问题的NP难性质，最终的公共团队博弈可能比原始博弈大。为了限制这种爆炸，我们提供了三个算法，每个算法都返回一个信息无损的抽象，大大减少了树的大小。这些抽象可以在不生成原始游戏树的情况下产生。最后，我们通过对Kuhn和Leduc扑克游戏的实验结果表明了所提出方法的有效性，这些实验结果是通过将最先进的两人零和游戏算法应用于转换后的游戏而获得的
英文摘要：
The peculiarity of adversarial team games resides in the asymmetric information available to the team members during the play, which makes the equilibrium computation problem hard even with zero-sum payoffs. The algorithms available in the literature work with implicit representations of the strategy space and mainly resort to Linear Programming and column generation techniques to enlarge incrementally the strategy space. Such representations prevent the adoption of standard tools such as abstraction generation, game solving, and subgame solving, which demonstrated to be crucial when solving huge, real-world two-player zero-sum games. Differently from these works, we answer the question of whether there is any suitable game representation enabling the adoption of those tools. In particular, our algorithms convert a sequential team game with adversaries to a classical two-player zero-sum game. In this converted game, the team is transformed into a single coordinator player who only knows information common to the whole team and prescribes to the players an action for any possible private state. Interestingly, we show that our game is more expressive than the original extensive-form game as any state/action abstraction of the extensive-form game can be captured by our representation, while the reverse does not hold. Due to the NP-hard nature of the problem, the resulting Public Team game may be exponentially larger than the original one. To limit this explosion, we provide three algorithms, each returning an information-lossless abstraction that dramatically reduces the size of the tree. These abstractions can be produced without generating the original game tree. Finally, we show the effectiveness of the proposed approach by presenting experimental results on Kuhn and Leduc Poker games, obtained by applying state-of-art algorithms for two-player zero-sum games on the converted games
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