AI 中文总结
本文研究多人离散出价博弈，证明其在温和假设下具有确定性，均值收益博弈存在值，定性博弈存在纯纳什均衡，且可达性博弈中判断联盟获胜的问题为PSPACE-hard。
AI 中文摘要
图上博弈是一种基础模型，其应用包括可归约为求解两人零和博弈的反应式综合，以及将多智能体系统建模为多人博弈的推理。本文研究一类称为出价博弈的图博弈，该博弈中玩家被分配预算，每轮通过拍卖确定由哪位玩家移动标记。两人出价博弈已被广泛研究，本文首次研究多人出价博弈，重点关注对玩家预算和出价施加粒度限制的离散出价。离散出价的原始动机来自实际应用，技术上的吸引力在于该博弈仅存在有限种配置。我们从考虑两个玩家联盟之间的博弈展开研究，证明在打破出价平局的机制满足温和假设时，出价博弈具有确定性：从每个初始配置出发，总有一个联盟拥有获胜策略。由此，我们确定了多人并发博弈中一个具有确定性的子类，并将该结果推广到均值收益博弈中值的存在性。利用确定性，我们证明定性博弈中始终存在纯纳什均衡。最后，我们证明判断给定配置下哪个联盟获胜的复杂性已属于PSPACE-hard，即使在可达性博弈中、即使预算以一元形式给出亦是如此，这与两人博弈形成鲜明对比——两人博弈即使预算以二进制形式给出，也被证明属于NP和coNP类。
英文摘要
Games on graphs constitute a fundamental model. Applications include reactive synthesis, which reduces to solving a zero-sum two-player game, and reasoning about multi-agent systems by modeling them as a multi-player game. We study a class of graph games called bidding games in which the players are allocated a budget, and in each turn, an auction determines which player moves the token. Two-player bidding games have been extensively studied. We study, for the first time, multi-player bidding games. We focus on discrete bidding, which imposes granularity restrictions on the players' budgets and bids. The original motivation for discrete bidding is practical applications, and technically, it is appealing that the game has only finitely-many configurations. We initiate our study by considering a game between two coalitions of players. We show that under mild assumptions on the mechanism that is applied to break bidding ties, bidding games are determined: from every initial configuration, one of the coalitions has a winning strategy. Thus, we identify a sub-class of multi-player concurrent games that is determined. We extend the result to existence of a value in mean-payoff games. Using determinacy, we show that a pure Nash equilibrium always exists in qualitative games. Finally, we show that the complexity of deciding which coalition wins from a given configuration is PSPACE-hard already in reachability games and already for budgets given in unary. This is in stark contrast to two-player games, which are known to be in NP and coNP even for budgets given in binary.
