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Incentive Stackelberg Mean-Payoff Games

机译：激励Stackelberg均值支付游戏

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摘要

We introduce and study incentive equilibria for multi-player mean-payoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria. Recall that a strategy profile is a Nash equilibrium if no player can improve his payoff by changing his strategy unilaterally. In the setting of incentive and leader equilibria, there is a distinguished player-called the leader-who can assign strategies to all other players, referred to as her followers. A strategy profile is a leader strategy profile if no player, except for the leader, can improve his payoff by changing his strategy unilaterally, and a leader equilibrium is a leader strategy profile with a maximal return for the leader. In the proposed case of incentive equilibria, the leader can additionally influence the behaviour of her followers by transferring parts of her payoff to her followers. The ability to incentivise her followers provides the leader with more freedom in selecting strategy profiles, and we show that this can indeed improve the leader's payoff in such games. The key fundamental result of the paper is the existence of incentive equilibria in mean-payoff games. We further show that the decision problem related to constructing incentive equilibria is NP-complete. On a positive note, we show that, when the number of players is fixed, the complexity of the problem falls in the same class as two-player mean-payoff games. We present an implementation of the proposed algorithms, and discuss experimental results that demonstrate the feasibility of the analysis.
机译：我们介绍并研究了多人均值支付游戏的激励均衡。激励均衡概括了经过充分研究的解决方案概念，例如纳什均衡和领导者均衡。回想一下，如果没有玩家能够通过单方面改变策略来提高自己的收益，那么策略概要就是纳什均衡。在激励和领导者均衡的背景下，有一个杰出的参与者称为领导者，可以将策略分配给所有其他参与者，称为她的跟随者。如果除领导者之外，没有其他玩家可以通过单方面更改其策略来提高收益，则战略配置文件是领导者策略配置文件，而领导者均衡是具有最大回报的领导者策略配置文件。在提议的激励均衡情况下，领导者可以通过将部分收益转移给跟随者来另外影响跟随者的行为。激励其追随者的能力为领导者提供了更多选择策略配置文件的自由，并且我们证明了，这确实可以提高领导者在此类游戏中的收益。本文的关键基本结果是在均值收益博弈中存在激励均衡。我们进一步证明，与构建激励均衡有关的决策问题是NP完全的。从积极的方面看，我们证明了，在玩家数量固定的情况下，问题的复杂性与两人平均付费游戏属于同一类。我们目前提出的算法的实现，并讨论了实验结果，证明了分析的可行性。

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