In recent years, it is a trend to integrate the ideas in game theory into the research of multi-robot system. In this paper, a team-competition model is proposed to solve a dynamic multi-robot task allocation problem. The allocation problem asks how to assign tasks to robots such that the most suitable robot is selected to execute the most appropriate task, which arises in many real-life applications. To be specific, we study multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once, which defines an extensive-form game with perfect recall. We also study a common variant where one team always selects its player before the other team in each round. Regarding the robots as the players in the first team and the tasks as the players in the second team, the sub-game perfect strategy of the first team computed via solving the team competition gives us a solution for allocating the tasks to the robots -- it specifies how to select the robot (according to some probability distribution if the two teams move simultaneously) to execute the upcoming task in each round, based on the results of the matches in the previous rounds. Throughout this paper, many properties of the sub-game perfect equilibria of the team competition game are proved. We first show that uniformly random strategy is a sub-game perfect equilibrium strategy for both teams when there are no redundant players. Secondly, a team can safely abandon its weak players if it has redundant players and the strength of players is transitive. We then focus on the more interesting case where there are redundant players and the strength of players is not transitive. In this case, we obtain several counterintuitive results. For example, a player might help improve the payoff of its team, even if it is dominated by the entire other team. We also study the extent to which the dominated players can increase the payoff. Very similar results hold for the aforementioned variant where the two teams take actions in turn.

中文翻译：

---

基于团队竞争模型的多机器人系统动态任务分配

近年来，将博弈论中的思想融入多机器人系统的研究已成为一种趋势。本文提出了一种团队竞争模型来解决动态多机器人任务分配问题。分配问题询问如何将任务分配给机器人，以便选择最合适的机器人来执行最合适的任务，这在许多现实应用中都会出现。具体来说，我们研究两支球队之间的多轮比赛，其中每支球队在每个回合中同时选择一名球员，并且每名球员最多可以玩一次，这定义了一款具有完美召回性的广泛比赛。我们还研究了一个常见的变体，其中一个团队在每个回合中总是先于另一个团队选择其球员。关于以机器人为第一团队的参与者和任务为第二团队的参与者，通过解决团队竞争而计算出的第一团队的子游戏完美策略为我们提供了一种将任务分配给机器人的解决方案-它指定了如何选择机器人（如果两支团队同时移动，则根据一定的概率分布）根据前一轮比赛的结果，在每一轮中执行即将到来的任务。在整个本文中，团队竞争游戏的子游戏完美均衡的许多性质都得到了证明。我们首先证明，在没有多余球员的情况下，均匀随机策略是两支球队的子博弈完美均衡策略。其次，如果一支球队有多余的球员并且球员的力量是可传递的，那么它可以安全地放弃弱者。然后，我们将关注更有趣的情况，即存在多余的参与者，而参与者的实力并不具有传递性。在这种情况下，我们获得了一些违反直觉的结果。例如，一个球员可能会帮助提高其团队的收益，即使它被整个其他团队所支配。我们还研究了主导者可以在多大程度上增加收益。对于上述变体，两个团队依次采取行动，结果非常相似。