We study a group formation game. Players with different strengths form groups before expending effort to win a prize. The prize has the nature of the reward for outdoing in competition such as holding a dominant position among players or being recognized as a dominant status. So, it has the nature of public goods within a winning group (group-specific public goods). In open membership game, we find that a single player stays alone and the others form a group together in equilibrium. The stand-alone player can be anyone except for the first and second strongest players in the contest. However, strong (Nash) equilibrium predicts that the weakest player is isolated. Similarly, we find that in exclusive membership game, every structure can emerge in equilibrium but the weakest player is isolated in the strong equilibrium.

我们研究了一个组队游戏。具有不同优势的玩家在努力赢得奖品之前组成小组。该奖项具有在竞争中胜出的奖励性质，例如在玩家中占据主导地位或被认可为主导地位。因此，它具有获胜组内公共物品的性质（特定于组的公共物品）。在开放的会员博弈中，我们发现一个人独自呆着，其他人组成一个平衡的群体。单机玩家可以是比赛中除了第一和第二强的玩家之外的任何人。然而，强（纳什）均衡预测最弱的参与者是孤立的。同样，我们发现在排他性成员博弈中，每个结构都可以在均衡中出现，但最弱的参与者在强均衡中是孤立的。