In this paper, we consider the $N$-person stag hunt game based on the two-person stag hunt game and assume that the payoff of successful stag hunters is larger than that of hare hunters, which is an important feature of the game, but is often ignored in previous works. We first study the evolutionary dynamics of cooperation for the game in infinite well-mixed populations by using the replicator equation, and find that there always exists only one interior equilibrium which is unstable. We then investigate the game in finite well-mixed populations by applying the Markov process, and observe that the equation of gradient of selection always has a unique interior root, which is consistent with the finding in infinite populations. We finally consider the game in structured populations by means of the pair approximation approach. We accordingly obtain the dynamical equation for weak selection to depict the evolutionary dynamics of cooperation in structured populations, and find that there still exists the case in which there is only one interior unstable equilibrium. Our work unveils the universal characteristics of cooperative dynamics in different scenarios for the $N$-person stag hunt game.

在本文中，我们考虑 $ñ$人型雄鹿狩猎游戏基于两人型雄鹿狩猎游戏，并假设成功的雄鹿狩猎者的收益大于野兔猎人的收益，这是游戏的重要特征，但在以前的作品中经常被忽略。我们首先使用复制器方程研究了在无限充分混合的种群中游戏合作的进化动力学，发现始终只有一个内部不稳定的平衡。然后，我们通过应用马尔可夫过程研究有限混合人口中的博弈，并观察到选择梯度方程始终具有唯一的内部根，这与在无限人口中的发现是一致的。我们最终通过对近似方法考虑结构化总体中的博弈。因此，我们获得了弱选择的动力学方程来描述结构化种群中合作的进化动力学，并且发现仍然存在只有一个内部不稳定平衡的情况。我们的工作揭示了不同情况下合作动力学的普遍特征。$ñ$人的雄鹿狩猎游戏。