We consider a version of the $N$-player snowdrift game in which the payoffs obtained by the players are delayed. The delay in payoffs is shown to lead to a Hopf bifurcation with an associated critical value of the time delay in the replicator dynamics. For time delays larger than the critical time delay, the replicator dynamics oscillate around the equilibrium instead of asymptotically approaching it. The dependence of this critical time delay on the parameters of the game is determined. After developing the analysis for the 2-player game, the same methodology is applied to the $N$-player version of the game to show how the results change as a function of $N,$ concluding with an analysis of the limiting case of large numbers of players.

我们考虑了 $ñ$玩家雪堆游戏，其中玩家获得的收益被延迟。结果表明，支付延迟会导致Hopf分叉，并伴随复制器动力学中时间延迟的相关临界值。对于大于临界时间延迟的时间延迟，复制器动力学会在平衡附近振荡，而不是渐近地接近平衡点。确定该关键时间延迟对游戏参数的依赖性。在对两人游戏进行分析后，将相同的方法应用于$ñ$游戏版本，以显示结果如何根据 $ñ，$ 最后分析了众多玩家的局限性情况。