Various Nash equilibrium results for a broad class of aggregative games are presented. The main ones concern equilibrium uniqueness. The setting presupposes that each player has \(\mathbb {R}_+\) as strategy set, makes smoothness assumptions but allows for a discontinuity of stand-alone payoff functions at 0; this possibility is especially important for various contest and oligopolistic games. Conditions are completely in terms of marginal reductions which may be considered as primitives of the game. For many games in the literature they can easily be checked. They automatically imply that conditional payoff functions are strictly quasi-concave. The results are proved by means of the Szidarovszky variant of the Selten–Szidarovszky technique. Their power is illustrated by reproducing quickly and improving upon various results for economic games.

提供了广泛类别的聚合博弈的各种纳什均衡结果。主要的问题涉及均衡唯一性。设置的前提是每个玩家都有\(\mathbb {R}_+\)作为策略集，做出平滑假设，但允许独立收益函数在 0 处不连续；这种可能性对于各种竞争和寡头垄断游戏尤其重要。条件完全是边际减少，可以将其视为游戏的原语。对于文献中的许多游戏，它们很容易被检查。它们自动暗示条件支付函数是严格准凹的。结果通过 Selten-Szidarovszky 技术的 Szidarovszky 变体证明。它们的力量通过快速复制和改进经济游戏的各种结果来说明。