This paper is concerned with the entire solutions defined in the whole space and for all time $t\in \mathbb{R}$ of a public good game model. The existence of the entire solutions is proved by super- and sub-solution method. Traveling fronts with possibly different wave speeds are used to construct the super- and sub-solutions, in particular, the traveling fronts of a variant of KPP equation are used to derive the t < 0 part of the super solutions.

中文翻译：

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公共品博弈模型的整体解决方案

本文关注在整个空间和所有时间定义的整个解决方案$吨\in \mathbb{R}$公共利益博弈模型。用超解法和子解法证明了全解的存在性。具有可能不同波速的行进用于构造超解和子解，特别是，使用KPP方程的变体的行进来推导超解的t < 0部分。