Generalized logit dynamic defines a time-dependent integro-differential equation with which a Nash equilibrium of an iterative game in a bounded and continuous action space is expected to be approximated. We show that the use of the exponential logit function is essential for the approximability, which will not be necessarily satisfied with functions with convex exponential-like functions such as q-exponential ones. We computationally analyze this issue and discuss influences of the choice of the logit function through an application to a fishing tourism problem in Japan.

翻译：广义logit动力学定义了一个时间依赖的积分-微分方程，预期通过该方程可逼近有界连续行动空间中迭代博弈的纳什均衡。我们证明了指数logit函数对于这种可逼近性是必要的，而具有凸指数类函数（如q指数函数）的函数未必满足这一性质。我们从计算角度分析了这一问题，并通过日本渔业旅游问题的应用讨论了logit函数选择的影响。