论文标题
用于空间不均匀进化游戏的替代拉格朗日计划
An alternate Lagrangian scheme for spatially inhomogeneous evolutionary games
论文作者
论文摘要
提出了一种在离散时间的替代拉格朗日方案，以将非线性连续性方程作为空间不均匀进化游戏的平均场限制的近似，描述了具有策略或标签的策略的空间分布式系统的演变，其付款也取决于抗逆转录机的当前位置。该方案是拉格朗日人，因为它可以追溯到位置和标签沿特征的演变，并且是替代的，因为它由以下两个步骤组成：首先，根据最佳性能标准对策略或标签的分布进行了更新，然后代理商将其用于进化其位置。在概率度量的空间中提供了一般的收敛结果。在复制器型系统和可逆的马尔可夫链的特殊情况下，该方案的变体也考虑了标签演化的明确步骤，并由隐性链代替，并提供了收敛结果。
An alternate Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of spatially distributed agents with strategies, or labels, whose payoff depends also on the current position of the agents. The scheme is Lagrangian, as it traces the evolution of position and labels along characteristics and is alternate, as it consists of the following two steps: first the distribution of strategies or labels is updated according to a best performance criterion and then this is used by the agents to evolve their position. A general convergence result is provided in the space of probability measures. In the special cases of replicator-type systems and reversible Markov chains, variants of the scheme, where the explicit step in the evolution of the labels is replaced by an implicit one, are also considered and convergence results are provided.
