概率测度空间的变分optimization解决了连锁店悖论
Variational optimization of probability measure spaces resolves the chain store paradox
摘要：
在对策论中，参与者有连续的预期支付函数，可以使用不动点定理来定位均衡。这种最优化方法要求参与者采用特定类型的概率测度空间。在这里，我们引入替代的概率测度空间，改变什么是现在的游戏的预期收益泛函的维数，连续性和可微性。优化这样的泛函需要广义变分和泛函最优化方法来定位新的平衡。这些变分方法可以调和博弈论预测和观察到的人类行为，正如我们通过解决连锁店悖论所说明的那样。我们的广义优化分析对经济学、人工智能、复杂系统理论、神经生物学以及生物进化和发展具有重要意义。
英文摘要：
In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game's expected payoff functionals. Optimizing such functionals requires generalized variational and functional optimization methods to locate novel equilibria. These variational methods can reconcile game theoretic prediction and observed human behaviours, as we illustrate by resolving the chain store paradox. Our generalized optimization analysis has significant implications for economics, artificial intelligence, complex system theory, neurobiology, and biological evolution and development.
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