Mathematical Sciences: Cooperative and Stochastic Games

这个项目将考虑合作和随机博弈。对于合作博弈，当假设参与者以不同程度的努力或诚意加入联盟时，将分析与Shapley值相关的问题。此外，还将考虑这类博弈的势函数概念。对于随机对策，将研究有效算法和均衡的存在性。本项目开发的模型适用于经济、金融、社会和军事科学等领域的许多现象。由于这些方法的通用性，广泛的知识领域将受益于这项资助的结果。

This project will consider cooperative and stochastic games. For cooperative games, questions related to Shapley value will be analyzed when the players are assumed to join coalitions with varying levels of effort or sincerity. In addition, the notion of potential function for this kind of games will be considered. For stochastic games, the existence of efficient algorithms and equilibria will be studied. Models developed in this project apply to a many phenomena in areas such as economics, finance, social and military science. Due to the generality of the methods a vast area of knowledge is to benefit from the results of this grant.