Abstract:  Static potential games, pioneered by Monderer and Shapley (1996) are non-cooperative games in which there exists an auxiliary function called static potential function, so that any player's change in utility function upon unilaterally deviating from her policy can be evaluated through the change in the value of this potential function. The introduction of the potential function is powerful as it simplifies the otherwise challenging task of searching for Nash equilibria in multi-agent non-cooperative games:  maximizers of potential functions lead to the game's Nash equilibria.

In this talk, we propose an analogous and new framework called $\alpha$-potential game for dynamic $N$-player games, with the potential function in the static setting replaced by an $\alpha$-potential function. We will present the analytical criteria for any game to be an $\alpha$-potential game, and identify several important classes of Markov $\alpha$-potential games. 
We will provide detailed analysis for games with mean-field interactions, distributed games, and the crowd aversion games, in which $\alpha$ is shown to depend on the number of players, the admissible policies, and the cost structure. We will also show the changes of $\alpha$ from open-loop to closed-loop settings. 

Bio：Dr. Xin Guo is the Coleman Fung Chair Professor in Financial Modeling at the University of California, Berkeley and an Amazon scholar.

Dr. Xin Guo's research lies broadly in the span of stochastic controls and games, machine learning, mathematical finance, and FinTech. She has co-authored more than 70 research publications and a book in Quantitative Trading which has been translated into Chinese and Japanese. 

Dr. Xin Guo is co-editor-in-chief of Frontier in Mathematical Finance, and has served as associate editors of many leading journals including Mathematical Finance and Operations Research. Her work using machine learning method for medical data analysis has lead to the FDA approved early cancer diagnosis methodology; her forecasting models implemented in Amazon has been adopted by Amazon finance planning and has led to over a hundred millions of dollars cost savings. 

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腾讯会议ID：249-424-961