Continuous guts poker and numerical optimization of generalized recursive games

08/04/2022

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by   Kevin Buck, et al.

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We study a type of generalized recursive game introduced by Castronova, Chen, and Zumbrun featuring increasing stakes, with an emphasis on continuous guts poker and 1 v. n coalitions. Our main results are to develop practical numerical algorithms with rigorous underlying theory for the approximation of optimal mutiplayer strategies, and to use these to obtain a number of interesting observations about guts. Outcomes are a striking 2-strategy optimum for n-player coalitions, with asymptotic advantage approximately 16%; convergence of Fictitious Play to symmetric Nash equilibrium; and a malevolent interactive n-player "bot" for demonstration.