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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 gutspoker and $1$ v. $n$ coalitions. Our main results are to develop practicalnumerical algorithms with rigorous underlying theory for the approximation ofoptimal mutiplayer strategies, and to use these to obtain a number ofinteresting observations about guts. Outcomes are a striking 2-strategy optimumfor $n$-player coalitions, with asymptotic advantage approximately $16\%$;convergence of Fictitious Play to symmetric Nash equilibrium; and a malevolentinteractive $n$-player "bot" for demonstration.

Continuous guts poker and numerical optimization of generalized recursive games