Continuous guts poker and numerical optimization of generalized recursive games

TL;DR

This paper develops numerical algorithms to approximate optimal strategies in continuous guts poker and recursive games, revealing a 2-strategy equilibrium with a significant advantage and demonstrating convergence to Nash equilibrium.

Contribution

It introduces practical algorithms with rigorous theory for multiplayer strategy optimization in generalized recursive games, focusing on continuous guts poker.

Findings

A 2-strategy equilibrium with ~16% advantage for n-player coalitions.

Convergence of Fictitious Play to symmetric Nash equilibrium.

Demonstration of a malevolent interactive n-player bot.

Abstract

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.