Perfect bayesian equilibrium in Kuhn poker

Abstract

In 1950, Harold W. Kuhn introduced a simplified version of poker referred to as Kuhn Poker and solved it using the notion of Nash Equilibrium. His pioneering work inspired subsequent scholars who applied similar methodologies to other poker versions. In contrast, we adopt a different procedure by employing Harsanyi’s approach to reach a Perfect Bayesian Equilibrium (PBE), a concept that emerged two decades after Kuhn’s original solutions. While computational techniques have greatly advanced the analysis of various poker variations, achieving a PBE remains elusive. Some studies suffer from methodological flaws, as they overlook the importance of incorporating beliefs into their analysis. In our research, we also conducted a rationality study and found that relaxing the sophistication of a player leads to a shift in optimal strategies towards more exploitative ones.