Bertrand's analysis of baccarat

Abstract

Joseph Bertrand [1822--1900], who is often credited with a model of duopoly that has a unique Nash equilibrium, made another significant contribution to game theory. Specifically, his 1888 analysis of baccarat was the starting point for Borel's investigation of strategic games in the 1920s. In this paper we show, with near certainty, that Bertrand's results on baccarat were borrowed, without attribution, from an 1881 paper of Albert Badoureau [1853--1923]. In addition, we discuss Borel's criticisms of Bertrand's analysis, one of which helps to explain why Badoureau's contribution was overlooked until now.