Bertrand's analysis of baccarat

TL;DR

This paper investigates Bertrand's 1888 analysis of baccarat, revealing it was likely borrowed from Badoureau's 1881 work, and discusses Borel's criticisms that contributed to the oversight of Badoureau's contribution.

Contribution

It uncovers the true origin of Bertrand's baccarat analysis and explains why Badoureau's earlier work was historically overlooked.

Findings

Bertrand's baccarat analysis was likely borrowed from Badoureau's 1881 paper.

Borel criticized Bertrand's analysis, which contributed to the oversight of Badoureau's work.

The paper clarifies the historical attribution of early game theory contributions.

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.