Computing Nash equilibria

A Nash equilibrium is a two-player strategic game – similar to the one we saw in the Analyzing simple two-player games recipe – that represents a steady state in which every player sees the best possible outcome. However, this doesn’t mean that the outcome linked to a Nash equilibrium is the best overall. Nash equilibria are more subtle than this. An informal definition of a Nash equilibrium is as follows: an action profile in which no individual player can improve their outcome, assuming that all other players adhere to the profile.

We will explore the notion of a Nash equilibrium with the classic game of rock-paper-scissors. The rules are as follows. Each player can choose one of the options: rock, paper, or scissors. Rock beats scissors, but loses to paper; paper beats rock, but loses to scissors; scissors beats paper, but loses to rock. Any game in which both players make the same choice is a draw. Numerically, we represent a win...