Nash equilibrium set function in dyadic mixed-strategy games

摘要

Dyadic two-person mixed strategy games form the case for which Nash equilibrium sets can be determined simply. In this paper the set of Nash equilibria in a particular game is determined as an intersection of graphs of optimal reaction mappings of the first and the second players. In contrast to other games, it is obtained not only an algorithm, but a multi-valued Nash equilibrium set function that gives directly as its values the Nash equilibrium sets corresponding to the values of payoff matrix instances. To give an expedient form to such a function definition, it is used a code written in the Wolfram language. Additionally, it is also applied a Wolfram language code to prove the main theoretic result.