A Study of Nash Equilibrium in Discrete Cases

Authors

Hallye Leleux, Louisiana Tech UniversityFollow

Document Type

Article

Publication Date

Spring 2022

Abstract

In game theory, Nash Equilibrium refers to a set of strategies in a non-cooperative game such that no player can benefit from changing their strategy. This paper examines the payoff matrices of the notable discrete games Battle of the Sexes, Matching Pennies, and The Prisoner’s Dilemma. We then create a custom discrete two player case and determine the pure and mixed strategy Nash Equilibria. After calculating the probabilities for each mixed strategy, we then determine the resulting payoff for each player and show how deviating from that strategy results in a lower payoff.

Recommended Citation

Leleux, Hallye, "A Study of Nash Equilibrium in Discrete Cases" (2022). Mathematics Senior Capstone Papers. 29.
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/29