Author(s)

H. W. Corley

Center on Stochastic Modeling, Optimization, & Statistics (COSMOS), University of Texas at Arlington, Arlington, USA.

The concept of a pure Nash equilibrium (NE) for a noncooperative game is simpler than that of a mixed NE, which always exists. However, pure NEs probably have more practical significance even though such a game may not have a pure NE. An efficient algorithm is presented here to determine whether an n-person game in normal form has a pure NE and, if so, to obtain all NEs. This algorithm uses the notion of regret, and the payoff matrix (PM) is transformed into a regret matrix (RM)—a loss matrix with an intuitive interpretation. The RM has the property that an action profile of the PM is a pure NE if and only if (0,· · ·,0) is the corresponding element of the RM. The computational complexity of the algorithm is O(N) in the number of individual utilities N in the PM, and so it is substantially faster than a total enumeration.

Pure Nash Equilibria, Algorithm for Pure Nash Equilibria, Regret Matrix, Pareto Nash Equilibrium

Corley, H. (2020) A Regret-Based Algorithm for Computing All Pure Nash Equilibria for Noncooperative Games in Normal Form. Theoretical Economics Letters, 10, 1253-1259. doi: 10.4236/tel.2020.106076.