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has been cited by the following article:

• TITLE: A Regret-Based Algorithm for Computing All Pure Nash Equilibria for Noncooperative Games in Normal Form

  AUTHORS: H. W. Corley

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

  JOURNAL NAME: Theoretical Economics Letters, Vol.10 No.6, December 11, 2020

  ABSTRACT: 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.