Acyclicity of Preferences, Nash Equilibria, and Subgame Perfect Equilibria: a Formal and Constructive Equivalence

Abstract. Sequential game and Nash equilibrium are basic key concepts in game theory. In 1953, Kuhn showed that every sequential game has a Nash equilibrium. The two main steps of the proof are as follows: First, a procedure expecting a sequential game as an input is defined as “backward induction” in game theory. Second, it is proved that the procedure yields a Nash equilibrium. “Backward induction” actually yields Nash equilibria that define a proper subclass of Nash equilibria. In 1965, Selten named this proper subclass subgame perfect equilibria. In game theory, payoffs are rewards usually granted at the end of a game. Although traditional game theory mainly focuses on real-valued payoffs that are implicitly ordered by the usual total order over the reals, there is a demand for results dealing with non totally ordered payoffs. In the mid 1950’s, works of Simon or Blackwell already involved partially ordered payoffs. This paper further explores the matter: it general...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Stéphane Le Roux
• Keywords: CORR 2007, Education, Game Theory, Nash Equilibrium, Sequential Game