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Equilibrium

In: The Theory of Extensive Form Games

Author

Listed:
  • Carlos Alós-Ferrer

    (University of Cologne)

  • Klaus Ritzberger

    (Institute for Advanced Studies)

Abstract

This chapter takes advantage of the findings in previous chapters and tackles a first problem in solution theory: Given a discrete game tree, what are the properties of a topology on the set of plays which guarantee that every perfect information game defined on this tree has a subgame perfect equilibrium, as long as the players’ preferences are continuous and decision points are suitably assigned? The main result of this chapter is a characterization: In such a (compact and perfectly normal) topology all nodes must be closed and the immediate predecessor function must map open sets to open sets. The necessity part of this characterization holds without compactness, the sufficiency part with a weaker separation axiom. Hence, ultimately the approach of this manuscript leads to the most general existence theorem for perfect information games.

Suggested Citation

  • Carlos Alós-Ferrer & Klaus Ritzberger, 2016. "Equilibrium," Springer Series in Game Theory, in: The Theory of Extensive Form Games, chapter 7, pages 163-222, Springer.
    • Handle: RePEc:spr:spschp:978-3-662-49944-3_7
    DOI: 10.1007/978-3-662-49944-3_7
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