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Brown's Original Fictitious Play

By Ulrich Berger

Abstract

What modern game theorists describe as 'fictitious play' is not the learning process George W. Brown defined in his 1951 paper. His original version differs in a subtle detail, namely the order of belief updating. In this note we revive Brown's original fictitious play process and demonstrate that this seemingly innocent detail allows for an extremely simple and intuitive proof of convergence in an interesting and large class of games: nondegenerate ordinal potential games.Fictitious Play, Learning Process, Ordinal Potential Games

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Citations

  1. (1996). A 2£2 game without the ¯ctitious play property.
  2. (1973). A class of games possessing pure-strategy Nash equilibria.
  3. (1998). A learning approach to auctions.
  4. (1991). Adaptive and sophisticated learning in normal form games.
  5. (1951). An iterative method of solving a game.
  6. (1997). and SjÄ ostrÄ om, T.
  7. (1992). Dynamical systems arising from game theory. Dissertation,
  8. (2003). Evolutionary game dynamics.
  9. (1997). Fictitious play and no-cycling conditions. Mimeo, The Technion.
  10. (2000). Fictitious play in 2£3 games.
  11. (2005). Fictitious play in 2£n games.
  12. (1996). Fictitious play property for games with identical interests.
  13. (1995). Fictitious play, Shapley polygons, and the replicator equation.
  14. (1957). Games and decisions.
  15. (1951). Iterative solution of games by Fictitious Play. In \Activity Analysis of Production and Allocation"
  16. (1992). Learning in games with strategic complementarities. Mimeo,
  17. (1959). Mathematical methods and theory in games, programming, and economics.
  18. (1998). On the convergence of ¯ctitious play.
  19. (1961). On the convergence of the learning process in a 2£2 non-zero-sum two-person game. Econometric Research Program,
  20. (1998). On the nonconvergence of Fictitious Play in coordination games.
  21. (1996). Potential games.
  22. (1949). Some notes on computation of games solutions.
  23. (1964). Some topics in two-person games.
  24. (1995). Stability for the best response dynamics.
  25. (1999). The convergence of Fictitious Play in 3£3 games with strategic complementarities.
  26. (1988). The theory of evolution and dynamical systems.
  27. (1998). The theory of learning in games.
  28. (1993). Three problems in learning mixed-strategy Nash equilibria.
  29. (2004). Two more classes of games with the ¯ctitious play property.

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