Fictitious play in an evolutionary environment
We consider continuous time versions of the fictitious play updating algorithm in an evolutionary environment. We derive two forms of continuous-time limit, both defining approximations to this algorithm. The first has the form of a first-order partial differential equation, which we solve explicitly. The dynamic for a distribution of strategies is also derived, which we show can be written in a form similar to a positive definite dynamic. The asymptotic solution (in the ultra long run) is discussed for 2-player, 2-strategy co-ordination and anti-coordination games, and we show convergence to Nash equilibrium in both cases. The second, and better, approximation is in the form of a diffusion equation. This is considerably more difficult to analyze. However, we derive a formal solution and show that it leads to the same asymptotic limit for the distribution of strategies as the 1st-order approximation for 2-player, 2-strategy anti-coordination games.
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- Fudenberg Drew & Kreps David M., 1993.
"Learning Mixed Equilibria,"
Games and Economic Behavior,
Elsevier, vol. 5(3), pages 320-367, July.
- Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
- Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
- Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
- Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
- Ed Hopkins, "undated". "Learning, Matching and Aggregation," Department of Economics 1996 : II, Edinburgh School of Economics, University of Edinburgh.
- Hopkins, E., 1995. "Learning, Matching and Aggregation," G.R.E.Q.A.M. 95a20, Universite Aix-Marseille III.
- Ed Hopkins, 1995. "Learning, Matching and Aggregation," ESE Discussion Papers 2, Edinburgh School of Economics, University of Edinburgh.
- Ed Hopkins, 1995. "Learning, Matching and Aggregation," Game Theory and Information 9512001, EconWPA.
- Ed Hopkins, "undated". "Learning, Matching and Aggregation," Discussion Papers 1996-2, Edinburgh School of Economics, University of Edinburgh.
- Ed Hopkins, "undated". "Learning, Matching and Aggregation," ELSE working papers 033, ESRC Centre on Economics Learning and Social Evolution.
- Canning, David, 1992. "Average behavior in learning models," Journal of Economic Theory, Elsevier, vol. 57(2), pages 442-472, August.
- Canning, D., 1990. "Average Behaviour In Learning Models," Papers 156, Cambridge - Risk, Information & Quantity Signals.
- D. Canning, 2010. "Average Behavior in Learning Models," Levine's Working Paper Archive 490, David K. Levine.
- Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
- Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
- Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, July.
- Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
- Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
- Hahn, Sunku, 1999. "The convergence of fictitious play in 3 x 3 games with strategic complementarities," Economics Letters, Elsevier, vol. 64(1), pages 57-60, July.
- Berger, Ulrich, 2007. "Two more classes of games with the continuous-time fictitious play property," Games and Economic Behavior, Elsevier, vol. 60(2), pages 247-261, August.
- Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January. Full references (including those not matched with items on IDEAS)
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