Gradient dynamics in population games: Some basic results
When each player in a population game continuously adjusts her action to move up the payoff gradient, then the state variable (the action distribution) obeys a nonlinear partial differential equation. We find conditions that render gradient adjustment myopically optimal and analyze two broad classes of population games. For one class, we use known results to establish the existence and uniqueness of solutions to the PDE. In some cases, these solutions exhibit shock waves or rarefaction waves. For a second class, we use a local form of Nash equilibrium to characterize the steady state solutions of the PDE and find sufficient conditions for asymptotic convergence.
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- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
- Akihiko Matsui & Kiminori Matsuyama, 1991.
"An Approach to Equilibrium Selection,"
1065, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
- Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2005.
"Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case,"
Sonderforschungsbereich 504 Publications
05-41, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
- Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009. "Brown-von Neumann-Nash dynamics: The continuous strategy case," Games and Economic Behavior, Elsevier, vol. 65(2), pages 406-429, March.
- Josef Hofbauer & Jörg Oechssler & Frank Riedel, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Bonn Econ Discussion Papers bgse38_2005, University of Bonn, Germany.
- Josef Hofbauer & Jörg Oechssler, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Working Papers 0424, University of Heidelberg, Department of Economics, revised Dec 2005.
- Josef Hofbauer & Joerg Oechssler & Frank Riedel, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Game Theory and Information 0512003, EconWPA.
- Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2005. "Brown-von Neumann-Nash dynamics : the continuous strategy case," Papers 05-41, Sonderforschungsbreich 504.
- Hart, Sergiu & Mas-Colell, Andreu, 2003.
"Regret-based continuous-time dynamics,"
Games and Economic Behavior,
Elsevier, vol. 45(2), pages 375-394, November.
- Jörg Oechssler & Frank Riedel, 2000.
"On the Dynamic Foundation of Evolutionary Stability in Continuous Models,"
Bonn Econ Discussion Papers
bgse7_2000, University of Bonn, Germany.
- Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December.
- Joerg Oechssler & Frank Riedel, 2000. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Game Theory and Information 0004004, EconWPA.
- Oechssler, Jörg & Riedel, Frank, 2000. "On the dynamic foundation of evolutionary stability in continuous models," SFB 373 Discussion Papers 2000,73, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Vives, X., 1988.
"Nash Equilibrium With Strategic Complementarities,"
UFAE and IAE Working Papers
107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2004. "Noisy Directional Learning and the Logit Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 581-602, October.
- Friedman, Daniel & Ostrov, Daniel N., 2008. "Conspicuous consumption dynamics," Games and Economic Behavior, Elsevier, vol. 64(1), pages 121-145, September.
- Sonnenschein, Hugo, 1982. "Price Dynamics Based on the Adjustment of Firms," American Economic Review, American Economic Association, vol. 72(5), pages 1088-96, December.
- Veblen, Thorstein, 1899. "The Theory of the Leisure Class," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number veblen1899.
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