Stable games and their dynamics
AbstractWe study a class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs of strategies to which revising agents are switching are always exceeded by the improvements in the payoffs of strategies which revising agents are abandoning. We prove that the set of Nash equilibria of a stable game is globally asymptotically stable under a wide range of evolutionary dynamics. Convergence results for stable games are not as general as those for potential games: in addition to monotonicity of the dynamics, integrability of the agents' revision protocols plays a key role.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Theory.
Volume (Year): 144 (2009)
Issue (Month): 4 (July)
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Web page: http://www.elsevier.com/locate/inca/622869
Population games Evolutionarily stable strategies Evolutionary dynamics Global stability Lyapunov functions;
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- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
- J. Swinkels, 2010.
"Adjustment Dynamics and Rational Play in Games,"
Levine's Working Paper Archive
456, David K. Levine.
- I. Gilboa & A. Matsui, 2010.
"Social Stability and Equilibrium,"
Levine's Working Paper Archive
534, David K. Levine.
- P. Taylor & L. Jonker, 2010. "Evolutionarily Stable Strategies and Game Dynamics," Levine's Working Paper Archive 457, David K. Levine.
- Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
- Benaim, Michel & Weibull, Jörgen W., 2000.
"Deterministic Approximation of Stochastic Evolution in Games,"
Working Paper Series
534, Research Institute of Industrial Economics, revised 30 Oct 2001.
- Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
- Sergiu Hart & Andreu Mas-Colell, 1999.
"A General Class of Adaptive Strategies,"
Game Theory and Information
9904001, EconWPA, revised 23 Mar 2000.
- Sandholm, William H., 2009. "Large population potential games," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1710-1725, July.
- Reinoud Joosten, 1996. "Deterministic evolutionary dynamics: a unifying approach," Journal of Evolutionary Economics, Springer, vol. 6(3), pages 313-324.
- Hofbauer, Josef & Sandholm, William H., 2007.
"Evolution in games with randomly disturbed payoffs,"
Journal of Economic Theory,
Elsevier, vol. 132(1), pages 47-69, January.
- Hofbauer,J. & Sandholm,W.H., 2003. "Evolution in games with randomly disturbed payoffs," Working papers 20, Wisconsin Madison - Social Systems.
- Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 565-590, November.
- D. Blackwell, 2010. "Controlled Random Walks," Levine's Working Paper Archive 465, David K. Levine.
- Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
- Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
- Gaunersdorfer Andrea & Hofbauer Josef, 1995.
"Fictitious Play, Shapley Polygons, and the Replicator Equation,"
Games and Economic Behavior,
Elsevier, vol. 11(2), pages 279-303, November.
- A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
- Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
- Fudenberg, Drew & Levine, David K., 1995.
"Consistency and cautious fictitious play,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 19(5-7), pages 1065-1089.
- Sandholm, William H., 2003. "Evolution and equilibrium under inexact information," Games and Economic Behavior, Elsevier, vol. 44(2), pages 343-378, August.
- Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
- Drew Fudenberg & David K. Levine, 1998.
"The Theory of Learning in Games,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262061945, January.
- Sandholm, William H. & DokumacI, Emin & Lahkar, Ratul, 2008. "The projection dynamic and the replicator dynamic," Games and Economic Behavior, Elsevier, vol. 64(2), pages 666-683, November.
- D. Foster & R. Vohra, 2010. "Regret in the On-line Decision Problem," Levine's Working Paper Archive 569, David K. Levine.
- Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
- Sung-Ha Hwang & Luc Rey-Bellet, 2011. "Decompositions of two player games: potential, zero-sum, and stable games," Working Papers 1116, Research Institute for Market Economy, Sogang University.
- Tabuchi, Takatoshi & Thisse, Jacques-François, 2011.
"A new economic geography model of central places,"
Journal of Urban Economics,
Elsevier, vol. 69(2), pages 240-252, March.
- Viossat, Yannick & Zapechelnyuk, Andriy, 2013.
"No-regret dynamics and fictitious play,"
Journal of Economic Theory,
Elsevier, vol. 148(2), pages 825-842.
- James D. Montgomery, 2010. "Intergenerational Cultural Transmission as an Evolutionary Game," American Economic Journal: Microeconomics, American Economic Association, vol. 2(4), pages 115-36, November.
- Yannick Viossat & Andriy Zapechelnyuk, 2012. "No-regret Dynamics and Fictitious Play," Working Papers hal-00713871, HAL.
- Michael J. Fox & Jeff S. Shamma, 2013. "Population Games, Stable Games, and Passivity," Games, MDPI, Open Access Journal, vol. 4(4), pages 561-583, October.
- Oyama, Daisuke, 2009.
"Agglomeration under forward-looking expectations: Potentials and global stability,"
Regional Science and Urban Economics,
Elsevier, vol. 39(6), pages 696-713, November.
- Oyama, Daisuke, 2006. "Agglomeration under Forward-Looking Expectations: Potentials and Global Stability," MPRA Paper 15239, University Library of Munich, Germany.
- Pietro Dindo & Jan Tuinstra, 2010.
"A class of evolutionary models for participation games with negative feedback,"
LEM Papers Series
2010/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
- Pietro Dindo & Jan Tuinstra, 2011. "A Class of Evolutionary Models for Participation Games with Negative Feedback," Computational Economics, Society for Computational Economics, vol. 37(3), pages 267-300, March.
- Lahkar, Ratul & Seymour, Robert M., 2013. "Reinforcement learning in population games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 10-38.
- Reinoud Joosten & Berend Roorda, 2011. "Attractive evolutionary equilibria," Papers on Economics and Evolution 2011-17, Max Planck Institute of Economics, Evolutionary Economics Group.
- Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.
- Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Max Planck Institute of Economics, Evolutionary Economics Group.
- Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.
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