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Stable games and their dynamics

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  • Hofbauer, Josef
  • Sandholm, William H.

Abstract

We 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 Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 4 (July)
Pages: 1665-1693.e4

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:4:p:1665-1693.e4

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Population games Evolutionarily stable strategies Evolutionary dynamics Global stability Lyapunov functions;

References

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  1. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July.
  2. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
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  13. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
  14. William H. Sandholm, 2005. "Negative Externalities and Evolutionary Implementation," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 885-915.
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  19. D. Foster & R. Vohra, 2010. "Regret in the On-line Decision Problem," Levine's Working Paper Archive 569, David K. Levine.
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Citations

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Cited by:
  1. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
  2. 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.
  3. 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.
  4. 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.
  5. William Sandholm, 2014. "Probabilistic Interpretations of Integrability for Game Dynamics," Dynamic Games and Applications, Springer, vol. 4(1), pages 95-106, March.
  6. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.
  7. TABUCHI, Takatoshi & THISSE, Jacques-François, . "A new economic geography model of central places," CORE Discussion Papers RP -2267, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Viossat, Yannick & Zapechelnyuk, Andriy, 2013. "No-regret dynamics and fictitious play," Journal of Economic Theory, Elsevier, vol. 148(2), pages 825-842.
  9. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
  10. 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.
  11. 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.
  12. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Computational Statistics, Springer, vol. 74(2), pages 147-161, October.
  13. Lahkar, Ratul & Seymour, Robert M., 2013. "Reinforcement learning in population games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 10-38.
  14. 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.
  15. Reinoud Joosten & Berend Roorda, 2011. "Attractive evolutionary equilibria," Papers on Economics and Evolution 2011-17, Philipps University Marburg, Department of Geography.
  16. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
  17. repec:hal:wpaper:hal-00713871 is not listed on IDEAS

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