Generalized risk-dominance and asymmetric dynamics
This paper proposes two (ordinal and cardinal) generalizations of [J.C. Harsanyi, R. Selten, A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge, MA and London, 1988] risk-dominance to multi-player, multi-action games. There are three reasons why generalized risk-dominance (GR-dominance) is interesting. Extending the logic of risk-dominance, GR-dominant actions can be interpreted as best responses to conjectures that satisfy a certain type of symmetry. Second, in a local interaction game of [G. Ellison, Learning, local interaction, and coordination, Econometrica 61 (5) (1993) 1047], if an action is risk-dominant in individual binary interactions with neighbors, it is also GR-dominant in the large game on a network. Finally, we show that GR-dominant actions are stochastically stable under a class of evolutionary dynamics. The last observation is a corollary to new abstract selection results that applies to a wide class of so-called asymmetric dynamics. In particular, I show that a (strictly) ordinal GR-dominant profile is (uniquely) stochastically stable under the approximate best-response dynamics of [M. Kandori, G.J. Mailath, R. Rob, Learning, mutation, and long run equilibria in games, Econometrica 61 (1) (1993) 29]. A (strictly) cardinal GR-dominant equilibrium is (uniquely) stochastically stable under a class of payoff-based dynamics that includes [L.E. Blume, The statistical-mechanics of strategic interaction, Games Econ. Behav. 5 (3) (1993) 387-424]. Among others, this leads to a generalization of a result from [G. Ellison, Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution, Rev. Econ. Stud. 67 (230) (2000) 17] on the -dominant evolutionary selection to all networks and the unique selection to all networks that satisfy a simple, sufficient condition.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
- Noldeke Georg & Samuelson Larry, 1993.
"An Evolutionary Analysis of Backward and Forward Induction,"
Games and Economic Behavior,
Elsevier, vol. 5(3), pages 425-454, July.
- Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
- G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
- P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
- Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993.
"Learning, Mutation, and Long Run Equilibria in Games,"
Econometric Society, vol. 61(1), pages 29-56, January.
- M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
- Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
- John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
- Atsushi Kajii & Stephen Morris, 1997.
"The Robustness of Equilibria to Incomplete Information,"
Econometric Society, vol. 65(6), pages 1283-1310, November.
- Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
- Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
- Lee In Ho & Szeidl Adam & Valentinyi Akos, 2003.
"Contagion and State Dependent Mutations,"
The B.E. Journal of Theoretical Economics,
De Gruyter, vol. 3(1), pages 1-29, February.
- Adam Szeidl & In Ho Lee & Akos Valentinyi, 2001. "Contagion and State Dependent Mutations," IEHAS Discussion Papers 0104, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
- Lee, In Ho & Szeidl, Adam & Valentinyi, Akos, 2000. "Contagion and state dependent mutations," Discussion Paper Series In Economics And Econometrics 0027, Economics Division, School of Social Sciences, University of Southampton.
- Ellison, Glenn, 1993.
"Learning, Local Interaction, and Coordination,"
Econometric Society, vol. 61(5), pages 1047-71, September.
- Andreas Blume & Ted Temzelides, 2003.
"On the geography of conventions,"
Springer, vol. 22(4), pages 863-873, November.
- Ted Temzelides, 2000. "On the Geography of Conventions," Econometric Society World Congress 2000 Contributed Papers 0117, Econometric Society.
- Hans Carlsson & Eric van Damme, 1993.
"Global Games and Equilibrium Selection,"
Levine's Working Paper Archive
122247000000001088, David K. Levine.
- Carlsson, H. & Van Damme, E., 1990. "Global Games And Equilibrium Selection," Papers 9052, Tilburg - Center for Economic Research.
- Carlsson, H. & van Damme, E.E.C., 1990. "Global games and equilibrium selection," Discussion Paper 1990-52, Tilburg University, Center for Economic Research.
- Carlsson, H. & van Damme, E.E.C., 1993. "Global games and equilibrium selection," Other publications TiSEM 49a54f00-dcec-4fc1-9488-4, Tilburg University, School of Economics and Management.
- Jackson, Matthew O. & Watts, Alison, 2002.
"On the formation of interaction networks in social coordination games,"
Games and Economic Behavior,
Elsevier, vol. 41(2), pages 265-291, November.
- Matthew O. Jackson & Alison Watts, 2000. "On the Formation of Interaction Networks in Social Coordination Games," Econometric Society World Congress 2000 Contributed Papers 0778, Econometric Society.
When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:216-248. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.