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From sets of equilibria to structures of interaction underlying binary games of strategic complements

  • Tomas Rodriguez Barraquer
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    Consider a setting in which agents can each take one of two ordered actions and in which the incentive of any given agent to take the high action is positively reinforced by the number of other agents that take it. Furthermore, assume that we don't know any other details about the game being played. What can we say about the details of the structure of the interaction between actions and incentives when we observe a set or a subset of all possible equilibria? In this paper we study 3 nested classes of games: (a) binary games of strategic complements; (b) games in (a) that admit a network representation: and (c) games in (b) in which the network is complete. Our main results are the following: It has long been established in the literature that the set of pure strategy Nash equilibria of any binary game of strategic complements among a set N of agents can be seen as a lattice on the set of all subsets of N under the partial order defined by the set inclusion relation. If the game happens to be strict in the sense that agents are never indifferent among outcomes (games in (a)), then the resulting lattice of equilibria satisfies a straightforward sparseness condition. (1) We show that, in fact, the games in (a) express all such lattices. (2) We characterize the collection of subsets of N that can be weakly expressed as the set of equilibria of some game of thresholds (games in (b)). (3) We characterize the collection of subsets of N that can be weakly expressed as the set of equilibria of some game of thresholds on the complete graph (games in (c)).

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    Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp655.

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    Length: 25 pages
    Date of creation: Dec 2013
    Date of revision:
    Handle: RePEc:huj:dispap:dp655
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    1. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    2. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344823, HAL.
    3. Antoni Calv�-Armengol & Eleonora Patacchini & Yves Zenou, 2009. "Peer Effects and Social Networks in Education," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1239-1267.
    4. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2010. "Network Games," Review of Economic Studies, Oxford University Press, vol. 77(1), pages 218-244.
    5. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Social Choice and Welfare, Springer, vol. 33(2), pages 177-209, August.
    6. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
    7. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
    8. Echenique, Federico, 2007. "Finding all equilibria in games of strategic complements," Journal of Economic Theory, Elsevier, vol. 135(1), pages 514-532, July.
    9. repec:att:wimass:9127 is not listed on IDEAS
    10. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 181-221, October.
    11. Echenique, Federico & Edlin, Aaron S., 2004. "Mixed equilibria are unstable in games of strategic complements," Berkeley Olin Program in Law & Economics, Working Paper Series qt1ht651hk, Berkeley Olin Program in Law & Economics.
    12. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
    13. repec:hal:journl:halshs-00445126 is not listed on IDEAS
    14. Decker, Christopher S. & Pope, Christopher R., 2005. "Adherence to environmental law: the strategic complementarities of compliance decisions," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 641-661, September.
    15. Antoni Calvó-Armengol & Matthew O. Jackson, 2010. "Peer Pressure," Journal of the European Economic Association, MIT Press, vol. 8(1), pages 62-89, 03.
    16. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, 09.
    17. Noemí Navarro, 2012. "Price and quality decisions under network effects," Cahiers de recherche 12-01, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
    18. Jackson, Matthew O. & Yariv, Leeat, 2006. "Diffusion of Behavior and Equilibrium Properties in Network Games," Working Papers 1264, California Institute of Technology, Division of the Humanities and Social Sciences.
    19. repec:hal:journl:halshs-00583867 is not listed on IDEAS
    20. Manski, Charles F, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 531-42, July.
    21. Lee, Lung-fei, 2007. "Identification and estimation of econometric models with group interactions, contextual factors and fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 333-374, October.
    22. Harrie De Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414, HAL.
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