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Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction, and Random Matching

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  • Stephen Morris

Abstract

Incomplete information, local interaction, and random matching games all share a common structure. A type or player interacts with various subsets of the set of all types/players. A type/player's total payoff is additive in the payoffs from these various interactions. This paper describes a general class of interaction games and shows how each of these three classes of games can be understood as special cases. Techniques and results from the incomplete information literature are translated into this more general framework; as a by-product, it is possible to give a complete characterization of equilibria robust to incomplete information (in the sense of Kajii and Morris [1995]) in many player binary action coordination games. Only equilibria that are robust in this sense [1] can spread contagiously and [2] are uninvadable under best response dynamics in a local interaction system. A companion paper, Morris [1997], uses these techniques to characterize features of local interaction systems that allow contagion.

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  • Stephen Morris, 1997. "Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction, and Random Matching," Research in Economics 97-08-072e, Santa Fe Institute.
    • Handle: RePEc:wop:safire:97-08-072e
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    1. 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, April.
    2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    3. Avner Shaked & Larry Samuelson & George J. Mailath, 1997. "Correlated equilibria and local interactions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 551-556.
    4. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-157, January.
    5. Stephen Morris, "undated". "Co-operation and Timing," Penn CARESS Working Papers b8d506ba7aa15345b602bb4eb, Penn Economics Department.
    6. Sugden, Robert, 1995. "The coexistence of conventions," Journal of Economic Behavior & Organization, Elsevier, vol. 28(2), pages 241-256, October.
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    Cited by:

    1. William H. Sandholm, 1998. "History-Independent Prediction In Evolutionary Game Theory," Rationality and Society, , vol. 10(3), pages 303-326, August.
    2. Antoine Billot, 2009. "How to shake the invisible hand (when Robinson meets Friday)," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(3), pages 257-270, September.
    3. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    4. Andrew Koh & Ricky Li & Kei Uzui, 2024. "Inertial Coordination Games," Papers 2409.08145, arXiv.org.
    5. Ianni, Antonella & Corradi, Valentina, 2000. "Consensus, contagion and clustering in a space-time model of public opinion formation," Discussion Paper Series In Economics And Econometrics 0009, Economics Division, School of Social Sciences, University of Southampton.
    6. Zamagni, Stefano, 2000. "Economic reductionism as a hindrance to the analysis of structural change: scattered notes," Structural Change and Economic Dynamics, Elsevier, vol. 11(1-2), pages 197-208, July.
    7. Corbae, Dean & Duffy, John, 2008. "Experiments with network formation," Games and Economic Behavior, Elsevier, vol. 64(1), pages 81-120, September.
    8. Ulrich Horst & Jos´e A. Scheinkman, 2006. "A Limit Theorem for Systems of Social Interactions," Levine's Bibliography 321307000000000177, UCLA Department of Economics.
    9. Stephen Morris & Hyun Song Shin, 2003. "Heterogeneity and Uniqueness in Interaction Games," Cowles Foundation Discussion Papers 1402, Cowles Foundation for Research in Economics, Yale University.
    10. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    11. Kets, Willemien & Kager, Wouter & Sandroni, Alvaro, 2022. "The value of a coordination game," Journal of Economic Theory, Elsevier, vol. 201(C).
    12. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.
    13. Robin Mason & Akos Valentinyi, 2003. "Independence, Heterogeneity and Uniqueness in Interaction Games," CERS-IE WORKING PAPERS 0303, Institute of Economics, Centre for Economic and Regional Studies.
    14. Oyama, Daisuke & Takahashi, Satoru, 2015. "Contagion and uninvadability in local interaction games: The bilingual game and general supermodular games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 100-127.
    15. Horst, Ulrich & Scheinkman, José A., 2009. "A limit theorem for systems of social interactions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 609-623, September.

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    Local interaction; game theory;

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