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Contagion and uninvadability in local interaction games: The bilingual game and general supermodular games

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  • Oyama, Daisuke
  • Takahashi, Satoru

Abstract

In a setting where an infinite population of players interact locally and repeatedly, we study the impacts of payoff structures and network structures on contagion of a convention beyond 2×2 coordination games. First, we consider the “bilingual game”, where each player chooses one of two conventions or adopts both (i.e., chooses the “bilingual option”) at an additional cost. For this game, we completely characterize when a convention spreads contagiously from a finite subset of players to the entire population in some network, and conversely, when a convention is never invaded by the other convention in any network. We show that the Pareto-dominant (risk-dominant, resp.) convention is contagious if the cost of bilingual option is low (high, resp.). Furthermore, if the cost is in a medium range, both conventions are each contagious in respective networks, and in particular, the Pareto-dominant convention is contagious only in some non-linear networks. Second, we consider general supermodular games, and compare networks in terms of their power of inducing contagion. We show that if there is a weight-preserving node identification from one network to another, then the latter is more contagion-inducing than the former in all supermodular games.

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  • 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.
  • Handle: RePEc:eee:jetheo:v:157:y:2015:i:c:p:100-127
    DOI: 10.1016/j.jet.2014.12.012
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    Cited by:

    1. Arigapudi, Srinivas, 2020. "Transitions between equilibria in bilingual games under logit choice," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 24-34.
    2. Oyama, Daisuke & Takahashi, Satoru, 2011. "On the relationship between robustness to incomplete information and noise-independent selection in global games," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 683-688.
    3. John Higgins & Tarun Sabarwal, 2021. "Control and Spread of Contagion in Networks," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202111, University of Kansas, Department of Economics.
    4. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    5. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    6. Chellig, Jordan & Durbac, Calina & Fountoulakis, Nikolaos, 2022. "Best response dynamics on random graphs," Games and Economic Behavior, Elsevier, vol. 131(C), pages 141-170.
    7. John Higgins & Tarun Sabarwal, 2022. "Control and spread of contagion in networks with global effects," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202213, University of Kansas, Department of Economics, revised Aug 2022.
    8. Daisuke Oyama & Satoru Takahashi, 2020. "Generalized Belief Operator and Robustness in Binary‐Action Supermodular Games," Econometrica, Econometric Society, vol. 88(2), pages 693-726, March.
    9. Daniel C. Opolot & Théophile T. Azomahou, 2021. "Strategic diffusion in networks through contagion," Journal of Evolutionary Economics, Springer, vol. 31(3), pages 995-1027, July.
    10. Daniel Christopher Opolot, 2022. "On the relationship between p-dominance and stochastic stability in network games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 307-351, June.
    11. Teruyoshi Kobayashi & Yoshitaka Ogisu & Tomokatsu Onaga, 2021. "Unstable diffusion in social networks," Papers 2109.14560, arXiv.org.
    12. Ryoji Sawa, 2022. "Statistical Inference in Evolutionary Dynamics," Working Papers e170, Tokyo Center for Economic Research.

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    More about this item

    Keywords

    Equilibrium selection; Strategic complementarity; Bilingual game; Network; Contagion; Uninvadability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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