Coordination in a skeptical two-group population

  • Juan Carlos González-Avella
  • Haydée LugoEmail author
  • Maxi San Miguel
Regular Article


This paper explores a situation in which a population split into two groups attempts to achieve the socially efficient outcome of a coordination game between the groups. But, in addition to the coordination game, a second kind of interaction takes place inside each group trying to fulfill internal social aims such as acceptance or approval. To achieve these strategic and social concerns, a learning process comes about inside each group. The accomplishment of the social concerns depends only upon the popularity of the strategies inside each social group. We refer here to skeptical individuals as those that do not feel so much coerced by social influence in relation to social objectives. Our study reveals that a skeptical population can achieve coordination between the two groups, but it can also evolve to other final states, namely, anticoordination, dynamical coexistence of strategies and payoff inferior equilibrium. We analyse the causes that give rise to these final states in the whole range of initial distributions of strategies. Our analysis discloses a highly nontrivial behaviour observed in many real-life situations: We find that for high levels of skepticism a society can coordinate in the socially efficient coordination outcome, which can not be obtained for lower levels of skepticism. We also describe how such coordination is possible in a risky environment. We provide numerical simulations that describe the complexity of the different scenarios.


Coordination games Social and strategic interactions Skeptical populations 



We thank the editor and the anonymous referees for their careful reviews on an earlier version of this paper. Haydée Lugo acknowledges financial support from Ministerio de Economía y Competitividad (Spain) under Project No. ECO2016-75992-P. Maxi San Miguel acknowledges financial support from Agencia Estatal de Investigación (AEI, Spain) and Fondo Europeo de Desarrollo Regional under project ESOTECOS FIS2015-63628-C2-2-R (MINECO/AEI/FEDER,UE).


  1. Alm J, McKee M (2004) Tax compliance as a coordination game. J Econ Behav Organ 54(3):297–312CrossRefGoogle Scholar
  2. Anderson L, Holt C (1997) Information cascades in the laboratory. Am Econ Rev 87(5):847–862Google Scholar
  3. Battalio R, Samuelson L, Van Huyck J (2001) Optimization incentives and coordination failure in laboratory stag hunt games. Econometrica 69:749–764CrossRefGoogle Scholar
  4. Bikhchandani S, Hirshleifer D, Welch I (1998) Learning from the behavior of others: conformity, fads, and informational cascades. J Econ Perspect 12(3):151–170CrossRefGoogle Scholar
  5. Blume L, Durlauf S (2003) Equilibrium concepts for social interaction models. Int Game Theory Rev 5:193–209CrossRefGoogle Scholar
  6. Charbit C (2011) Governance of public policies in decentralised contexts: the multi-level approach. OECD regional development working papers, 2011/04, OECD Publishing
  7. Chisholm D (1992) Coordination without hierarchy: informal structures in multiorganizational systems. University of California Press, BerkeleyGoogle Scholar
  8. Clark K, Kay S, Sefton M (2001) When are nash equilibria self enforcing? An experimental analysis. Int J Game Theory 29:495–515CrossRefGoogle Scholar
  9. Conradt L, Roper TJ (2005) Consensus decision making in animals. Trends Ecol Evol 20:449–456CrossRefGoogle Scholar
  10. Crawford VP, Gneezy U, Rottenstreich Y (2008) The power of focal points is limited: even minute payoff asymmetry may yield large coordination failures. Am Econ Rev 98(4):1443–58CrossRefGoogle Scholar
  11. Friedman D (1996) Equilibrium in evolutionary games: some experimental results. Econ J 106:1–15CrossRefGoogle Scholar
  12. Granovetter M (1978) Threshold models of collective behaviour the American. J Sociol 83:1420–1443Google Scholar
  13. Harsanyi JC, Selten R (1988) A general theory of equilibrium selection in games, vol 1. MIT Press Books, CambridgeGoogle Scholar
  14. Lugo H, San Miguel M (2015) Learning and coordinating in a multilayer network. Sci Rep 5:7776CrossRefGoogle Scholar
  15. Maynard Smith J (1982) Evolution and the theory of games. Cambridge University Press, CambridgeGoogle Scholar
  16. Straub Paul G (1995) Risk dominance and coordination failures in static games. Q Rev Econ Financ 35(4):339–363CrossRefGoogle Scholar
  17. Weidenholzer S (2010) Coordination games and local interactions: a survey of the game theoretic literature. Games 1(4):551–585CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Edifici Europa - Planta baja Galileo Galilei, Parc BitMallorcaSpain
  2. 2.ICAE and Department of Economic AnalysisUniversidad Complutense de MadridMadridSpain
  3. 3.IFISC (CSIC-UIB)Campus Universitat de les Illes BalearsPalma de MallorcaSpain

Personalised recommendations