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The evolution of conventions under condition-dependent mistakes

  • Ennio Bilancini
  • Leonardo BoncinelliEmail author
Research Article

Abstract

We study the long-run conventions emerging in a stag-hunt game when agents are myopic best responders. Our main novel assumption is that errors converge to zero at a rate that is positively related to the payoff earned in the past. To fully explore the implications of this error model, we introduce a further novelty in the way we model the interaction structure, assuming that with positive probability agents remain matched together in the next period. We find that, if interactions are sufficiently persistent over time, then the payoff-dominant convention emerges in the long run, while if interactions are quite volatile, then the maximin convention can emerge even if it is not risk-dominant. We contrast these results with those obtained under two alternative error models: uniform mistakes and payoff-dependent mistakes.

Keywords

Risk-dominant Payoff-dominant Maximin Stag hunt Stochastic stability 

JEL Classification

C72 C73 

Notes

References

  1. Agrawal, A.: Genetic loads under fitness-dependent mutation rates. J. Evol. Biol. 15(6), 1004–1010 (2002)Google Scholar
  2. Agrawal, A.F., Wang, A.D.: Increased transmission of mutations by low-condition females: evidence for condition-dependent dna repair. PLoS Biol. 6(2), e30 (2008)Google Scholar
  3. Alós-Ferrer, C., Netzer, N.: The logit-response dynamics. Games Econ. Behav. 68(2), 413–427 (2010)Google Scholar
  4. Alós-Ferrer, C., Netzer, N.: Robust stochastic stability. Econ. Theory 58(1), 31–57 (2015).  https://doi.org/10.1007/s00199-014-0809-z Google Scholar
  5. Alós-Ferrer, C., Weidenholzer, S.: Contagion and efficiency. J. Econ. Theory 143(1), 251–274 (2008)Google Scholar
  6. Anwar, A.W.: On the co-existence of conventions. J. Econ. Theory 107(1), 145–155 (2002)Google Scholar
  7. Bergin, J., Lipman, B.L.: Evolution with state-dependent mutations. Econometrica 64, 943–956 (1996)Google Scholar
  8. Bhaskar, V., Vega-Redondo, F.: Migration and the evolution of conventions. J. Econ. Behav. Organ. 55(3), 397–418 (2004)Google Scholar
  9. Bilancini, E., Boncinelli, L.: Social coordination with locally observable types. Econ. Theory 65(4), 975–1009 (2018).  https://doi.org/10.1007/s00199-017-1047-y Google Scholar
  10. Binmore, K., Samuelson, L.: Muddling through: noisy equilibrium selection. J. Econ. Theory 74(2), 235–265 (1997)Google Scholar
  11. Blume, L.E.: The statistical mechanics of strategic interaction. Games Econ. Behav. 5(3), 387–424 (1993)Google Scholar
  12. Blume, L.E.: Population games. In: Arthur, S.D.L., Durlauf, B. (eds.) The Economy as an Evolving Complex System II, pp. 425–460. Addison-Wesley, Reading (1997)Google Scholar
  13. Blume, L.E.: How noise matters. Games Econ. Behav. 44(2), 251–271 (2003)Google Scholar
  14. Blume, A., Temzelides, T.: On the geography of conventions. Econ. Theory 22(4), 863–873 (2003).  https://doi.org/10.1007/s00199-002-0350-3 Google Scholar
  15. Boncinelli, L., Pin, P.: The stochastic stability of decentralized matching on a graph. Games Econ. Behav. 108, 239–244 (2018)Google Scholar
  16. Carvalho, J.-P.: Coordination and culture. Econ. Theory 64(3), 449–475 (2017).  https://doi.org/10.1007/s00199-016-0990-3 Google Scholar
  17. Cotton, S.: Condition-dependent mutation rates and sexual selection. J. Evol. Biol. 22(4), 899–906 (2009)Google Scholar
  18. Efferson, C., Roca, C.P., Vogt, S., Helbing, D.: Sustained cooperation by running away from bad behavior. Evol. Hum. Behav. 37(1), 1–9 (2016)Google Scholar
  19. Ellison, G.: Learning, local interaction, and coordination. Econometrica 61, 1047–1071 (1993)Google Scholar
  20. Ellison, G.: Learning from personal experience: one rational guy and the justification of myopia. Games Econ. Behav. 19(2), 180–210 (1997)Google Scholar
  21. Ely, J.C.: Local conventions. Adv. Theor. Econ. 2(1) (2002)Google Scholar
  22. Foster, D., Young, P.: Stochastic evolutionary game dynamics. Theor. Popul. Biol. 38(2), 219–232 (1990)Google Scholar
  23. Freidlin, M.I., Wentzell, A.D.: Random perturbations. In: Random Perturbations of Dynamical Systems, pp. 15–43. Springer, Berlin (1998)Google Scholar
  24. Frey, V., Corten, R., Buskens, V.: Equilibrium selection in network coordination games: an experimental study. Rev. Netw. Econ. 11(3) (2012)Google Scholar
  25. Goyal, S., Vega-Redondo, F.: Network formation and social coordination. Games Econ. Behav. 50(2), 178–207 (2005)Google Scholar
  26. Harsanyi, J.C., Selten, R.: A General Theory of Equilibrium Selection in Games, vol. 1. The MIT Press, Cambridge (1988)Google Scholar
  27. Haselton, M.G., Buss, D.M.: Error management theory: a new perspective on biases in cross-sex mind reading. J. Pers. Soc. Psychol. 78(1), 81 (2000)Google Scholar
  28. Huttegger, S., Skyrms, B.: Emergence of a signaling network with “probe and adjust”. In: Sterelny, K., Calcott, B., Joyce, R. (eds.) Signaling, Commitment, and Emotion. MIT Press, Cambridge (2012)Google Scholar
  29. Hwang, S.-H., Newton, J.: Payoff-dependent dynamics and coordination games. Econ. Theory 64(3), 589–604 (2017)Google Scholar
  30. Hwang, S.-H., Naidu, S., Bowles, S.: Social conflict and the evolution of unequal conventions. Technical report, Santa Fe Institute Working Paper (2016)Google Scholar
  31. Hwang, S.-H., Lim, W., Neary, P., Newton, J.: Conventional contracts, intentional behavior and logit choice: equality without symmetry. Games Econ. Behav. 110, 273–294 (2018)Google Scholar
  32. Jackson, M.O., Watts, A.: On the formation of interaction networks in social coordination games. Games Econ. Behav. 41(2), 265–291 (2002)Google Scholar
  33. Kandori, M., Rob, R.: Evolution of equilibria in the long run: a general theory and applications. J. Econ. Theory 65(2), 383–414 (1995)Google Scholar
  34. Kandori, M., Mailath, G.J., Rob, R.: Learning, mutation, and long run equilibria in games. Econometrica 61, 29–56 (1993)Google Scholar
  35. Klaus, B., Newton, J.: Stochastic stability in assignment problems. J. Math. Econ. 62, 62–74 (2016)Google Scholar
  36. Lee, I.H., Szeidl, A., Valentinyi, A.: Contagion and state dependent mutations. Adv. Theor. Econ. 3(1) (2003)Google Scholar
  37. Lewis, D.: Convention: A Philosophical Study, p. 2008. Wiley, Hoboken (1969)Google Scholar
  38. Lim, W., Neary, P.R.: An experimental investigation of stochastic adjustment dynamics. Games Econ. Behav. 100, 208–219 (2016)Google Scholar
  39. Macy, M.W., Willer, R.: From factors to actors: computational sociology and agent-based modeling. Annu. Rev. Sociol. 28, 143–166 (2002)Google Scholar
  40. Maruta, T.: Binary games with state dependent stochastic choice. J. Econ. Theory 103(2), 351–376 (2002)Google Scholar
  41. Mäs, M., Nax, H.H.: A behavioral study of noise in coordination games. J. Econ. Theory 162, 195–208 (2016)Google Scholar
  42. McKelvey, R.D., Palfrey, T.R.: Quantal response equilibria for normal form games. Games Econ. Behav. 10(1), 6–38 (1995)Google Scholar
  43. Morris, S.: Contagion. Rev. Econ. Stud. 67(1), 57–78 (2000)Google Scholar
  44. Myerson, R.B.: Refinements of the Nash equilibrium concept. Int. J. Game Theory 7(2), 73–80 (1978)Google Scholar
  45. Naidu, S., Hwang, S.-H., Bowles, S.: Evolutionary bargaining with intentional idiosyncratic play. Econ. Lett. 109(1), 31–33 (2010)Google Scholar
  46. Nax, H.H., Pradelski, B.S.: Evolutionary dynamics and equitable core selection in assignment games. Int. J. Game Theory 44(4), 903–932 (2015)Google Scholar
  47. Nax, H.H., Burton-Chellew, M.N., West, S.A., Young, H.P.: Learning in a black box. J. Econ. Behav. Organ. 127, 1–15 (2016)Google Scholar
  48. Neary, P.R.: Competing conventions. Games Econ. Behav. 76(1), 301–328 (2012)Google Scholar
  49. Nesse, R.M.: Natural selection and the regulation of defenses: a signal detection analysis of the smoke detector principle. Evol. Hum. Behav. 26(1), 88–105 (2005)Google Scholar
  50. Newton, J.: Coalitional stochastic stability. Games Econ. Behav. 75(2), 842–854 (2012)Google Scholar
  51. Newton, J.: The Deconstruction of Conventions, 19 July 2018. Available at SSRN https://ssrn.com/abstract=3216269 (2018a)
  52. Newton, J.: Evolutionary game theory: a renaissance. Games 9(2), 31 (2018b)Google Scholar
  53. Newton, J., Sawa, R.: A one-shot deviation principle for stability in matching problems. J. Econ. Theory 157, 1–27 (2015)Google Scholar
  54. Norman, T.W.: Rapid evolution under inertia. Games Econ. Behav. 66(2), 865–879 (2009)Google Scholar
  55. Oechssler, J.: Decentralization and the coordination problem. J. Econ. Behav. Organ. 32(1), 119–135 (1997)Google Scholar
  56. Peski, M.: Generalized risk-dominance and asymmetric dynamics. J. Econ. Theory 145(1), 216–248 (2010)Google Scholar
  57. Pradelski, B.S., Young, H.P.: Learning efficient Nash equilibria in distributed systems. Games Econ. Behav. 75(2), 882–897 (2012)Google Scholar
  58. Robson, A.J., Vega-Redondo, F.: Efficient equilibrium selection in evolutionary games with random matching. J. Econ. Theory 70(1), 65–92 (1996)Google Scholar
  59. Sawa, R., Wu, J.: Prospect dynamic and loss dominance. Games Econ. Behav. 112, 98–124 (2018)Google Scholar
  60. Sharp, N.P., Agrawal, A.F.: Evidence for elevated mutation rates in low-quality genotypes. Proc. Natl. Acad. Sci. 109(16), 6142–6146 (2012)Google Scholar
  61. Shaw, F., Baer, C.: Fitness-dependent mutation rates in finite populations. J. Evol. Biol. 24(8), 1677–1684 (2011)Google Scholar
  62. Shi, F.: Comment on on the co-existence of conventions [J. Econ. Theory 107 (2002)]. J. Econ. Theory 1(148), 418–421 (2013)Google Scholar
  63. Skyrms, B.: The Stag Hunt and the Evolution of Social Structure. Cambridge University Press, Cambridge (2004)Google Scholar
  64. Staudigl, M., Weidenholzer, S.: Constrained interactions and social coordination. J. Econ. Theory 152, 41–63 (2014)Google Scholar
  65. Thuijsman, F., Peleg, B., Amitai, M., Shmida, A.: Automata, matching and foraging behavior of bees. J. Theor. Biol. 175(3), 305–316 (1995)Google Scholar
  66. Van Damme, E., Weibull, J.W.: Evolution in games with endogenous mistake probabilities. J. Econ. Theory 106(2), 296–315 (2002)Google Scholar
  67. Weidenholzer, S.: Coordination games and local interactions: a survey of the game theoretic literature. Games 1(4), 551–585 (2010)Google Scholar
  68. Weidenholzer, S.: Long-run equilibria, dominated strategies, and local interactions. Games Econ. Behav. 75(2), 1014–1024 (2012)Google Scholar
  69. Young, H.P.: The evolution of conventions. Econometrica 61, 57–84 (1993)Google Scholar
  70. Young, H.P.: Individual Strategy and Social Structure: An Evolutionary Theory of Institutions. Princeton University Press, Princeton (2001)Google Scholar
  71. Young, H.P.: Learning by trial and error. Games Econ. Behav. 65(2), 626–643 (2009)Google Scholar
  72. Young, H.P.: The evolution of social norms. Annu. Rev. Econ. 7(1), 359–387 (2015)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.IMT School of Advanced StudiesLuccaItaly
  2. 2.Dipartimento di Scienze per l’Economia e l’ImpresaUniversità degli Studi di FirenzeFlorenceItaly

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