Directional behavioral spillover and cognitive load effects in multiple repeated games

Abstract

In this study, we use a novel design to test for directional behavioral spillover and cognitive load effects in a set of multiple repeated games. Specifically, in our experiment, each subject plays a common historical game with two different matches for 100 rounds. After 100 rounds, the subject switches to a new game with one match and continues playing the historical game with the other match. This design allows us to identify the direction of any behavioral spillover. Our results show that participants exhibit both behavioral spillover and cognitive load effects. First, for pairs of Prisoners’ Dilemma and Alternation games, we find that subjects apply strategies from the historical game when playing the new game. Second, we find that those who participate in a Self Interest game as either their historical or new game achieve Pareto efficient outcomes more often in the Prisoners’ Dilemma and Alternation games compared to their control counterparts. Overall, our results show that, when faced with a new game, participants use strategies that reflect both behavioral spillover and cognitive load effects.

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Fig. 1

Notes

  1. 1.

    To measure the behavioral variation in a game, we apply a standard entropy measure to the outcome distributions (Shannon 1948), which we will explain in detail in Sect. 4.

  2. 2.

    Graduate students from the Economics Department are excluded from the list.

  3. 3.

    We also repeat all analyses replacing the second 100 rounds with all rounds beyond 100, and find similar results.

  4. 4.

    If an observation has either AC or AS as the best fitting strategy along with other best fitting strategies, we simply categorize it as an AC (AS) type. This simplification enables us to decrease the proportion of multiple-type strategies.

  5. 5.

    38% subjects in PD (SA) control sessions have the same best fitting strategies. For subjects in treatments, 48% of them have the same best fitting strategies in PD, 29% in SA, and 88% in SI treatments.

  6. 6.

    Compared to PD control, subjects are weakly more likely to keep selfish strategies in (PD,PD) \(\rightarrow\) (PD,SI) (0.47 vs. 0.33, \(p=0.087\), one-sided test of proportions). However, it is worthwhile to note that the selfish strategy Grim Trigger can produce CC outcome, and this result does not contradict our outcome level analyses.

References

  1. Abreu, D., & Rubinstein, A. (1988). The structure of nash equilibrium in repeated games with finite automata. Econometrica, 56(6), 1259–1281.

    Article  Google Scholar 

  2. Ahn, T.-K., Ostrom, E., Schmidt, D., Shupp, R., & Walker, J. (2001). Cooperation in PD games: Fear, greed, and history of play. Public Choice, 106, 137–155.

    Article  Google Scholar 

  3. Albert, M., Guth, W., & Kirchler, E. (2007). Are we nice(r) to nice(r) people?—An experimental analysis. Experimental Economics, 10(1), 53–69.

    Article  Google Scholar 

  4. Aoki, M. (1994). The contingent governance of teams: Analysis of institutional complementarity. International Economic Review, 35(3), 657–676.

    Article  Google Scholar 

  5. Aoki, M. (2001). Toward a comparative institutional analysis. Cambridge, MA: Cambridge University Press.

    Google Scholar 

  6. Bednar, J., Chen, Y., Liu, T. X., & Page, S. E. (2012a). Behavioral spillovers and cognitive load in multiple games: An experimental study. Games and Economic Behavior, 74(1), 12–31.

    Article  Google Scholar 

  7. Bednar, J., Jones-Rooy, A., & Page, S. E. (2015). Choosing a future based on the past: Institutions, behavior, and path dependence. European Journal of Political Economy, 40, 312–322.

    Article  Google Scholar 

  8. Bednar, J., & Page, S. E. (2007). Can game(s) theory explain culture?: The emergence of cultural behavior in multiple games. Rationality and Society, 19(1), 65–97.

    Article  Google Scholar 

  9. Bednar, J., & Page, S.E. (2018). When order affects performance: Culture, behavioral spillovers, and institutional path dependence. American Political Science Review, 112(1), 82–98.

    Article  Google Scholar 

  10. Bednar, J., Page, S. E., & Toole, J. (2012b). Revised-path dependence. Political Analysis, 20(2), 146–156.

    Article  Google Scholar 

  11. Bettenhausen, K., & Murnighan, J. K. (1985). The emergence of norms in competitive decision-making groups. Administrative Science Quarterly, 30, 350–372.

    Article  Google Scholar 

  12. Bettenhausen, K., & Murnighan, J. K. (1991). The development of an intragroup norm and the effects of interpersonal and structural challenges. Administrative Science Quarterly, 36, 20–35.

    Article  Google Scholar 

  13. Boeker, W. (1989). Strategic change: The effects of founding and history. Academy of Management Journal, 32(3), 489–515.

    Google Scholar 

  14. Cason, T., & Gangadharan, L. (2013). Cooperation spillovers and price competition in experimental markets. Economic Inquiry, 51(3), 1715–1730.

    Article  Google Scholar 

  15. Cason, T. N., Lau, S.-H. P., & Mui, V.-L. (2013). Learning, teaching, and turn taking in the repeated assignment game. Economic Theory, 54(2), 335–357.

    Article  Google Scholar 

  16. Cason, T., Savikhin, A., & Sheremeta, R. (2012). Behavioral spillovers in coordination games. European Economic Review, 56(3), 233–245.

    Article  Google Scholar 

  17. Chen, Y., & Plott, C. R. (1996). The Groves–Ledyard mechanism: An experimental study of institutional design. Journal of Public Economics, 59, 335–364.

    Article  Google Scholar 

  18. Cooper, D. J., & Kagel, J. H. (2008). Learning and transfer in signaling games. Economic Theory, 34(3), 415–439.

    Article  Google Scholar 

  19. Devetag, G. (2005). Precedent transfer in coordination games: An experiment. Economics Letters, 89(2), 227–232.

    Article  Google Scholar 

  20. Duffy, J., & Fehr, D. (2018) (Forthcoming). Equilibrium selection in similar repeated games: Experimental evidence on the role of precedents. Experimental Economics.

  21. Engle-Warnick, J., & Slonim, R. L. (2006). Inferring repeated-game strategies from actions: Evidence from trust game experiments. Economic Theory, 28(3), 603–632.

    Article  Google Scholar 

  22. Fiorina, M. P., & Plott, C. R. (1978). Committee decisions under majority rule: An experimental study. The American Political Science Review, 72(2), 575–598.

    Article  Google Scholar 

  23. Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiment. Experimental Economics, 10(2), 171–178.

    Article  Google Scholar 

  24. Friedman, J. W. (1971). A non-cooperative equilibrium for supergames. The Review of Economic Studies, 38(1), 1–12.

    Article  Google Scholar 

  25. Gilboa, I., & Schmeidler, D. (1995). Case-based decision theory. The Quarterly Journal of Economics, 110(3), 605–639.

    Article  Google Scholar 

  26. Hanaki, N., Sethi, R., Erev, I., & Peterhansl, A. (2005). Learning strategies. Journal of Economic Behavior and Organization, 56(4), 523–542.

    Article  Google Scholar 

  27. Kagel, J. H. (1995). Auctions: A survey of experimental research. In J. H. Kagel & A. E. Roth (Eds.), Handbook of Experimental Economics. Princeton: Princeton University Press.

    Google Scholar 

  28. Kagel, J. H., & Levin, D. (1986). The winner’s curse and public information in common value auctions. American Economic Review, 76, 894–920.

    Google Scholar 

  29. Knez, M., & Camerer, C. (2000). Increasing cooperation in prisoner’s dilemmas by establishing a precedent of efficiency in coordination games. Organizational Behavior and Human Decision Processes, 82, 194–216.

    Article  Google Scholar 

  30. Lei, V., Noussair, C. N., & Plott, C. R. (2001). Nonspeculative bubbles in experimental asset markets: Lack of common knowledge of rationality vs. actual irrationality. Econometrica, 69(4), 831–859.

    Article  Google Scholar 

  31. McCarter, M. W., Samak, A. C., & Sheremeta, R. M. (2014). Divided loyalists or conditional cooperators? Creating consensus about cooperation in multiple simultaneous social dilemmas. Group & Organization Management, 39(6), 744–771.

    Article  Google Scholar 

  32. Mengel, F., & Sciubba, E. (2010). Extrapolation and structural similarity in games. Economics Letters, 125(3), 381–385.

    Article  Google Scholar 

  33. North, D. C. (2005). Understanding the process of economic change. Princeton, NJ: Princeton University Press.

    Google Scholar 

  34. Page, S. E. (2006). Path dependence. Quarterly Journal of Political Science, 1, 87–115.

    Article  Google Scholar 

  35. Plott, C. R. (1982). Industrial organization theory and experimental economics. Journal of Economic Literature, 20(4), 1485–1527.

    Google Scholar 

  36. Plott, C. R. (1994). Experimental methods in economics and political science: The design and testing of policy options. Human Dimensions Quarterly, 1(2), 5–8.

    Google Scholar 

  37. Plott, C. R., Rullère, J.-L., & Villeval, M. C. (2011). Introduction to the special issue on behavioral and experimental public economics. Journal of Public Economic Theory, 13(5), 631–637.

    Article  Google Scholar 

  38. Putnam, R. D. (1993). Making democracy work: Civic traditions in modern Italy. Princeton, NJ: Princeton University Press.

    Google Scholar 

  39. Rubinstein, A. (1986). Finite automata play the repeated prisoner’s dilemma. Journal of Economic Theory, 39(1), 83–96.

    Article  Google Scholar 

  40. Samuelson, L. (2001). Analogies, adaptations, and anomalies. Journal of Economic Theory, 97(2), 320–366.

    Article  Google Scholar 

  41. Savikhin, A., & Sheremeta, R. M. (2013). Simultaneous decision-making in competitive and cooperative environments. Economic Inquiry, 51(2), 1311–1323. (Forthcoming).

    Article  Google Scholar 

  42. Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423.

    Article  Google Scholar 

  43. Van Huyck, J. B., Battalio, R. C., & Beil, R. O. (1991). Strategic uncertainty, equilibrium selection, and coordination failure in average opinion games. The Quarterly Journal of Economics, 106(3), 885–910.

    Article  Google Scholar 

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Acknowledgements

We would like to thank Andrea Jones-Rooy, Zhewei Song and Chao Tang for excellent research assistance, Nancy Kotzian, two anonymous referees and the co-editor, Marie Claire Villeval, for their thoughtful and constructive comments. The financial support from the National Science Foundation through Grant no. BCS-1111019 to Chen and the Natural Science Foundation of China through grant no. 71403140 to Liu is gratefully acknowledged. The research has been approved by the University of Michigan IRB.

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Correspondence to Yan Chen.

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Liu, T.X., Bednar, J., Chen, Y. et al. Directional behavioral spillover and cognitive load effects in multiple repeated games. Exp Econ 22, 705–734 (2019). https://doi.org/10.1007/s10683-018-9570-7

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Keywords

  • Multiple games
  • Repeated games
  • Behavioral spillovers
  • Cognitive load
  • Entropy

JEL Classification

  • C72
  • C91
  • D03