Heterogeneous guilt sensitivities and incentive effects

Abstract

Psychological games of guilt aversion assume that preferences depend on (beliefs about) beliefs and on the guilt sensitivity of the decision-maker. We present an experiment designed to measure guilt sensitivities at the individual level for various stake sizes. We use the data to estimate a structural choice model that allows for heterogeneity, and permits that guilt sensitivities depend on stake size. We find substantial heterogeneity of guilt sensitivities in our population, with 60% of decision makers displaying stake-dependent guilt sensitivity. For these decision makers, we find that average guilt sensitivities are significantly different from zero for all stakes considered, while significantly decreasing with the level of stakes.

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Notes

  1. 1.

    In general, psychological game theory takes into account that people’s utilities do not only depend on material payoffs, but also on their beliefs about others’ behavior, as well as beliefs about the beliefs of others. See Geanakoplos et al. (1989) and Battigalli and Dufwenberg (2009) for general frameworks of games with belief-dependent preferences.

  2. 2.

    Self-serving bias on the other hand has not shown to be related to stake sizes. See Babcock and Loewenstein (1997) for a discussion.

  3. 3.

    Holt and Laury (2002) find that the degree of risk aversion increases with stakes. Bellemare et al. (2008) find that the marginal disutility of disadvantageous inequality is decreasing with stakes while the marginal disutility of advantageous inequality is decreasing with stakes for young, highly educated people (see also Yang et al. 2012). Gibson et al. (2013) find that the percentage of truth-tellers decreases with the costs of truthfulness. On the other hand, Carpenter et al. (2005) report that multiplying the stakes by 10 does not have a statistically significant effect on the share a dictator allocates to a passive player. For general surveys, see Camerer and Hogarth (1999) and Gneezy et al. (2011).

  4. 4.

    See Krupka and Weber (2013) for an experimental study that points out the relevance of dictator games for understanding how social norms influence behavior.

  5. 5.

    The method circumvents the problem of possible spurious correlation between beliefs and behavior by letting the dictator make choices conditional on first-order beliefs of the passive player. See Vanberg (2008), Reuben et al. (2009), Ellingsen et al. (2010), and Bellemare et al. (2011) for other methods that circumvent the problem.

  6. 6.

    They model belief-dependent preferences as a combination of guilt sensitivity and intention-based reciprocity, with trustees’ willingness to share being increasing (decreasing) in his second-order belief if guilt sensitivity (intention-based reciprocity) prevails in the questionnaire.

  7. 7.

    Note that unlike in ‘typical’ dictator games, in our experiments, dictators can condition their choice on the first-order belief of the matched passive player.

  8. 8.

    Following Battigalli and Dufwenberg (2007)’s model of simple guilt, we assume that utility functions are linear in the stake level throughout the paper. However, these properties also hold for utility functions that are power functions of the stake level.

  9. 9.

    Trautmann and van de Kuilen (2015) compare the effect of different belief elicitation methods and find that subjects do not behave differently depending on whether beliefs are incentivized or not (see also Armantier and Treich 2013). Therefore, we decided not to incentivize the measurement of first-order beliefs.

  10. 10.

    Supplementary of Appendix includes detailed instructions. Passive players and dictators were respectively referred to as Players A and B during the experiment.

  11. 11.

    This method to elicit switchpoints corresponds to the ‘minimum acceptable offer’ procedure often used to elicit the strategy of responders in ultimatum games (see e.g., Güth et al. 1982; Schotter and Sopher 2007). In another experiment using a mini trust game where players could switch back and forth between r and l as much as they liked (reported in Bellemare et al. 2017), we found that the vast majority of players did not switch more than once (see also Attanasi et al. 2013). Furthermore, for those few players that switched more than once or switched in the ‘wrong’ way, no systematic tendency could be discovered in their behavior.

  12. 12.

    Due to an error in the computer program, the data from 2 dictators were not usable, leaving us with 140 dictators.

  13. 13.

    Another important reason for not informing the dictators was that we tried to keep instructions as similar as possible to those in other dictator treatments (reported in Bellemare et al. 2017).

  14. 14.

    In a similar vein, it is possible to show predictions under non-linear inequality aversion. Suppose that the utility of choosing the selfish option r is equal to \(54 s - \gamma \cdot m(32s)\) where the function m() captures the disutility from advantageous inequality aversion. It can easily be seen that dictators with quadratic inequality aversion \(m(a)=a^2\) choose l for all s if \(\gamma \ge 0.0039\) and r otherwise. Moreover, dictators with square-root inequality aversion \(m(a)=\sqrt{a}\) choose l for \(s=1,2,4\) if \(\gamma \ge 0.943\). They choose r for \(s=1\) and l for \(s=2,4\) if \(\gamma \ge 0.666\), and choose r for 1, 2 and l for \(s=4\) if \(\gamma \ge 0.472\).

  15. 15.

    Our identification regions are based on the model of simple guilt aversion by Battigalli and Dufwenberg (2007). They should be considered as conservative lower bounds in case players are motivated by simple guilt aversion as well as distributional concerns. Assuming that dictators are also motivated by Fehr and Schmidt (1999)’s model of inequality aversion implies that they should choose l if \(\beta \ge \frac{2{-}15\gamma }{13\theta }\). The higher the dictator’s sensitivity to advantageous inequality, the lower the threshold. For \(\gamma\) bigger or equal to 2/15 (0.13333), the dictator should choose l independent of \(\beta\). Fehr and Schmidt (1999) report an average sensitivity to advantageous inequality of 0.315 (in Table 3 on page 844). Using this coefficient implies that all dictators in our experiment that are motivated both by guilt aversion and inequality aversion should have chosen the nice option l independent of \(\beta\).

  16. 16.

    We experimented with a specification which modeled the distribution of \(\left( \theta ^1,\theta ^2,\theta ^4\right)\) as a discrete distribution: \(\left( \theta ^1_k,\theta ^2_k,\theta ^4_k\right)\) with probability \(\omega _k\) for \(k = 1,2,\ldots ,7\). This specification led to a lower log-likelihood function (when evaluated at the solution) than our preferred specification despite the higher number of model parameters of the discrete specification (the discrete and our preferred specifications model the joint distribution of \(\left( \theta ^1,\theta ^2,\theta ^4\right)\) using respectively 27 and 11 parameters). Numerically unstable solutions were obtained when we further increased the number of mass points of the discrete distribution.

  17. 17.

    These numbers are computed using \(\frac{1}{N}\sum _{i=1}^{N}\widehat{\omega }_{ji}\) for each class j, where \(\widehat{\omega }_{ji}\) are computed using equations (8)–(10) evaluated at the estimated parameter values reported in Table 2.

  18. 18.

    The predicted conditional posterior probability of player i is obtained by evaluating \(\left( \omega _{1i} \frac{1}{R}\sum_{r=1}^{R}\left[ \Pi_{\forall s} \Pi_{j=1}^{11}l_{ij}\left( y_{ij}^{s};\theta _{i}^{s,r},\lambda \right) \right] \right) /\widetilde{L}_i\) at the estimated values of the model parameters, where \(\widetilde{L}_i\) is given in (11).

  19. 19.

    This is because the threshold for the second-order belief at which guilt-sensitive individuals switch from right to left (condition (2)) decreases as stakes increase. Intuitively, increasing stakes has the same effect as increasing \(\rho\) when the utility function is \(u(x)=1-e^{-\rho x}\).

  20. 20.

    Calculations available upon request.

References

  1. Abdellaoui, M., Barrios, C., & Wakker, P. P. (2007). Reconciling introspective utility with revealed preference: Experimental arguments based on prospect theory. Journal of Econometrics, 138, 356–378.

    Article  Google Scholar 

  2. Andreoni, J., & Bernheim, B. D. (2009). Social image and the 50–50 norm: A theoretical and experimental analysis of audience effects. Econometrica, 77, 1607–1636.

    Article  Google Scholar 

  3. Armantier, O., & Treich, N. (2013). Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging. European Economic Review, 62, 17–40.

    Article  Google Scholar 

  4. Attanasi, G., Battigalli, P., & Manzoni, E. (2015). Incomplete-information models of guilt aversion in the trust game. Management Science, 62(3), 648–667.

    Article  Google Scholar 

  5. Attanasi, G., Battigalli, P., and Nagel, R. (2013). Disclosure of belief-dependent preferences in a trust game. Mimeo.

  6. Babcock, L., & Loewenstein, G. (1997). Explaining bargaining impasse: The role of self-serving biases. The Journal of Economic Perspectives, 11(1), 109–126.

    Article  Google Scholar 

  7. Battigalli, P., & Dufwenberg, M. (2007). Guilt in games. American Economic Review Papers and Proceedings, 97, 170–176.

    Article  Google Scholar 

  8. Battigalli, P., & Dufwenberg, M. (2009). Dynamic psychological games. Journal of Economic Theory, 144, 1–35.

    Article  Google Scholar 

  9. Baumeister, R., Stillwell, A., & Heatherton, T. (1994). Guilt: An interpersonal approach. Psychological Bulletin, 115, 243–267.

    Article  Google Scholar 

  10. Bellemare, C., Kröger, S., & van Soest, A. (2008). Measuring inequity aversion in a heterogeneous population using experimental decisions and subjective probabilities. Econometrica, 76, 815–839.

    Article  Google Scholar 

  11. Bellemare, C., Sebald, A., & Strobel, M. (2011). Measuring the willingness to pay to avoid guilt: Estimation using equilibrium and stated belief models. Journal of Applied Econometrics, 26, 437–453.

    Article  Google Scholar 

  12. Bellemare, C., Sebald, A., & Suetens, S. (2017). A note on testing guilt aversion. Games and Economic Behavior, 102, 233–239.

    Article  Google Scholar 

  13. Bicchieri, C. (2006). The grammar of society: The nature and dynamics of social norms. Cambridge University Press.

  14. Bicchieri, C., & Xiao, E. (2009). Do the right thing: But only if others do so. Journal of Behavioral Decision Making, 22(2), 191–208.

    Article  Google Scholar 

  15. Bicchieri, C., Xiao, E., & Muldoon, R. (2011). Trustworthiness is a social norm, but trusting is not. Politics, Philosophy, and Economics, 10, 170–187.

    Article  Google Scholar 

  16. Camerer, C., & Hogarth, R. (1999). The effects of financial incentives in experiments: A review and capital-labor-production framework. Journal of Risk and Uncertainty, 19, 7–42.

    Article  Google Scholar 

  17. Carpenter, J., Verhoogen, E., & Burks, S. (2005). The effect of stakes in distribution experiments. Economics Letters, 86, 393–398.

    Article  Google Scholar 

  18. Charness, G., & Dufwenberg, M. (2006). Promises and partnerships. Econometrica, 74, 1579–1601.

    Article  Google Scholar 

  19. Ellingsen, T., Johannesson, M., Tjötta, S., & Torsvik, G. (2010). Testing guilt aversion. Games and Economic Behavior, 68, 95–107.

    Article  Google Scholar 

  20. Fehr, E., & Schmidt, K. (1999). A theory of fairness, competition and cooperation. Quarterly Journal of Economics, 114, 817–868.

    Article  Google Scholar 

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

    Article  Google Scholar 

  22. Geanakoplos, J., Pearce, D., & Stacchetti, E. (1989). Psychological games and sequential rationality. Games and Economic Behavior, 1, 60–79.

    Article  Google Scholar 

  23. Gibson, R., Tanner, C., & Wagner, A. (2013). Preferences for truthfulness: Heterogeneity among and within individuals. American Economic Review, 103, 532–548.

    Article  Google Scholar 

  24. Gneezy, U., Meier, S., & Rey-Biel, P. (2011). When and why incentives (don’t) work to modify behavior. Journal of Economic Perspective, 25, 191–210.

    Article  Google Scholar 

  25. Greiner, B. (2004). The online recruitment system ORSEE 2.0—A guide for the organization of experiments in economics. Technical report, University of Cologne, Working Paper Series in Economics 10.

  26. Güth, W., Schmittberger, R., & Schwarze, B. (1982). An experimental analysis of ultimatum bargaining. Journal of Economic Behavior and Organization, 3(4), 367–388.

    Article  Google Scholar 

  27. Holt, C., & Laury, S. (2002). Risk aversion and incentive effects. American Economic Review, 92, 1644–1655.

    Article  Google Scholar 

  28. Khalmetski, K., Ockenfels, A., & Werner, P. (2015). Surprising gifts: Theory and laboratory evidence. Journal of Economic Theory, 159, 163–208.

    Article  Google Scholar 

  29. Krupka, E. L., & Weber, R. A. (2013). Identifying social norms using coordination games: Why does dictator game sharing vary? Journal of the European Economic Association, 11, 495–524.

    Article  Google Scholar 

  30. Noussair, C. N., Trautmann, S. T., & van de Kuilen, G. (2014). Higher order risk attitudes, demographics, and financial decisions. Review of Economic Studies, 81, 325–355.

    Article  Google Scholar 

  31. Reuben, E., Sapienza, P., & Zingales, L. (2009). Is mistrust self-fulfilling? Economics Letters, 104, 89–91.

    Article  Google Scholar 

  32. Schotter, A., & Sopher, B. (2007). Advice and behavior in intergenerational ultimatum games: An experimental approach. Games and Economic Behavior, 58(2), 365–393.

    Article  Google Scholar 

  33. Selten, R. (1967). Die Strategiemethode zur Erforschung des Eingeschränkt Rationalen Verhaltens im Rahmen eines Oligopolexperiments. In H. Sauermann (Ed.), Beiträge zur Experimentellen Wirtschaftsforschung (pp. 136–168). Tübingen: J. C. B. Mohr.

    Google Scholar 

  34. Smith, V., & Walker, J. (1993). Monetary rewards and decision costs in experimental economics. Economic Inquiry, 31, 245–261.

    Article  Google Scholar 

  35. Trautmann, S. T., & van de Kuilen, G. (2015). Belief elicitation: A horse race among truth serums. Economic Journal (forthcoming).

  36. Vanberg, C. (2008). Why do people keep their promises? An experimental test of two explanations. Econometrica, 76, 1467–1480.

    Article  Google Scholar 

  37. Yang, Y., Onderstal, S., & Schram, A. (2012). Inequity aversion revisited. Working paper, University of Amsterdam.

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Acknowledgements

The authors thank audiences of seminars at the universities of Amsterdam, Copenhagen, Frankfurt, Gothenborg, Heidelberg, Innsbruck, Mannheim, Munich, Pennsylvania, and Tilburg, at the Max Planck Institute of Economics in Jena, at the Nordic Conference of Behavioral and Experimental Economics in Stockholm, and at IMEBE in Madrid for helpful comments. Furthermore, we would like to thank the editor and two anonymous referees for very helpful comments. Suetens acknowledges financial support from the Netherlands Organization for Scientific Research (NWO) through the VIDI program (Project No. 452-11-012).

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Correspondence to Alexander Sebald.

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Bellemare, C., Sebald, A. & Suetens, S. Heterogeneous guilt sensitivities and incentive effects. Exp Econ 21, 316–336 (2018). https://doi.org/10.1007/s10683-017-9543-2

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Keywords

  • Guilt sensitivity
  • Psychological game theory
  • Heterogeneity
  • Stakes
  • Dictator game

JEL Classification

  • A13
  • C91