Inequality aversion causes equal or unequal division in alternating-offer bargaining

Kohler, Stefan (2013): Inequality aversion causes equal or unequal division in alternating-offer bargaining.

Abstract

This note presents a solution to Rubinstein (1982)'s open-ended, alternating-offer bargaining problem for two equally patient bargainers that exhibit similar degrees of inequality aversion. Inequality-averse bargainers may perceive envy if being worse off and guilt if being better off, but they still reach agreement in the first period under complete information. If the perceived guilt is strong, then the inequality-averse bargainers split the bargaining surplus equally regardless of their degree of envy. If guilt is weak, then the agreed split is tilted away from the Rubinstein division towards a more unequal split. Envy and weak guilt have opposite effects on the bargaining outcome, and envy has a greater marginal impact than weak guilt. Similarly inequality-averse bargainers agree on the Rubinstein division if the strength of envy equals the discounted strength of guilt. As both bargainers sensation of inequality aversion diminishes, the bargaining outcome converges to the Rubinstein division.

• Item Type: MPRA Paper
• Language: English
• Keywords: alternating offers; bargaining; bargaining power; behavioral economics; envy; equity; fairness; guilt; negotiation; social preferences
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory; D - Microeconomics > D3 - Distribution; D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

References

Barr, A., Wallace, C., Ensminger, J., Henrich, J., Barrette, C., Bolyanatz, A., Cardenas, J.-C., Gurven, M., Gwako, E., Lesorogol, C., Marlowe, F., McElreath, R., Tracer, D., & Ziker, J. (2009). Homo Aequalis: A cross-society experimental analysis of three bargaining games. University of Oxford, Department of Economics: Economics Series Working Papers 422.

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.

Bolton, G. E., & Ockenfels, A. (2000). ERC: A theory of equity, reciprocity and competition. American Economic Review, 90, 166–193.

Camerer, C. F. (2003). Behavioral Game Theory. Experiments in Strategic Interaction. The roundtable series in behavioral economics. Princeton: Princeton University Press.

Cooper, D. J., & Kagel, J. H. (n.d.). Other regarding preferences: A selective survey of experimental results. In J. H. Kagel, & A. E. Roth (Eds.), Handbook of Experimental Economics, Volume 2. Princeton: Princeton University Press.

De Bruyn, A., & Bolton, G. E. (2008). Estimating the influence of fairness on bargaining behavior. Management Science, 54, 1774–1791.

Engelmann, D. (2012). How not to extend models of inequality aversion. Journal of Economic Behavior & Organization, 81, 599–605.

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

Goeree, J. K., & Holt, C. A. (2000). Asymmetric inequality aversion and noisy behavior in alternating-offer bargaining games. European Economic Review, 44, 1079–1089.

Herreiner, D., & Puppe, C. (2009). Envy freeness in experimental fair division problems. Theory and Decision, 67, 65–100.

Kohler, S. (2008). Inequality aversion and stochastic decision-making: Experimental evidence from Zimbabwean villages after land reform. In A. Innocenti, & P. Sbriglia (Eds.), Games, Rationality and Behavior: Essays on Behavioral Game Theory and Experiments (pp. 63–100). Basingstoke: Palgrave McMillan.

Kohler, S. (2011). Altruism and fairness in experimental decisions. Journal of Economic Behavior & Organization, 80, 101–109.

Kohler, S. (2012a). Guilt causes equal or unequal division in alternating-offer bargaining. University Library of Munich, Germany: MPRA Paper 40760.

Kohler, S. (2012b). Incomplete information about social preferences explains equal division and delay in bargaining. Games, 3, 119–137.

Kohler, S. (2013a). Envy can promote more equal division in alternating-offer bargaining. Journal of Neuroscience, Psychology, and Economics, 6, 31–41.

Kohler, S. (2013b). More fair play in an ultimatum game after resettlement in Zimbabwe: A field experiment and a structural model. PloS one, 8, e64791.

Mauleon, A., & Vannetelbosch, V. (2013). Relative concerns and delays in bargaining with private information. Games, 4, 329–338.

Montero, M. (2007). Inequity aversion may increase inequity. Economic Journal, 117, C192–C204.

Montero, M. (2008). Altruism, spite and competition in bargaining games. Theory and Decision, 65, 125–151.

Roth, A. E. (1985). A note on risk aversion in a perfect equilibrium model of bargaining. Econometrica, 53, 207.

Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica, 50, 97–109.

Shaked, A., & Sutton, J. (1984). Involuntary unemployment as a perfect equilibrium in a bargaining model. Econometrica, 52, 1351–1364.

Smith, R. (Ed.) (2008). Envy: Theory and Research. New York: Oxford University Press.

Tan, J. H. W., & Bolle, F. (2006). On the relative strengths of altruism and fairness. Theory and Decision, 60, 35–67.

Zwick, R., Rapoport, A., & Howard, J. C. (1992). Two-person sequential bargaining behavior with exogenous breakdown. Theory and Decision, 32, 241–268.