Generosity in bargaining: Fair or fear?

Breitmoser, Yves and Tan, Jonathan H.W. (2010): Generosity in bargaining: Fair or fear?

Abstract

Are "generous" bargaining offers made out of fairness or in fear of rejection? We disentangle risk and social references by analyzing experimental behavior in three majority bargaining games: (1) a random-proposer game with infinite time horizon; 2) a one round proposer game with disagreement payoffs equal to the infinite horizon continuation payoffs; and, (3) a demand commitment game. Inequity aversion predicts very differently across these games, but risk aversion does not. Observed strategies violate neither stationarity nor truncation consistency. This allows us to use structural models of bargaining behavior to estimate the latent type shares of subjects with CES, inequity averse, and Prospect theoretic preferences. The Prospect theoretic, i.e. reference-dependent, model of utility explains the observations far better than any mixture of alternative models.

• Item Type: MPRA Paper
• Language: English
• Keywords: coalitional bargaining, non-cooperative modeling, random utility model, quantal response equilibrium, laboratory experiment
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D78 - Positive Analysis of Policy Formulation and Implementation; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Abreu, D. and Gul, F. (2000). Bargaining and reputation. Econometrica, 68(1):85–117.

Amemiya, T. (1978). On a two-step estimation of a multivariate logit model. Journal of Econometrics, 8(1):13–21.

Andreoni, J., Castillo, M., and Petrie, R. (2003). What do bargainers’ preferences look like? experiments with a convex ultimatum game. American Economic Review, 93(3):672–685.

Andreoni, J. and Miller, J. (2002). Giving according to garp: An experimental test of the consistency of preferences for altruism. Econometrica, 70(2):737–753.

Ansolabehere, S., Snyder Jr, J., and Ting, M. (2003). Bargaining in bicameral legislatures: When and why does malapportionment matter? The American Political Science Review, 97(3):471–481.

Arcidiacono, P. and Jones, J. (2003). Finite mixture distributions, sequential likelihood and the em algorithm. Econometrica, 71(3):933–946.

Auger, A., Hansen, N., Perez Zerpa, J., Ros, R., and Schoenauer, M. (2009). Experimental comparisons of derivative free optimization algorithms. Experimental Algorithms, pages 3–15.

Baron, D. and Ferejohn, J. (1989). Bargaining in legislatures. The American Political Science Review, 83(4):1181–1206.

Baron, D. and Kalai, E. (1993). The simplest equilibrium of a majority rule division game. Journal of Economic Theory, 61(2):290–301.

Battaglini, M. and Palfrey, T. (2007). The dynamics of distributive politics. Northwestern University, CMS-EMS Discussion Paper, 1451.

Binmore, K., McCarthy, J., Ponti, G., Samuelson, L., and Shaked, A. (2002). A backward induction experiment. Journal of Economic Theory, 104(1):48–88.

Bolton, G. and Ockenfels, A. (2000). ERC: A theory of equity, reciprocity, and competition. American Economic Review, 90(1):166–193.

Breitmoser, Y. (2009). Demand commitments in majority bargaining or how formateurs get their way. International Journal of Game Theory, 38(2):183–191.

Breitmoser, Y., Tan, J., and Zizzo, D. (2010). Understanding perpetual R&D races. Economic Theory, 44(3):445–467.

Butler, C. (2008). Prospect Theory and Coercive Bargaining. Journal of Conflict Resolution, 51(2):227–250.

Camerer, C. (2003). Behavioral game theory: Experiments in strategic interaction, volume 544. Princeton University Press Princeton, NJ.

Camerer, C. and Thaler, R. (1995). Anomalies: Ultimatums, dictators and manners. The Journal of Economic Perspectives, pages 209–219.

Cardona, D. and Ponsatí, C. (2007). Bargaining one-dimensional social choices. Journal of Economic Theory, 137(1):627–651.

Cho, S. and Duggan, J. (2003). Uniqueness of stationary equilibria in a one-dimensional model of bargaining. Journal of Economic Theory, 113(1):118–130.

Costa-Gomes, M. and Zauner, K. (2003). Learning, non-equilibrium beliefs, and non-pecuniary payoffs in an experimental game. Economic Theory, 22(2):263–288.

Cox, J., Friedman, D., and Gjerstad, S. (2007). A tractable model of reciprocity and fairness. Games and Economic Behavior, 59(1):17–45.

Croson, R. (1996). Information in ultimatum games: An experimental study. Journal of Economic Behavior and Organization, 30(2):197–212.

Diermeier, D., Eraslan, H., and Merlo, A. (2002). Coalition governments and comparative constitutional design. European Economic Review, 46(4-5):893–907.

Diermeier, D., Eraslan, H., and Merlo, A. (2003). A structural model of government formation. Econometrica, 71(1):27–70.

Eraslan, H. (2002). Uniqueness of stationary equilibrium payoffs in the baron–ferejohn model. Journal of Economic Theory, 103(1):11–30.

Fehr, E. and Schmidt, K. (1999). A theory of fairness, competition, and cooperation. Quarterly Journal of Economics, 114(3):817–868.

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

Forsythe, R., Horowitz, J., Savin, N., and Sefton, M. (1994). Fairness in simple bargaining experiments. Games and Economic Behavior, 6(3):347–369.

Fréchette, G. (2009). Learning in a multilateral bargaining experiment. Journal of Econometrics, 153(2):183–195.

Fréchette, G., Kagel, J., and Morelli, M. (2005a). Behavioral identification in coalitional bargaining: An experimental analysis of demand bargaining and alternating offers. Econometrica, 73(6):1893–1937.

Fréchette, G., Kagel, J., and Morelli, M. (2005b). Nominal bargaining power, selection protocol, and discounting in legislative bargaining. Journal of Public Economics, 89(8):1497–1517.

Goeree, J. and Holt, C. (2000). Asymmetric inequality aversion and noisy behavior in alternating-offer bargaining games. European Economic Review, 44(4-6):1079–1089.

Güth, W. (1995). On ultimatum bargaining experiments -- a personal review. Journal of Economic Behavior and Organization, 27(3):329–344.

Güth, W., Schmittberger, R., and Schwarze, B. (1982). An experimental analysis of ultimatum bargaining. Journal of Economic Behavior and Organization, 3(4):367–88.

Harrington, J. (1990). The power of the proposal maker in a model of endogenous agenda formation. Public Choice, 64(1):1–20.

Jackson, M. and Moselle, B. (2002). Coalition and party formation in a legislative voting game. Journal of Economic Theory, 103(1):49–87.

Kagel, J., Kim, C., and Moser, D. (1996). Fairness in ultimatum games with asymmetric information and asymmetric payoffs. Games and Economic Behavior, 13(1):100–110.

Knight, B. (2005). Estimating the value of proposal power. American Economic Review, 95(5):1639–1652.

Koszegi, B. (2010). Utility from anticipation and personal equilibrium. Economic Theory, 44(3):415–444.

Koszegi, B. and Rabin, M. (2006). A model of reference-dependent preferences. Quarterly Journal of Economics, 121(4):1133–1165.

Koszegi, B. and Rabin, M. (2007). Reference-dependent risk attitudes. The American Economic Review, 97(4):1047–1073.

Levitt, S. and Snyder Jr, J. (1997). The impact of federal spending on House election outcomes. Journal of Political Economy, 105(1):30–53.

Li, D. (2007). Bargaining with history-dependent preferences. Journal of Economic Theory, 136(1):695–708.

McFadden, D. (1984). Econometric analysis of qualitative response models. Handbook of econometrics, 2:1395–1457.

McKelvey, R. and Palfrey, T. (1995). Quantal response equilibria for normal form games. Games and Economic Behavior, 10(1):6–38.

McKelvey, R. and Palfrey, T. (1998). Quantal response equilibria for extensive form games. Experimental Economics, 1(1):9–41.

Montero, M. (2007). Inequity aversion may increase inequity. The Economic Journal, 117(519):192–204.

Moré, J. and Wild, S. (2009). Benchmarking derivative-free optimization algorithms. SIAM Journal on Optimization, 20(1):172–191.

Okada, A. and Riedl, A. (2005). Inefficiency and social exclusion in a coalition formation game: experimental evidence. Games and Economic Behavior, 50(2):278–311.

Poulsen, A. and Tan, J. (2007). Information acquisition in the ultimatum game: An experimental study. Experimental Economics, 10(4):391–409.

Powell, M. (2008). Developments of newuoa for minimization without derivatives. IMA journal of numerical analysis, 28(4):649.

Rosenthal, R. (1989). A bounded-rationality approach to the study of noncooperative games. International Journal of Game Theory, 18(3):273–292.

Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica, 50(1):97–109.

Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2):461–464.

Shalev, J. (2000). Loss aversion equilibrium. International Journal of Game Theory, 29(2):269–287.

Shalev, J. (2002). Loss aversion and bargaining. Theory and decision, 52(3):201–232.

Snyder Jr, J., Ting, M., and Ansolabehere, S. (2005). Legislative bargaining under weighted voting. American Economic Review, 95(4):981–1004.

Stahl, I. (1972). Bargaining theory. Stockholm school of economics.

Straub, P. G. and Murnighan, J. K. (1995). An experimental investigation of ultimatum games: Information, fairness, expectations, and lowest acceptable ofers. Journal of Economic Behavior and Organization, 27(3):345–364.

Yi, K. (2005). Quantal-response equilibrium models of the ultimatum bargaining game. Games and Economic Behavior, 51(2):324–348.

Yildirim, H. (2007). Proposal power and majority rule in multilateral bargaining with costly recognition. Journal of Economic Theory, 136(1):167–196.

Yildiz, M. (2003). Bargaining without a common prior-an immediate agreement theorem. Econometrica, 71(3):793–811.