Expected Utility Preferences versus Prospect Theory Preferences in Bargaining

Khan, Abhimanyu (2018): Expected Utility Preferences versus Prospect Theory Preferences in Bargaining.

Abstract

Are individuals always better off when their preferences can be represented by expected utility? I study this question in a bargaining game where individuals bargain over a pie of fixed size, and I contrast the share received in the long-run by expected utility maximisers with the share they would receive if their preferences were described by prospect theory preferences instead when, in either case, they bargain with expected utility maximisers. I present a necessary and sufficient condition for individuals to obtain a higher share of the pie if their preferences obey prospect theory rather than expected utility. I decompose the effect that the three features that characterise prospect theory preferences -- reference point dependence, loss-aversion and probability weighting -- have on the bargaining outcome, and show that loss-aversion does not have any effect on the outcome of the bargaining process, reference-point dependent preference confers an unambiguous advantage and probability weighting is unambiguously disadvantageous. This ties in with the main result outlined earlier: if the upward pull of reference point dependence is relatively stronger than the downward push of probability weighting, then individuals are better off with prospect theory preferences than with expected utility preferences, and vice-versa.

• Item Type: MPRA Paper
• Language: English
• Keywords: bargaining, expected utility prospect theory, reference point dependence, loss aversion, probability weighting
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory; D - Microeconomics > D0 - General > D01 - Microeconomic Behavior: Underlying Principles; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness

References

Allais M. (1953). Le comportement de l'homme rationnel devant le risque: critique des postulats et axiomes de l'école Américaine. Econometrica. 21 (4): 503–546.

Green J (1987). ``Making Book Against Oneself," The Independence Axiom, and Nonlinear Utility Theory. Quarterly Journal of Economics 102 (4): 785-796

Ellison G (2000). Basins of Attraction, Long Run Stochastic Stability, and the Speed of Step-by-Step Evolution. Review of Economic Studies 67 (1): 17-45

Kahnemann D and Tversky A (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica 47 (2): 263-292

Kahnemann D and Tversky A (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty 5: 297-323

Kandori M, Mailath G and Rob R (1993). Learning, Mutation, and Long Run Equilibria in Games. Econometrica 61 (1): 29-56

Koszegi B and Rabin M (2006). A Model of Reference Dependent Utility. Quarterly Journal of Economics 121 (4): 1133-1165

Machina M (1989). Dynamic Consistency and Non-Expected Utility Models of Choice Under Uncertainty. Journal of Economic Literature 27 (4): 1622-1668

Nash, J (1950). The Bargaining Problem. Econometrica 18 (2): 155-162

Quiggin J (1982). A Theory of Anticipated Utility. Journal of Economic Behaviour and Organisation 3 (4): 323-343

von Nuemann J and Morgenstern O (1944). Theory of Games and Economic Behaviour. Princeton University Press

Young HP (1993a). The evolution of conventions. Econometrica 61 (1): 57-84

Young HP (1993b). An evolutionary model of bargaining. Journal of Economic Theory 59 (1): 145-168