Multi-Player War of Attrition with Asymmetric Incomplete Information

Li, Hongcheng (2019): Multi-Player War of Attrition with Asymmetric Incomplete Information.

Abstract

This paper models a multi-player war of attrition game with asymmetric incomplete information on the private provision of one public good to investigate the effect of ex-ante asymmetry. In the unique equilibrium, asymmetry leads to a stratified behavior pattern such that one player provides the good instantly with a positive probability, while each of the others has no probability of provision before a certain moment which is idiosyncratic. Comparative statics show that one with less patience, lower cost of provision, and higher reputation in valuation provides uniformly faster. The cost of delay is mainly determined by the strongest type, namely the highest type of the instant-exit player. This paper considers two types of introduction of asymmetry: raising the strongest type tends to improve efficiency, whereas controlling the strongest type aligns the effect of asymmetry with the sign of an intuitive measure of the cost of symmetry.

• Item Type: MPRA Paper
• Language: English
• Keywords: war of attrition, public good, ex-ante asymmetry, multiple players, incomplete information
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D74 - Conflict ; Conflict Resolution ; Alliances ; Revolutions

References

Abreu, Dilip and Faruk Gul (2000), "Bargaining and reputation." Econometrica, 68, 85-117.

Alesina, Alberto and Allan Drazen (1991), "Why Are Stabilizations Delayed?." American Economic Review, 81, 1170-1188.

Bergstrom, Theodore, Lawrence Blume, and Hal Varian (1986), "On the Private Provision of Public Goods." Journal of Public Economics, 29, 25-49.

Bilodeau, Marc and Al Slivinski (1996), Toilet Cleaning and Department Chairing: Volunteering a Public Service." Journal of Public Economics, 59, 299-308.

Bliss, Christopher and Barry Nalebuff (1984), "Dragon-Slaying and Ballroom Dancing: The Private Supply of a Public Good." Journal of Public Economics, 25, 1-12.

Bulow, Jeremy and Paul Klemperer (1999), "The Generalized War of Attrition." American Economic Review, 89, 175-189.

Casella, Alessandra and Barry Eichengreen (1996), "Can Foreign Aid Accelerate Stabilisation." The Economic Journal, 106, 605-619.

Fudenberg, Drew and Jean Tirole (1986), "A Theory of Exit in Duopoly." Econometrica, 54, 943-960.

Ghemawat, Pankaj and Barry Nalebuff (1985), "Exit." RAND Journal of Economics, 16.2, 184-194.

Ghemawat, Pankaj and Barry Nalebuff (1990), "The Devolution of Declining Industries." The Quarterly Journal of Economics, 105, 167-186.

Grandstein, Mark (1992), "Time Dynamics and Incomplete Information in the Private Provision of Public Goods." Journal of Political Economy, 100, 581-597.

Hillman, Arye L. and John G. Riley (1989), "Politically Contestable Rents and Transfers." Economics & Politics, 1, 17-39.

Horner, Johannes and Nicolas Sahuguet (2010), "A War of Attrition with Endogenous Effort Levels." Economic Theory, 47, 1-27.

Kambe, Shinsuke (1999), "Bargaining with Imperfect Commitment." Games and Economic Behavior, 28, 217-237.

Kambe, Shinsuke (2019), "An N-Person War of Attrition with the Possibility of a Non-Compromising Type." Theoretical Economics.

Kornhauser, Lewis, Ariel Rubinstein, and Charles Wilson (1988), "Reputation and Patience in the'War of Attrition'." Economica, 56, 15-24.

Myatt, David P. (2005), "Instant Exit from the Asymmetric War of Attrition." University of Oxford, Department of Economics, 160.

Nalebuff, Barry and John Riley (1985), "Asymmetric Equilibria in the War of Attrition." Journal of Theoretical Biology, 113, 517-527.

Ponsati, Clara and Jozsef Sakovics (1995), "The War of Attrition with Incomplete Information." Mathematical Social Sciences, 29, 239-254.

Ponsati, Clara and Jozsef Sakovics (1996), "Multiperson Bargaining over Two Alternatives." Games and Economic Behavior, 12, 226-244.

Powell, Robert (2017), "Taking Sides in Wars of Attrition." American Political Science Review, 111, 219-236.

Riley, John G. (1980), "Strong Evolutionary Equilibrium and the War of Attrition." Journal of Theoretical Biology, 82, 383-400.

Sahuguet, Nicolas (2006), "Volunteering for Heterogeneous Tasks." Games and Economic Behavior, 56, 333-349.

Whinston, Michael D. (1988), "Exit with Multiplant Firms." RAND Journal of Economics, 19, 568-588.