The second-price auction solves King Solomon's dilemma

Mihara, H. Reiju (2008): The second-price auction solves King Solomon's dilemma.

Abstract

Consider the problem of allocating k identical, indivisible objects among n agents, where k is less than n. The planner's objective is to give the objects to the top k valuation agents at zero costs to the planner and the agents. Each agent knows her own valuation of the object and whether it is among the top k. Modify the (k+1)st-price sealed-bid auction by introducing a small participation fee and the option not to participate in it. This strikingly simple mechanism (modified auction) implements the desired outcome in iteratively weakly undominated strategies. Moreover, no pair of agents can profitably deviate from the equilibrium by coordinating their strategies or bribing each other.

• Item Type: MPRA Paper
• Language: English
• Keywords: Solomon's problem; implementation; entry fees; Olszewski's mechanism; collusion; bribes
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; D - Microeconomics > D6 - Welfare Economics > D61 - Allocative Efficiency ; Cost-Benefit Analysis; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

[1] P. K. Bag and H. Sabourian. Distributing awards efficiently: More on King Solomon’s problem. Games and Economic Behavior, 53:43–58, 2005.

[2] J. Glazer and C.-T. A. Ma. Efficient allocation of a “prize”—King Solomon’s dilemma. Games and Economic Behavior, 1:222–233, 1989.

[3] J. Moore. Implementation, contracts, and renegotiation in environments with complete information. In J.-J. Laffont, editor, Advances in Eco- nomic Theory: Sixth World Congress, Volume I, chapter 5, pages 182– 282. Cambridge University Press, Cambridge, 1992.

[4] W. Olszewski. A simple and general solution to King Solomon’s problem. Games and Economic Behavior, 42:315–318, 2003.

[5] M. Perry and P. J. Reny. A general solution to King Solomon’s dilemma. Games and Economic Behavior, 26:279–285, 1999.

[6] C.-Z. Qin and C.-L. Yang. Make a guess: A robust mechanism for King Solomon’s dilemma. Economic Theory, 2007. DOI 10.1007/s00199-007- 0304-x.