The second-price auction solves King Solomon's dilemma

Mihara, H. Reiju (2011): The second-price auction solves King Solomon's dilemma. Forthcoming in: Japanese Economic Review

Abstract

The planner wants to give k identical, indivisible objects to the top k valuation agents at zero costs. 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 simple mechanism implements the desired outcome in iteratively 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; mechanism design; implementation; iterative elimination of weakly dominated strategies; 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

Bag, P. K. and H. Sabourian (2005) “Distributing Awards Efficiently: More on King Solomon’s Problem”, Games and Economic Behavior, Vol. 53, pp. 43–58.

Glazer, J. and C.-T. A. Ma (1989) “Efficient Allocation of a “Prize”—King Solomon’s Dilemma”, Games and Economic Behavior, Vol. 1, pp. 222–233.

Moore, J. (1992) “Implementation, Contracts, and Renegotiation in Environments with Complete Information”, in Laffont, J.-J. ed. Advances in Economic Theory: Sixth World Congress, Volume I, Cambridge: Cambridge University Press, Chap. 5, pp. 182–282.

Moulin, H. (1979) “Dominance Solvable Voting Schemes”, Econometrica, Vol. 47, pp. 1337–1351.

Olszewski, W. (2003) “A simple and general solution to King Solomon’s problem”, Games and Economic Behavior, Vol. 42, pp. 315–318.

Perry, M. and P. J. Reny (1999) “A General Solution to King Solomon’s Dilemma”, Games and Economic Behavior, Vol. 26, pp. 279–285.

Qin, C.-Z. and C.-L. Yang (2009) “Make a Guess: A Robust Mechanism for King Solomon’s Dilemma”, Economic Theory, Vol. 39, pp. 259–268.