The second-price auction solves King Solomon's dilemma

TL;DR

This paper demonstrates that a modified second-price auction with a participation fee and optional abstention effectively allocates identical objects to top valuation agents, ensuring strategic stability and resistance to collusion.

Contribution

It introduces a simple, strategic mechanism modification that guarantees the desired allocation and stability in auction settings.

Findings

The modified auction achieves the targeted allocation in equilibrium.

The mechanism prevents profitable deviations through collusion or bribery.

It ensures strategic stability in the allocation process.

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.