Priority Right Auction for Komi Setting

Abstract

We develop an auction system that determines a fair number of komi for holding black stones in a GO game, and hence the right to the first move. It is modeled as a priority right pricing problem that demands for budget-balanced and egalitarian conditions, where a negative utility is associated with the losers.

We first derive an impossibility result for strategy-proof deterministic protocols. We then design a randomize protocol under which being truthful is always a (weakly) best response for every player. Moreover, the conditions of egalitarian and budget-balancedness are achieved. One can further show that being truthful is a strict best response to another truthful bidder, when the players are risk-averse with respect to their differences of utilities.

A particularly interesting technical result we are able to establish is the uniqueness of such a randomized protocol. We then derive that there is no randomized strategy-proof protocol for this problem. Our results can be generalized to many players.

This study captures the issue of pricing priority right in a competitive environment and has other applications in games, political sciences and economics.

Keywords: priority right, komi, egalitarian, budget-balancedness, strategy-proof

JEL Classification: C72, D44, D63