Equilibrium solution to the lowest unique positive integer game

• Published in 2010
• Added on 2012-06-22

We address the equilibrium concept of a reverse auction game so that no one can enhance the individual payoff by a unilateral change when all the others follow a certain strategy. In this approach the combinatorial possibilities to consider become very much involved even for a small number of players, which has hindered a precise analysis in previous works. We here present a systematic way to reach the solution for a general number of players, and show that this game is an example of conflict between the group and the individual interests.

Links

• http://arxiv.org/abs/1001.1065
• http://arxiv.org/pdf/1001.1065v1

Other information

BibTeX entry

@article{Baek2010,
	key = {Baek2010},
	type = {article},
	title = {Equilibrium solution to the lowest unique positive integer game},
	author = {Baek, Seung Ki and Bernhardsson, Sebastian},
	abstract = {We address the equilibrium concept of a reverse auction game so that no one can enhance the individual payoff by a unilateral change when all the others follow a certain strategy. In this approach the combinatorial possibilities to consider become very much involved even for a small number of players, which has hindered a precise analysis in previous works. We here present a systematic way to reach the solution for a general number of players, and show that this game is an example of conflict between the group and the individual interests.},
	comment = {},
	date_added = {2012-06-22},
	date_published = {2010-01-01},
	urls = {http://arxiv.org/abs/1001.1065,http://arxiv.org/pdf/1001.1065v1},
	collections = {Protocols and strategies,Fun maths facts},
	archivePrefix = {arXiv},
	arxivId = {1001.1065},
	doi = {10.1142/S0219477510000071},
	eprint = {1001.1065},
	keywords = {game,lowest unique positive integer,nash equilibrium,projection operator},
	month = {jan},
	number = 0,
	pages = 8,
	url = {http://arxiv.org/abs/1001.1065 http://arxiv.org/pdf/1001.1065v1},
	volume = 0,
	year = 2010,
	primaryClass = {math.CO},
	urldate = {2012-06-22}
}