TY - GEN

T1 - Regret minimization and the price of total anarchy

AU - Blum, Avrim

AU - Hajiaghayi, Mohammad Taghi

AU - Roth, Aaron

AU - Ligett, Katrina

PY - 2008

Y1 - 2008

N2 - We propose weakening the assumption made when studying the price of anarchy: Rather than assume that self-interested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret minimization can be done via simple, efficient algorithms even in many settings where the number of action choices for each player is exponential in the natural parameters of the problem. We prove that despite our weakened assumptions, in several broad classes of games, this "price of total anarchy" matches the Nash price of anarchy, even though play may never converge to Nash equilibrium. In contrast to the price of anarchy and the recently introduced price of sinking [15], which require all players to behave in a prescribed manner, we show that the price of total anarchy is in many cases resilient to the presence of Byzantine players, about whom we make no assumptions. Finally, because the price of total anarchy is an upper bound on the price of anarchy even in mixed strategies, for some games our results yield as corollaries previously unknown bounds on the price of anarchy in mixed strategies.

AB - We propose weakening the assumption made when studying the price of anarchy: Rather than assume that self-interested players will play according to a Nash equilibrium (which may even be computationally hard to find), we assume only that selfish players play so as to minimize their own regret. Regret minimization can be done via simple, efficient algorithms even in many settings where the number of action choices for each player is exponential in the natural parameters of the problem. We prove that despite our weakened assumptions, in several broad classes of games, this "price of total anarchy" matches the Nash price of anarchy, even though play may never converge to Nash equilibrium. In contrast to the price of anarchy and the recently introduced price of sinking [15], which require all players to behave in a prescribed manner, we show that the price of total anarchy is in many cases resilient to the presence of Byzantine players, about whom we make no assumptions. Finally, because the price of total anarchy is an upper bound on the price of anarchy even in mixed strategies, for some games our results yield as corollaries previously unknown bounds on the price of anarchy in mixed strategies.

KW - Algorithmic game theory

KW - Nash equilibria

KW - Regret minimization

UR - http://www.scopus.com/inward/record.url?scp=57049137244&partnerID=8YFLogxK

U2 - 10.1145/1374376.1374430

DO - 10.1145/1374376.1374430

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AN - SCOPUS:57049137244

SN - 9781605580470

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 373

EP - 382

BT - STOC'08

PB - Association for Computing Machinery

T2 - 40th Annual ACM Symposium on Theory of Computing, STOC 2008

Y2 - 17 May 2008 through 20 May 2008

ER -