Does Nash Envy Immunity

The most popular stability notion in games should be Nash equilibrium under the rationality of players who maximize their own payoff individually. In contrast, in many scenarios, players can be (partly) irrational with some unpredictable factors. Hence a strategy profile can be more robust if it is resilient against certain irrational behaviors. In this paper, we propose a stability notion that is resilient against envy. A strategy profile is said to be envy-proof if each player cannot gain a competitive edge with respect to the change in utility over the other players by deviation. Together with Nash equilibrium and another stability notion called immunity, we show how these separate notions are related to each other, whether they exist in games, and whether and when a strategy profile satisfying these notions can be efficiently found. We answer these questions by starting with the general two player game and extend the discussion for the approximate stability and for the corresponding fault-tolerance notions in multi-player games.

[1]  R. Aumann Acceptable points in games of perfect information. , 1960 .

[2]  Eitan Zemel,et al.  Nash and correlated equilibria: Some complexity considerations , 1989 .

[3]  D. Kempe,et al.  The effects of altruism and spite on games , 2011 .

[4]  Aaron Roth,et al.  The Price of Malice in Linear Congestion Games , 2008, WINE.

[5]  Stefan Schmid,et al.  The Price of Malice: A Game-Theoretic Framework for Malicious Behavior in Distributed Systems , 2009, Internet Math..

[6]  Silvio Micali Rational and resilient protocols , 2014, PODC '14.

[7]  Jonathan Katz,et al.  Bridging Game Theory and Cryptography: Recent Results and Future Directions , 2008, TCC.

[8]  Omer Reingold,et al.  Fault tolerance in large games , 2008, EC '08.

[9]  Shien Jin Ong,et al.  Fairness with an Honest Minority and a , 2008 .

[10]  W. Hoeffding Probability Inequalities for sums of Bounded Random Variables , 1963 .

[11]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Aranyak Mehta,et al.  Playing large games using simple strategies , 2003, EC '03.

[13]  J. Wooders,et al.  Coalition-Proof Equilibrium , 1996 .

[14]  Aaron Roth,et al.  Mechanism design in large games: incentives and privacy , 2012, ITCS.

[15]  Jonathan Katz,et al.  Byzantine Agreement with a Rational Adversary , 2012, ICALP.

[16]  Omer Reingold,et al.  Partial exposure in large games , 2010, Games Econ. Behav..

[17]  Vincent Conitzer,et al.  New complexity results about Nash equilibria , 2008, Games Econ. Behav..

[18]  Pablo Azar,et al.  Super-efficient rational proofs , 2013, EC '13.

[19]  Moshe Babaioff,et al.  Congestion games with malicious players , 2007, EC '07.

[20]  Silvio Micali,et al.  Rational proofs , 2012, STOC '12.