We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players <i>n</i> and a constant number of actions <i>m</i>. Our main result states that even for constant <i>ε</i>, the query complexity of an <i>ε</i>-well-supported Nash equilibrium is exponential in <i>n</i>.
Completely uncoupled dynamic is a repited play of a game, when in every given time the action of every player depends only on his own payo¤s in the past. In this paper we try to formulate the minimal set of necessary conditions that guarantee a convergence to a Nash equilibrium in completely uncoupled model. The main results are: 1. The convergence to a… (More)
We study lower bounds on the query complexity of determining correlated equilibrium. In particular, we consider a query model in which an <i>n</i>-player game is specified via a black box that returns players' utilities at pure action profiles. In this model, we establish that in order to compute a correlated equilibrium, any <i>deterministic</i> algorithm… (More)
We study the problem of reaching a pure Nash equilibrium in multi-person games that are repeatedly played, under the assumption of uncoupledness: EVERY player knows only his own payoff function. We consider strategies that can be implemented by finite-state automata, and characterize the minimal number of states needed in order to guarantee that a pure Nash… (More)
We prove that in every normal form <i>n</i>-player game with <i>m</i> actions for each player, there exists an approximate Nash equilibrium in which each player randomizes uniformly among a set of <i>O</i>(log <i>m</i> + log <i>n</i>) pure actions. This result induces an <i>O</i>(<i>N</i> <sup>log log <i>N</i></sup>)-time algorithm for computing an… (More)
We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(log m+log n) pure strategies. This result induces an N log log N algorithm for computing an approximate Nash equilibrium in games where the number of actions is polynomial in the… (More)
We conjecture that PPAD has a PCP-like complete problem, seeking a near equilibrium in which all but very few players have very little incentive to deviate. We show that, if one assumes that this problem requires exponential time, several open problems in this area are settled. The most important implication, proved via a " birthday repetition " reduction,… (More)
Communication is a crucial ingredient in every kind of collaborative work. But what is the least possible amount of communication required for a given task? We formalize this question by introducing a new framework for distributed computation, called oblivious protocols. We investigate the power of this model by considering two concrete examples, the… (More)