We examine a voluntary participation problem in public good provision when each agent has a demand level for a public good. The demand level of an agent for a public good is the minimum level of the public good from which she can receive a positive benefit. We show that in the voluntary participation game, the efficient level of the public good is provided at a subgame perfect Nash equilibrium....

We focus on the problem of computing an -Nash equilibrium of a bimatrix game, when is an absolute constant. We present a simple algorithm for computing a 3 4 -Nash equilibrium for any bimatrix game in strongly polynomial time and we next show how to extend this algorithm so as to obtain a (potentially stronger) parameterized approximation. Namely, we present an algorithm that computes a 2+λ 4 -...

It is known that Nash equilibria and approximate Nash equilibria not necessarily optimize social optima of bimatrix games. In this paper, we show that for every fixed ε > 0, every bimatrix game (with values in [0, 1]) has an ε-approximate Nash equilibrium with the total payoff of the players at least a constant factor, (1 − √ 1− ε), of the optimum. Furthermore, our result can be made algorithmi...

The Complexity of Nash Equilibria by Constantinos Daskalakis Doctor of Philosophy in Computer Science University of California, Berkeley Professor Christos H. Papadimitriou, Chair The Internet owes much of its complexity to the large number of entities that run it and use it. These entities have different and potentially conflicting interests, so their interactions are strategic in nature. Ther...

The Complexity of Nash Equilibria by Constantinos Daskalakis Doctor of Philosophy in Computer Science University of California, Berkeley Professor Christos H. Papadimitriou, Chair The Internet owes much of its complexity to the large number of entities that run it and use it. These entities have different and potentially conflicting interests, so their interactions are strategic in nature. Ther...

A mechanism implements a social choice correspondence f in mixed Nash equilibrium if, at any preference profile, the set of all (pure and mixed) Nash equilibrium outcomes coincides with the set of f -optimal alternatives for all cardinal representations of the preference profile. Unlike Maskin’s definition, our definition does not require each optimal alternative to be the outcome of a pure equ...

We compare two different formulations of the deblurring problem: one (variational) is de ned by minimization of a single objective function and another one is based on a generalized Nash equilibrium balance of two objective functions. The latter results in the algorithm where the denoising and deblurring operations are decoupled. For image modeling we use the recent BM3D-frames. Simulation expe...

According to conventional wisdom, Nash equilibrium in a game “involves” common knowledge of the payoff functions, of the rationality of the players, and of the strategies played. The basis for this wisdom is explored, and it turns out that considerably weaker conditions suffice. First, note that if each player is rational and knows his own payoff function, and the strategy choices of the player...

We provide a natural learning process in which the joint frequency of (time-averaged) empirical play converges into the set of convex combinations of Nash equilibria. Furthermore, the actual distribution of players’ actions is close to some (approximate) Nash equilibria on most rounds (on all but a vanishing fraction of the rounds). In this process, all players rationally choose their actions u...