226 research outputs found
The Query Complexity of Correlated Equilibria
We consider the complexity of finding a correlated equilibrium of an
-player game in a model that allows the algorithm to make queries on
players' payoffs at pure strategy profiles. Randomized regret-based dynamics
are known to yield an approximate correlated equilibrium efficiently, namely,
in time that is polynomial in the number of players . Here we show that both
randomization and approximation are necessary: no efficient deterministic
algorithm can reach even an approximate correlated equilibrium, and no
efficient randomized algorithm can reach an exact correlated equilibrium. The
results are obtained by bounding from below the number of payoff queries that
are needed
The Better Half of Selling Separately
Separate selling of two independent goods is shown to yield at least 62% of
the optimal revenue, and at least 73% when the goods satisfy the Myerson
regularity condition. This improves the 50% result of Hart and Nisan (2017,
originally circulated in 2012)
Evolutionarily stable strategies of random games, and the vertices of random polygons
An evolutionarily stable strategy (ESS) is an equilibrium strategy that is
immune to invasions by rare alternative (``mutant'') strategies. Unlike Nash
equilibria, ESS do not always exist in finite games. In this paper we address
the question of what happens when the size of the game increases: does an ESS
exist for ``almost every large'' game? Letting the entries in the
game matrix be independently randomly chosen according to a distribution ,
we study the number of ESS with support of size In particular, we show
that, as , the probability of having such an ESS: (i) converges to
1 for distributions with ``exponential and faster decreasing tails'' (e.g.,
uniform, normal, exponential); and (ii) converges to for
distributions with ``slower than exponential decreasing tails'' (e.g.,
lognormal, Pareto, Cauchy). Our results also imply that the expected number of
vertices of the convex hull of random points in the plane converges to
infinity for the distributions in (i), and to 4 for the distributions in (ii).Comment: Published in at http://dx.doi.org/10.1214/07-AAP455 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Cooperative games in strategic form
In this paper we view bargaining and cooperation as an interaction superimposed on a strategic form game. A multistage bargaining procedure for N players, the “proposer commitment” procedure, is presented. It is inspired by Nash’s two-player variable-threat model; a key feature is the commitment to “threats.” We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies the traditional coalitional function may not be adequate when utilities are not transferable.Bargaining, Commitment, Nash variable threat
Stochastic uncoupled dynamics and Nash equilibrium
In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence to Nash equilibria, and present a number of possibility and impossibility results. Basically, we show that if in addition to random moves some recall is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it su±ces to recall the last two periods of play.Uncoupled, Nash equilibrium, stochastic dynamics, bounded recall
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