31,596 research outputs found
Structure of Extreme Correlated Equilibria: a Zero-Sum Example and its Implications
We exhibit the rich structure of the set of correlated equilibria by
analyzing the simplest of polynomial games: the mixed extension of matching
pennies. We show that while the correlated equilibrium set is convex and
compact, the structure of its extreme points can be quite complicated. In
finite games the ratio of extreme correlated to extreme Nash equilibria can be
greater than exponential in the size of the strategy spaces. In polynomial
games there can exist extreme correlated equilibria which are not finitely
supported; we construct a large family of examples using techniques from
ergodic theory. We show that in general the set of correlated equilibrium
distributions of a polynomial game cannot be described by conditions on
finitely many moments (means, covariances, etc.), in marked contrast to the set
of Nash equilibria which is always expressible in terms of finitely many
moments
On the Structure of the Set of Correlated Equilibria in Two-by-Two Bimatrix Games
The paper studies the structure of the set of correlated equilibria for 2x2-bimatrix games. We find that the extreme points of the (convex) set of correlated equilibria can be determined very easily from the Nash equilibria of the game
On the Structure of the Set of Correlated Equilibria in Two-by-Two Bimatrix Games
The paper studies the structure of the set of correlated equilibria for 2x2-bimatrix games. We find that the extreme points of the (convex) set of correlated equilibria can be determined very easily from the Nash equilibria of the game.Correlated equilibrium;bimatrix game
Is Having a Unique Equilibrium Robust?
We investigate whether having a unique equilibrium (or a given number of
equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium
and correlated equilibrium. We show that the set of n-player finite games with
a unique correlated equilibrium is open, while this is not true of Nash
equilibrium for n>2. The crucial lemma is that a unique correlated equilibrium
is a quasi-strict Nash equilibrium. Related results are studied. For instance,
we show that generic two-person zero-sum games have a unique correlated
equilibrium and that, while the set of symmetric bimatrix games with a unique
symmetric Nash equilibrium is not open, the set of symmetric bimatrix games
with a unique and quasi-strict symmetric Nash equilibrium is
Nash Equilibria in the Response Strategy of Correlated Games
In nature and society problems arise when different interests are difficult
to reconcile, which are modeled in game theory. While most applications assume
uncorrelated games, a more detailed modeling is necessary to consider the
correlations that influence the decisions of the players. The current theory
for correlated games, however, enforces the players to obey the instructions
from a third party or "correlation device" to reach equilibrium, but this
cannot be achieved for all initial correlations. We extend here the existing
framework of correlated games and find that there are other interesting and
previously unknown Nash equilibria that make use of correlations to obtain the
best payoff. This is achieved by allowing the players the freedom to follow or
not to follow the suggestions of the correlation device. By assigning
independent probabilities to follow every possible suggestion, the players
engage in a response game that turns out to have a rich structure of Nash
equilibria that goes beyond the correlated equilibrium and mixed-strategy
solutions. We determine the Nash equilibria for all possible correlated
Snowdrift games, which we find to be describable by Ising Models in thermal
equilibrium. We believe that our approach paves the way to a study of
correlations in games that uncovers the existence of interesting underlying
interaction mechanisms, without compromising the independence of the players
Openness of the set of games with a unique correlated equilibrium
La question que cet article cherche à résoudre est de savoir si le fait d'avoir un équilibre unique (ou un nombre donné d'équilibre) est une propriété robuste à la perturbation des paiements. Cette question est étudiée pour des jeux sous forme normale, et à la fois pour le concept d'équilibre de Nash et pour celui d'équibre corrélé. Nous montrons que l'ensemble des jeux finis à n-joueurs ayant un unique équilibre corrélé est ouvert, ce qui n'est pas vrai pour l'équilibre de Nash quand n>2. Le lemme crucial est qu'un équilibre corrélé unique est un équilibre de Nash quasi-strict. Des résultats liés sont également présentés. Nous montrons notamment que les jeux à deux joueurs et à somme nulle génériques ont un unique équilibre corrélé, et étudions le caractère ouvert de divers ensembles de jeux définis par le nombre et les propriétés de leurs équilibres (équilibres stricts, quasi-strict, symétriques, etc.).
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