4,679 research outputs found
Iterated Strict Dominance in General Games
We offer a definition of iterated elimination of strictly dominated strategies (IESDS) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS by means of a "stability" criterion, and offer a sufficient and necessary epistemic condition for IESDS. We show by an example that IESDS may generate spurious Nash equilibria in the class of Reny's better-reply secure games. We provide sufficient/necessary conditions under which IESDS preserves the set of Nash equilibria. Nous donnons une définition de l’élimination itérative des stratégies qui sont strictement donimées (EISSD) pour les jeux avec un nombre fini (ou infini) de joueurs , des ensembles de stratégies compactes (ou non-compactes), et des fonctions de gains continues (ou non-continues). Le processus EISSD est bien défini et indépendant de l’ordre d’élimination. Nous donnons une caractérisation du processus EISSD en utilisant un critère de stabilité et offrons une condition épistémologique. Nous démontrons que le processus EISSD peut produire des équilibres faux dans la classe des jeux de meilleures réponses sécuritaires de Reny. Nous donnons des conditions nécessaires et suffisantes pour que le processus EISSD conserve l’ensemble des équilibre de Nash.game theory, strict dominance, iterated elimination, Nash equilibrium, Reny's better-reply secure games., théorie des jeux, dominance stricte, élimination itérative, équilibre de Nash, jeux de meilleures réponses sécuritaires de Reny
Incomplete Information and Iterated Strict Dominance
The solution concept of iterated strict dominance for static games with complete information recursively deletes choices that are inferior. Here, we devise such an algorithm for the more general case of incomplete information. The ensuing solution concept of generalized iterated strict dominance is characterized in terms of common belief in rationality as well as in terms of best response sets. Besides, we provide doxastic conditions that are necessary and sufficient for modelling complete information from a one-person perspective
The Many Faces of Rationalizability
The rationalizability concept was introduced in \cite{Ber84} and
\cite{Pea84} to assess what can be inferred by rational players in a
non-cooperative game in the presence of common knowledge. However, this notion
can be defined in a number of ways that differ in seemingly unimportant minor
details. We shed light on these differences, explain their impact, and clarify
for which games these definitions coincide. Then we apply the same analysis to
explain the differences and similarities between various ways the iterated
elimination of strictly dominated strategies was defined in the literature.
This allows us to clarify the results of \cite{DS02} and \cite{CLL05} and
improve upon them. We also consider the extension of these results to strict
dominance by a mixed strategy. Our approach is based on a general study of the
operators on complete lattices. We allow transfinite iterations of the
considered operators and clarify the need for them. The advantage of such a
general approach is that a number of results, including order independence for
some of the notions of rationalizability and strict dominance, come for free.Comment: 39 pages, appeared in The B.E. Journal of Theoretical Economics: Vol.
7 : Iss. 1 (Topics), Article 18. Available at:
http://www.bepress.com/bejte/vol7/iss1/art1
On Iterated Dominance, Matrix Elimination, and Matched Paths
We study computational problems arising from the iterated removal of weakly
dominated actions in anonymous games. Our main result shows that it is
NP-complete to decide whether an anonymous game with three actions can be
solved via iterated weak dominance. The two-action case can be reformulated as
a natural elimination problem on a matrix, the complexity of which turns out to
be surprisingly difficult to characterize and ultimately remains open. We
however establish connections to a matching problem along paths in a directed
graph, which is computationally hard in general but can also be used to
identify tractable cases of matrix elimination. We finally identify different
classes of anonymous games where iterated dominance is in P and NP-complete,
respectively.Comment: 12 pages, 3 figures, 27th International Symposium on Theoretical
Aspects of Computer Science (STACS
The Role of Monotonicity in the Epistemic Analysis of Strategic Games
It is well-known that in finite strategic games true common belief (or common
knowledge) of rationality implies that the players will choose only strategies
that survive the iterated elimination of strictly dominated strategies. We
establish a general theorem that deals with monotonic rationality notions and
arbitrary strategic games and allows to strengthen the above result to
arbitrary games, other rationality notions, and transfinite iterations of the
elimination process. We also clarify what conclusions one can draw for the
customary dominance notions that are not monotonic. The main tool is Tarski's
Fixpoint Theorem.Comment: 20 page
Iterated weak dominance and interval-dominance supermodular games
This paper extends Milgrom and Robert's treatment of supermodular games in two ways. It points out that their main characterization result holds under a weaker assumption. It refines the arguments to provide bounds on the set of strategies that survive iterated deletion of weakly dominated strategies. I derive the bounds by iterating the best-response correspondence. I give conditions under which they are independent of the order of deletion of dominated strategies. The results have implications for equilibrium selection and dynamic stability in games
The Complexity of Iterated Strategy Elimination
We consider the computational complexity of the question whether a certain
strategy can be removed from a game by means of iterated elimination of
dominated strategies. In particular, we study the influence of different
definitions of domination and of the number of different payoff values. In
addition, the consequence of restriction to constant-sum games is shown
Epistemic Analysis of Strategic Games with Arbitrary Strategy Sets
We provide here an epistemic analysis of arbitrary strategic games based on
the possibility correspondences. Such an analysis calls for the use of
transfinite iterations of the corresponding operators. Our approach is based on
Tarski's Fixpoint Theorem and applies both to the notions of rationalizability
and the iterated elimination of strictly dominated strategies.Comment: 8 pages Proc. of the 11th Conference on Theoretical Aspects of
Rationality and Knowledge (TARK XI), 2007. To appea
Direct Proofs of Order Independence
We establish a generic result concerning order independence of a dominance
relation on finite games. It allows us to draw conclusions about order
independence of various dominance relations in a direct and simple way.Comment: 9 page
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