共查询到20条相似文献,搜索用时 15 毫秒
1.
Stephen Morris 《International Journal of Game Theory》1999,28(3):385-408
Suppose we replace “knowledge” by “belief with probability p” in standard definitions of common knowledge. Very different notions arise depending on the exact definition of common knowledge
used in the substitution. This paper demonstrates those differences and identifies which notion is relevant in each of three
contexts: equilibrium analysis in incomplete information games, best response dynamics in incomplete information games, and
agreeing to disagree/no trade results. 相似文献
2.
David McAdams 《International Journal of Game Theory》2007,35(3):427-453
I study monotonicity of equilibrium strategies in first-price auctions with asymmetric bidders, risk aversion, affiliated
types, and interdependent values. Every mixed-strategy equilibrium is shown to be outcome-equivalent to a monotone pure-strategy
equilibrium under the “priority rule” for breaking ties. This provides a missing link to establish uniqueness in the “general
symmetric model” of Milgrom and Weber (Econometrica 50:1089–1122, 1982). Non-monotone equilibria can exist under the “coin-flip
rule” but they are distinguishable: all non-monotone equilibria have positive probability of ties whereas all monotone equilibria
have zero probability of ties. This provides a justification for the standard empirical practice of restricting attention
to monotone strategies.
Hendricks et al. (2003) provide an overview of recent empirical work. For a survey of experimental work, see Kagel and Levin
(2002). 相似文献
3.
Dr. J. Cave 《International Journal of Game Theory》1987,16(1):15-41
In this paper, we discuss equilibrium and perfect equilibrium in a simplified model of the supergame. We assume that players can observe the mixed moves employed by all players at each previous stage. For this model, we obtain a complete characterization of the set of equilibrium outcomes, and a fairly weak sufficient condition for this set to coincide with the set of perfect equilibrium outcomes.Inter alia, simple proofs of the Folk Theorem and the result that the requirement of perfection does not eliminate any equilibrium outcomes for the undiscounted supergame are presented. 相似文献
4.
We demonstrate that, if there are sufficiently many players, any Bayesian equilibrium of an incomplete information game can
be “ε-purified” . That is, close to any Bayesian equilibrium there is an approximate Bayesian equilibrium in pure strategies. Our
main contribution is obtaining this result for games with a countable set of pure strategies. In order to do so we derive
a mathematical result, in the spirit of the Shapley–Folkman Theorem, permitting countable strategy sets. Our main assumption
is a “large game property,” dictating that the actions of relatively small subsets of players cannot have large affects on
the payoffs of other players.
E. Cartwright and M. Wooders are indebted to Phillip Reny, Frank Page and two anonymous referees for helpful comments. 相似文献
5.
V. S. Levchenkov 《Computational Mathematics and Modeling》2008,19(1):102-115
A new approach to the solution of one-step games is constructed, without using the concept of mixed strategy. The notion of
a “set” solution of a bimatrix game is defined. It is shown that this solution always exists and may be found by a finite
procedure. Examples are given illustrating the form of the “set” solution and the structure of the set of best responses for
various levels of information availability to the players regarding the opponent’s behavior.
__________
Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 341–356, 2004. 相似文献
6.
Licun Xue 《International Journal of Game Theory》2000,29(3):339-357
This paper defines “negotiation-proof Nash equilibrium', a notion that applies to environments where players can negotiate
openly and directly prior to the play of a noncooperative game. It recognizes the possibility that a group of self-interested
players may choose, voluntarily and without binding agreement, to coordinate their choice of strategies and make joint objections;
moreover, it takes the perfect foresight of rational players fully into account. The merit of the notion of negotiation-proof
Nash equilibrium is twofold: (1) It offers a way to rectify the nestedness assumption and myopia embedded in the notion of
coalition-proof Nash equilibrium. (2) The negotiation process is formalized by a “graph”, which serves as a natural extension to the approach that models
preplay communication by an extensive game.
Received: October 1998/Final version: May 2000 相似文献
7.
The value of information has been the subject of many studies in a strategic context. The central question in these studies
is how valuable the information hidden in the chance moves of a game is for one or more of the players. Generally speaking,
only the extra possibilities that are beneficial for the players have been considered so far. In this note we study the value
of information for a special class of two-person games. For these games we also investigate how “badly” the players can do,
both with and without knowing the result of the chance move. In this way one can determine to what extent the players are
restricted in their possibilities by the fact that some information is hidden in the chance moves of the games. This allows
for a comparison of the influence of the chance move to the control that the players have over the game result. 相似文献
8.
Manuel Abellanas Ma Dolores López Javier Rodrigo Isabel Lillo 《International Journal of Game Theory》2011,40(3):449-459
Spatial models of two-player competition in spaces with more than one dimension almost never have pure-strategy Nash equilibria,
and the study of the equilibrium positions, if they exist, yields a disappointing result: the two players must choose the
same position to achieve equilibrium. In this work, a discrete game is proposed in which the existence of Nash equilibria
is studied using a geometric argument. This includes a definition of equilibrium which is weaker than the classical one to
avoid the uniqueness of the equilibrium position. As a result, a “region of equilibrium” appears, which can be located by
geometric methods. In this area, the players can move around in an “almost-equilibrium” situation and do not necessarily have
to adopt the same position. 相似文献
9.
Mark Voorneveld 《International Journal of Game Theory》2006,34(1):105-121
The t-solutions introduced in R. W. Rosenthal (1989, Int J Game Theory 18:273–292) are quantal response equilibria based on the linear probability model. Choice probabilities in t-solutions are related to the determination of leveling taxes in taxation problems. The set of t-solutions coincides with the set of Nash equilibria of a game with quadratic control costs. Evaluating the set of t-solutions for increasing values of t yields that players become increasingly capable of iteratively eliminating never-best replies and eventually only play rationalizable actions with positive probability. These features are not shared by logit quantal response equilibria. Moreover, there exists a path of t-solutions linking uniform randomization to Nash equilibrium 相似文献
10.
We consider the following “silent duel” of m players with a possible economic interpretation. Each player has one “bullet”, which she can shoot at any time during the time interval [0,1]. The probability that the i-th player hits the “target” at moment t is given by an increasing accuracy function f
i
(t). The winner is the player who hits the target first. Under natural assumptions on the functions f
i
(t) we prove the existence and uniqueness of a Nash equilibrium point in this game, and we provide an explicit construction of this equilibrium. This construction allows us to obtain exact solutions for many specific examples. Some of them are presented.This work was partly supported by RBRF grants 03-01-00479. 相似文献
11.
Professor A. Yu. Garnaev 《International Journal of Game Theory》1992,20(3):269-276
We consider two zero-sum search games in which a searcher moves along a continuous trajectory in a search setQ. The probability of detection depends on the distance between the two players. The problem is open loop, i.e. neither player receives any information about the other as the game progresses. The payoff to a hider is the elapsed time before detection. Optimal mixed strategies are obtained. 相似文献
12.
13.
Ferenc Forgó 《Central European Journal of Operations Research》2011,19(2):201-213
A correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is applied for two-person finite
games in extensive form with perfect information. Randomization by an umpire takes place over the leaves of the game tree.
At every decision point players have the choice either to follow the recommendation of the umpire blindly or freely choose
any other action except the one suggested. This scheme can lead to Pareto-improved outcomes of other correlated equilibria.
Computational issues of maximizing a linear function over the set of soft correlated equilibria are considered and a linear-time
algorithm in terms of the number of edges in the game tree is given for a special procedure called “subgame perfect optimization”. 相似文献
14.
Flemming Tops?e 《Journal of Global Optimization》2009,43(4):553-564
Inspired by previous work on information theoretical optimization problems, the basics of an axiomatic theory of certain special
two-person zero-sum games is developed. One of the players, “Observer”, is imagined to have a “mind”, the other, “Nature”,
not. These ideas lead to un-symmetric modeling as the two players are treated quite differently. Basic concavity- and convexity
results as well as a general minimax theorem are derived from the axioms. 相似文献
15.
S. A. Nazarov 《Journal of Mathematical Sciences》1996,80(5):1989-2034
The asymptotic series for solutions of the mixed boundary-value problem for the Poisson equation in a domain, which is a junction
of singularly degenerating domains, are constructed. In this paper, which is the first part of the publication, the three-dimensional
problem (“wheel hub with spokes”) and the analogous two-dimensional problems are considered. The methods of matched and compound
asymptotic expansions are used. It is shown that a special self-adjoint extension of the operator of the limit problem in
the “hub” supplied by the straight-line segments (“limits of spokes”) can be chosen as an asymptotical model of the problem
in question; the extension parameters are to be some integral characteristics of the boundary-layer problems. Bibliography:
39 titles.
Translated from Trudy Seminara imeni I. G. Petrovskogo. No. 18, pp. 3–78, 1995. 相似文献
16.
Proper rationalizability and backward induction 总被引:1,自引:0,他引:1
Frank Schuhmacher 《International Journal of Game Theory》1999,28(4):599-615
This paper introduces a new normal form rationalizability concept, which in reduced normal form games corresponding to generic
finite extensive games of perfect information yields the unique backward induction outcome. The basic assumption is that every
player trembles “more or less rationally” as in the definition of a ε-proper equilibrium by Myerson (1978). In the same way
that proper equilibrium refines Nash and perfect equilibrium, our model strengthens the normal form rationalizability concepts
by Bernheim (1984), B?rgers (1994) and Pearce (1984). Common knowledge of trembling implies the iterated elimination of strategies
that are strictly dominated at an information set. The elimination process starts at the end of the game tree and goes backwards
to the beginning.
Received: October 1996/Final version: May 1999 相似文献
17.
A. A. Vasin A. A. Sharikova 《Moscow University Computational Mathematics and Cybernetics》2011,35(1):47-55
We address the problem of how to improve the efficiency of markets of similar goods (electric power, gas, and other resources).
One way to undermine the market dominance of some companies is the possibility of forward contracts. Here a model of the spot
and forward markets functioning as Curnout auctions is studied using the example of symmetrical oligopoly. Suppliers try to
maximize their profit by this two-stage game’s strategies of traded subgame equilibrium (TSE). The conditions for equilibrium
achieved by correlated mixed strategies are elucidated: either a “bull” or “bear” market is established according to a chance
factor. The optimum strategies of rational bidders are found to depend on the reserve price and a risk-avoiding parameter.
TSE is compared to the Nash equilibria for one-stage models. 相似文献
18.
Michael Davis 《Mathematical Intelligencer》1994,16(4):21-28
The short answer to the question just posed seems to be, “Not much.” Since I have given “the long answer” elsewhere,12 I can summarize it here. Berg could see no point in writing Bromley. What could he write to someone he believed guilty of
plagiarism? What could such a letter accomplish? He did, however, write to New York University Press; to all the universities
involved, and to the Works’ English publisher (Pickering and Chatto), who said they passed the letter on to Campbell-Kelly
(30 June 1990); to a great many professional societies in Australia, England, and the United States; to a great many governmental
agencies and some politicians in those countries; to some publications, both academic and popular; to the Pope and several
cardinals; and to a miscellany of other individuals. Generally, those in the best position to do something—for example, the
three universities involved —did not even answer Berg’s letter. Others often did answer, but their answer was generally that
they were in no position to do anything.
That was how matters stood when I published my first article on “the Berg Affair”.12 Its publication finally roused those best positioned to answer. Late in 1993, Galler, Bromley, and Campbell-Kelly wrote letters
to the editor of Accountability in Research criticizing me for not getting their side of the story before I published Berg’s.
Campbell-Kelly threatened the journal’s publisher with a lawsuit if I (or it) did not retract. The three also provided some
insight into what their explanation of events might be. Bromley, though listed prominently in ads for the Works, claimed to
have had only a small part, merely advising Campbell-Kelly on selection and arrangement of the papers printed in Volumes 2
and 3. Campbell-Kelly confirmed that Bromley took no part in the detailed editing or in the provision of documents. That work
was performed by one C.J.D. (“Jim”) Roberts, a “London-based independent scholar” who was “editorial consultant to the Works”
(and, apparently, worked directly under Campbell-Kelly). Roberts seems to deserve more public credit than he has so far received.
According to Campbell-Kelly, it was Roberts who, making a systematic search for unknown holdings of Babbage, turned up the
original of the letter to Quetelet by writing the Royal Library (one “tiny triumph” among many). Campbell-Kelly also claimed
that neither he nor Roberts knew of Berg’s prior discovery. 相似文献
19.
Acceptable moves for the “worthwhile-to-move” incremental principle are such that “advantages-to-move” are higher than some
fraction of “costs-to-move”. When combined with optimization, this principle gives raise to adaptive local search proximal
algorithms. Convergence results are given in two distinctive cases, namely low local costs-to-move and high local costs-to-move.
In this last case, one obtains a dynamic cognitive approach to Ekeland’s ϵ-variational principle. Introduction of costs-to-move in the algorithms yields robustness and stability properties. 相似文献
20.
Guilherme Carmona 《International Journal of Game Theory》2006,34(1):131-151
We study the properties of finitely complex, symmetric, globally stable, and semi-perfect equilibria. We show that: (1) If a strategy satisfies these properties then players play a Nash equilibrium of the stage game in every period; (2) The set of finitely complex, symmetric, globally stable, semi-perfect equilibrium payoffs in the repeated game equals the set of Nash equilibria payoffs in the stage game; and (3) A strategy vector satisfies these properties in a Pareto optimal way if and only if players play some Pareto optimal Nash equilibrium of the stage game in every stage. Our second main result is a strong anti-Folk Theorem, since, in contrast to what is described by the Folk Theorem, the set of equilibrium payoffs does not expand when the game is repeated.This paper is a revised version of Chapter 3 of my Ph.D. thesis, which has circulated under the title “An Interpretation of Nash Equilibrium Based on the Notion of Social Institutions”. 相似文献