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1.
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
2.
A new quantitative definition of the “power index” is proposed for a voter in weighted voting systems (WV-schemes), where
the voters a priori do not have equal rights. The proposed “power index” is generated in a self-consistent manner from information
about the number of times that a voter enters any winning coalition in the WV-scheme. Explicit formulas are derived for computing
the “power index”. The discussion is illustrated with prototype examples.
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Translated from Prikladnaya Matematika i Informatika, No. 25, pp. 81–98, 2007. 相似文献
3.
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
4.
We study a bargaining procedure of coalition formation in the class of hedonic games, where players’ preferences depend solely
on the coalition they belong to. We provide an example of nonexistence of a pure strategy stationary perfect equilibrium,
and a necessary and sufficient condition for existence. We show that when the game is totally stable (the game and all its
restrictions have a nonempty core), there always exists a no-delay equilibrium generating core outcomes. Other equilibria
exhibiting delay or resulting in unstable outcomes can also exist. If the core of the hedonic game and its restrictions always
consist of a single point, we show that the bargaining game admits a unique stationary perfect equilibrium, resulting in the
immediate formation of the core coalition structure. 相似文献
5.
We study coalition formation games with externalities where each agent’s payoff depends on the entire partition. As in Bloch
(Games Econ Behav 14:90–123, 1996) and Ray and Vohra (Games Econ Behav 26:268–336, 1999), we assume that coalitions form sequentially and agreements are irreversible. Instead of a fixed order protocol, we use
a “bidding mechanism” (see Pérez-Castrillo and Wettstein in Am Econ Rev 92(5):1577–1587, 2002) to determine proposals and transfers among the agents. We show that such a mechanism facilitates the attainment of efficiency;
in particular, our game admits a Markov perfect equilibrium with the property of full dynamic efficiency. In addition, the
aggregate equilibrium payoffs of our game exhibit monotonicity in time. Nevertheless, inefficient equilibria can also emerge. 相似文献
6.
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.
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Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 341–356, 2004. 相似文献
7.
Classical cooperative game theory is no longer a suitable tool for those situations where the values of coalitions are not
known with certainty. We consider a dynamic context where at each point in time the coalitional values are unknown but bounded by a polyhedron. However, the average value of each coalition in the long run is known with certainty. We design “robust”
allocation rules for this context, which are allocation rules that keep the coalition excess bounded while guaranteeing each
player a certain average allocation (over time). We also present a joint replenishment application to motivate our model.
We thank two anonymous referees for their valuable comments. 相似文献
8.
Given their importance in determining the outcome of many economic interactions, different models have been proposed to determine
how social networks form and which structures are stable. In Bala and Goyal (Econometrica 68, 1181–1229, 2000), the one-sided link formation model has been considered, which is based on a noncooperative game of network formation. They
found that the empty networks, the wheel in the one-way flow of benefits case and the center-sponsored star in the two-way
flow case play a fundamental role since they are strict Nash equilibria of the corresponding games for a certain class of
payoff functions. In this paper, we first prove that all these network structures are in weakly dominated strategies whenever
there are no strict Nash equilibria. Then, we exhibit a more accurate selection device between these network architectures
by considering “altruistic behavior” refinements. Such refinements that we investigate here in the framework of finite strategy
sets games have been introduced by the authors in previous papers. 相似文献
9.
Robert Samuel Simon 《Israel Journal of Mathematics》2006,156(1):285-309
A stochastic game isvalued if for every playerk there is a functionr
k:S→R from the state spaceS to the real numbers such that for every ε>0 there is an ε equilibrium such that with probability at least 1−ε no states is reached where the future expected payoff for any playerk differs fromr
k(s) by more than ε. We call a stochastic gamenormal if the state space is at most countable, there are finitely many players, at every state every player has only finitely many
actions, and the payoffs are uniformly bounded and Borel measurable as functions on the histories of play. We demonstrate
an example of a recursive two-person non-zero-sum normal stochastic game with only three non-absorbing states and limit average
payoffs that is not valued (but does have ε equilibria for every positive ε). In this respect two-person non-zero-sum stochastic
games are very different from their zero-sum varieties. N. Vieille proved that all such non-zero-sum games with finitely many
states have an ε equilibrium for every positive ε, and our example shows that any proof of this result must be qualitatively
different from the existence proofs for zero-sum games. To show that our example is not valued we need that the existence
of ε equilibria for all positive ε implies a “perfection” property. Should there exist a normal stochastic game without an
ε equilibrium for some ε>0, this perfection property may be useful for demonstrating this fact. Furthermore, our example sews
some doubt concerning the existence of ε equilibria for two-person non-zero-sum recursive normal stochastic games with countably
many states.
This research was supported financially by the German Science Foundation (Deutsche Forschungsgemeinschaft) and the Center
for High Performance Computing (Technical University, Dresden). The author thanks Ulrich Krengel and Heinrich Hering for their
support of his habilitation at the University of Goettingen, of which this paper is a part. 相似文献
10.
A. S. Nowak 《Journal of Optimization Theory and Applications》2010,144(1):88-106
We study a model of intergenerational stochastic game with general state space in which each generation consists of n players. The main objective is to prove the existence of a perfect stationary equilibrium in an infinite-horizon intergenerational
game in which cooperation is assumed inside every generation. A suitable change in the terminology used in this paper provides
a new equilibrium theorem for stochastic games with so-called “hyperbolic players”. A discussion of perfect equilibria in
games of noncooperative generations is also given. Some applications to economic theory are included. 相似文献
11.
JesÚs Crespo Cuaresma 《Mathematical Intelligencer》2001,23(3):23-26
Summary and Conclusions First impressions are not always right, especially in this field mostly inhabited by impossibility theorems. The actual properties
of the voting procedure constructed violate the intuition that motivated the rule. The Rolling Stones’s sentence with which
this paper started is quite apposite to Public Choice, where getting “what you want” is usually more difficult than it seems. 相似文献
12.
Parkash Chander 《International Journal of Game Theory》2007,35(4):539-556
This paper reinterprets the γ-core (Chander and Tulkens in Int Tax Pub Financ 2:279–293, 1995; in Int J Game Theory 26:379–401,
1997) and justifies it as well as its prediction that the efficient coalition structure is stable in terms of the coalition
formation theory. The problem of coalition formation is formulated as an infinitely repeated game in which the players must
choose whether to cooperate or not. It is shown that a certain equilibrium of this game corresponds to the γ-core assumption
that when a coalition forms the remaining players form singletons, and that the grand coalition is an equilibrium coalition
structure.
An earlier version of this paper was presented at the conference on Game Theory and Its Applications held in Mumbai in 2003
and was subsequently circulated as CORE Discussion Paper 2003/46. 相似文献
13.
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
14.
Anton Stefanescu 《International Journal of Game Theory》2000,29(3):391-412
Uniform competitive solutions are stable configurations of proposals predicting coalition formation and effective payoffs.
Such “solutions” exist for almost all properly defined cooperative games and, therefore, can be proposed as substitute of
the core. The new existence results obtained in the present paper concern also the case when the coalitional function of a
game has empty values. All concepts and results are implemented in the competitive analysis of the exchange economies.
Received: July 1997/Final version: February 2000 相似文献
15.
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
16.
The problem of strategic stability of long-range cooperative agreements in dynamic games with coalition structures is investigated. Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments.From these, the time-consistent cooperative agreement can be strategically supported by ε-Nash or strong ε-Nash equilibria. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibria can be constructed. 相似文献
17.
Ady Pauzner 《International Journal of Game Theory》2000,29(2):189-209
Economic models usually assume that agents play precise best responses to others' actions. It is sometimes argued that this
is a good approximation when there are many agents in the game, because if their mistakes are independent, aggregate uncertainty
is small. We study a class of games in which players' payoffs depend solely on their individual actions and on the aggregate
of all players' actions. We investigate whether their equilibria are affected by mistakes when the number of players becomes
large. Indeed, in generic games with continuous payoff functions, independent mistakes wash out in the limit. This may not be the case if payoffs are discontinuous. As a
counter-example we present the n players Nash bargaining game, as well as a large class of “free-rider games.”
Received: November 1997/Final version: December 1999 相似文献
18.
Wojciech Połowczuk Piotr Więcek Tadeusz Radzik 《Mathematical Methods of Operations Research》2007,65(1):141-152
This paper gives wide characterization of n-person non-coalitional games with finite players’ strategy spaces and payoff functions having some concavity or convexity
properties. The characterization is done in terms of the existence of two-point-strategy Nash equilibria, that is equilibria
consisting only of mixed strategies with supports being one or two-point sets of players’ pure strategy spaces. The structure
of such simple equilibria is discussed in different cases. The results obtained in the paper can be seen as a discrete counterpart
of Glicksberg’s theorem and other known results about the existence of pure (or “almost pure”) Nash equilibria in continuous
concave (convex) games with compact convex spaces of players’ pure strategies. 相似文献
19.
J. W. Sander 《Mathematica Slovaca》2007,57(6):501-514
The rules of the game MetaSquares as well as computational results suggest to follow a “lattice” strategy. This strategy is
presented, and by counting lattice points it is shown to be essentially best possible.
相似文献
20.
In this paper, we deal with ranking problems arising from various data mining applications where the major task is to train
a rank-prediction model to assign every instance a rank. We first discuss the merits and potential disadvantages of two existing
popular approaches for ranking problems: the ‘Max-Wins’ voting process based on multi-class support vector machines (SVMs)
and the model based on multi-criteria decision making. We then propose a confidence voting process for ranking problems based
on SVMs, which can be viewed as a combination of the SVM approach and the multi-criteria decision making model. Promising
numerical experiments based on the new model are reported.
The research of the last author was supported by the grant #R.PG 0048923 of NESERC, the MITACS project “New Interior Point
Methods and Software for Convex Conic-Linear Optimization and Their Application to Solve VLSI Circuit Layout Problems” and
the Canada Researcher Chair Program. 相似文献