共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
In this paper, we deal with Aubin cores and bargaining sets in convex cooperative fuzzy games. We first give a simple and
direct proof to the well-known result (proved by Branzei et al. (Fuzzy Sets Syst 139:267–281, 2003)) that for a convex cooperative
fuzzy game v, its Aubin core C(v) coincides with its crisp core C
cr
(v). We then introduce the concept of bargaining sets for cooperative fuzzy games and prove that for a continuous convex cooperative
fuzzy game v, its bargaining set coincides with its Aubin core, which extends a well-known result by Maschler et al. for classical cooperative
games to cooperative fuzzy games. We also show that some results proved by Shapley (Int J Game Theory 1:11–26, 1971) for classical
decomposable convex cooperative games can be extended to convex cooperative fuzzy games. 相似文献
3.
Jean-François Mertens 《International Journal of Game Theory》1998,27(3):343-357
In a repeated two-person zero-sum game with incomplete information on one side, the values v
n
of the n-stage games converge to the value v
∞ of the infinite game with worst case error ∼(ln n/n)1/3.
Received February 1995/Revised Version May 1997 相似文献
4.
I. N. Korman 《Vestnik St. Petersburg University: Mathematics》2010,43(4):220-226
Given a connected undirected graph ϕ with vertex set N, cooperative games (N, v) are considered in which players can cooperate only when the corresponding vertices form a connected subgraph in the graph
ϕ. For such games, two generalizations of the bargaining set M
1
i
, which was introduced by Aumann and Maschler, are investigated. 相似文献
5.
Judith Timmer 《Mathematical Methods of Operations Research》2006,64(1):95-106
This paper introduces and studies the compromise value for cooperative games with random payoffs, that is, for cooperative games where the payoff to a coalition of players is a random variable. This value is a compromise between utopia payoffs and minimal rights and its definition is based on the compromise value for NTU games and the τ-value for TU games. It is shown that the nonempty core of a cooperative game with random payoffs is bounded by the utopia payoffs and the minimal rights. Consequently, for such games the compromise value exists. Further, we show that the compromise value of a cooperative game with random payoffs coincides with the τ-value of a related TU game if the players have a certain type of preferences. Finally, the compromise value and the marginal value, which is defined as the average of the marginal vectors, coincide on the class of two-person games. This results in a characterization of the compromise value for two-person games.I thank Peter Borm, Ruud Hendrickx and two anonymous referees for their valuable comments. 相似文献
6.
A class of zero-sum, two-person stochastic games is shown to have a value which can be calculated by transfinite iteration
of an operator. The games considered have a countable state space, finite action spaces for each player, and a payoff sufficiently
general to include classical stochastic games as well as Blackwell’s infiniteG
δ games of imperfect information.
Research supported by National Science Foundation Grants DMS-8801085 and DMS-8911548. 相似文献
7.
We consider an infinitely repeated two-person zero-sum game with incomplete information on one side, in which the maximizer
is the (more) informed player. Such games have value v
∞ (p) for all 0≤p≤1. The informed player can guarantee that all along the game the average payoff per stage will be greater than or equal to
v
∞ (p) (and will converge from above to v
∞ (p) if the minimizer plays optimally). Thus there is a conflict of interest between the two players as to the speed of convergence
of the average payoffs-to the value v
∞ (p). In the context of such repeated games, we define a game for the speed of convergence, denoted SG
∞ (p), and a value for this game. We prove that the value exists for games with the highest error term, i.e., games in which v
n (p)− v
∞ (p) is of the order of magnitude of . In that case the value of SG
∞ (p) is of the order of magnitude of . We then show a class of games for which the value does not exist. Given any infinite martingale 𝔛∞={X
k }∞
k=1, one defines for each n : V
n (𝔛∞) ≔E∑n
k=1 |X
k+1 − X
k|. For our first result we prove that for a uniformly bounded, infinite martingale 𝔛∞, V
n (𝔛∞) can be of the order of magnitude of n
1/2−ε, for arbitrarily small ε>0.
Received January 1999/Final version April 2002 相似文献
8.
9.
In cooperative dynamic games, a stringent condition—that of subgame consistency—is required for a dynamically stable cooperative solution. In particular, under a subgame-consistent cooperative solution
an extension of the solution policy to a subgame starting at a later time with a state brought about by prior optimal behavior
will remain optimal. This paper extends subgame-consistent solutions to dynamic (discrete-time) cooperative games with random
horizon. In the analysis, new forms of the Bellman equation and the Isaacs–Bellman equation in discrete-time are derived.
Subgame-consistent cooperative solutions are obtained for this class of dynamic games. Analytically tractable payoff distribution
mechanisms, which lead to the realization of these solutions, are developed. This is the first time that subgame-consistent
solutions for cooperative dynamic games with random horizon are presented. 相似文献
10.
Tamás Solymosi 《International Journal of Game Theory》2002,31(1):1-11
It is well known that in three-person transferable-utility cooperative games the bargaining set ℳi
1 and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced
games are discussed in the literature in which the bargaining set ℳi
1 (for the grand coalition) is larger then the core. This paper answers the equivalence question in the remaining four-person
case. We prove that in any four-person game and for arbitrary coalition structure, whenever the core is not empty, it coincides
with the bargaining set ℳi
1. Our discussion employs a generalization of balancedness to games with coalition structures.
Received: August 2001/Revised version: April 2002 相似文献
11.
Sergiu Hart Salvatore Modica David Schmeidler 《International Journal of Game Theory》1994,23(4):347-358
A joint derivation of utility and value for two-person zero-sum games is obtained using a decision theoretic approach. Acts map states to consequences. The latter are lotteries over prizes, and the set of states is a product of two finite sets (m rows andn columns). Preferences over acts are complete, transitive, continuous, monotonie and certainty-independent (Gilboa and Schmeidler (1989)), and satisfy a new axiom which we introduce. These axioms are shown to characterize preferences such that (i) the induced preferences on consequences are represented by a von Neumann-Morgenstern utility function, and (ii) each act is ranked according to the maxmin value of the correspondingm × n utility matrix (viewed as a two-person zero-sum game). An alternative statement of the result deals simultaneously with all finite two-person zero-sum games in the framework of conditional acts and preferences.We are indebted to Jacques Drèze, Andreu Mas-Colell, Roger Myerson and Reinhard Selten for helpful comments. 相似文献
12.
J. M. Bilbao C. Chacón A. Jiménez-Losada E. Lebrón 《Annals of Operations Research》2008,158(1):117-131
Interior operator games arose by abstracting some properties of several types of cooperative games (for instance: peer group
games, big boss games, clan games and information market games). This reason allow us to focus on different problems in the
same way. We introduced these games in Bilbao et al. (Ann. Oper. Res. 137:141–160, 2005) by a set system with structure of antimatroid, that determines the feasible coalitions, and a non-negative vector, that
represents a payoff distribution over the players. These games, in general, are not convex games. The main goal of this paper
is to study under which conditions an interior operator game verifies other convexity properties: 1-convexity, k-convexity (k≥2 ) or semiconvexity. But, we will study these properties over structures more general than antimatroids: the interior operator
structures. In every case, several characterizations in terms of the gap function and the initial vector are obtained. We
also find the family of interior operator structures (particularly antimatroids) where every interior operator game satisfies
one of these properties. 相似文献
13.
14.
In this paper we introduce the ℬ-prenucleolus for a transferable utility game (N,v), where ℬ⊆2
N
. The ℬ-prenucleolus is a straightforward generalization of the ordinary prenucleolus, where only the coalitions in ℬ determine
the outcome. We impose a combinatorial structure on the collection ℬ which enables us to compute the ℬ-prenucleolus in ?(n
3|ℬ|) time. The algorithm can be used for computing the nucleolus of several classes of games, among which is the class of
minimum cost spanning tree games.
Received: September 4, 1995 / Accepted: May 5, 1997?Published online June 8, 2000 相似文献
15.
M. Josune Albizuri 《Annals of Operations Research》2009,172(1):363-374
In this paper we define a solution for multichoice games which is a generalization of the Owen coalition value (Lecture Notes
in Economics and Mathematical Systems: Essays in Honor of Oskar Morgenstern, Springer, New York, pp. 76–88, 1977) for transferable utility cooperative games and the Egalitarian solution (Peters and Zanks, Ann. Oper. Res. 137, 399–409,
2005) for multichoice games. We also prove that this solution can be seen as a generalization of the configuration value and the
dual configuration value (Albizuri et al., Games Econ. Behav. 57, 1–17, 2006) for transferable utility cooperative games. 相似文献
16.
Digraph games are cooperative TU-games associated to digraph competitions: domination structures that can be modeled by directed
graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles for
a group of individuals within the framework of social choice theory. Brink and Gilles (2000) defined theβ-measure of a digraph competition as the Shapley value of the corresponding digraph game. This paper provides a new characterization
of theβ-measure. 相似文献
17.
L. C. Westphal 《Mathematical Programming》1976,10(1):124-133
It has been shown that two-person zero-sum separable games are associated with a maximization problem involving the cones and dual cones of the generalized moments of the players' mixed strategy sets. In this note it is observed that those results extend almost immediately to two-person nonzero-sum separable games, but that then-person extension does not follow except in a special case. 相似文献
18.
Quitting games are multi-player sequential games in which, at every stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; each player i then receives a payoff r
S
i, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is zero.? We exhibit a four-player
quitting game, where the “simplest” equilibrium is periodic with period two. We argue that this implies that all known methods
to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail in general, and provide
some geometric intuition for this phenomenon.
Received: October 2001 相似文献
19.
Edward M. Bolger 《International Journal of Game Theory》2000,29(1):93-99
In Bolger [1993], an efficient value was obtained for a class of games called games with n players and r alternatives. In these games, each of the n players must choose one and only one of the r alternatives. This value can be used to determine a player’s “a priori” value in such a game. In this paper, we show that
the value has a consistency property similar to the “consistency” for TU games in Hart/Mas-Colell [1989] and we present a
set of axioms (including consistency) which characterizes this value.
The games considered in this paper differ from the multi-choice games considered by Hsiao and Raghavan [1993]. They consider
games in which the actions of the players are ordered in the sense that, if i >j, then action i carries more “weight” than action j.
These games also differ from partition function games in that the worth of a coalition depends not only on the partitioning
of the players but also on the action chosen by each subset of the partition.
Received: April 1994/final version: June 1999 相似文献
20.
This note extends the solution concept of the core for cooperative games to multi-choice games. We propose an extension of
the theorem of Bondareva (Problemy Kybernetiki 10:119–139, 1963) and Shapley (Nav Res Logist Q 14:453–460, 1967) to multi-choice games. Also, we introduce a notion of reduced games for multi-choice games and provide an axiomatization
of the core on multi-choice games by means of corresponding notion of consistency and its converse. 相似文献