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1.
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
2.
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
3.
4.
The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically
determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution
first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin,
pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative
infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related
to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in
this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining
problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement
point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s
alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty
is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159,
1992) also implements the L-Nash solution. 相似文献
5.
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
6.
Maschler, Owen and Peleg (1988) constructed a dynamic system for modelling a possible negotiation process for players facing
a smooth n-person pure bargaining game, and showed that all paths of this system lead to the Nash point. They also considered the non-convex
case, and found in this case that the limiting points of solutions of the dynamic system belong to the Nash set. Here we extend
the model to i) general convex pure bargaining games, and to ii) games generated by “divide the cake” problems. In each of
these cases we construct a dynamic system consisting of a differential inclusion (generalizing the Maschler-Owen-Peleg system
of differential equations), prove existence of solutions, and show that the solutions converge to the Nash point (or Nash
set). The main technical point is proving existence, as the system is neither convex valued nor continuous. The intuition
underlying the dynamics is the same as (in the convex case) or analogous to (in the division game) that of Maschler, Owen,
and Peleg.
Received August 1997/Final version May 1998 相似文献
7.
Ori Haimanko 《International Journal of Game Theory》2000,29(3):451-468
We investigate quasi-values of finite games – solution concepts that satisfy the axioms of Shapley (1953) with the possible
exception of symmetry.
Following Owen (1972), we define “random arrival', or path, values: players are assumed to “enter' the game randomly, according to independently distributed arrival times, between
0 and 1; the payoff of a player is his expected marginal contribution to the set of players that have arrived before him.
The main result of the paper characterizes quasi-values, symmetric with respect to some coalition structure with infinite
elements (types), as random path values, with identically distributed random arrival times for all players of the same type.
General quasi-values are shown to be the random order values (as in Weber (1988) for a finite universe of players).
Pseudo-values (non-symmetric generalization of semivalues) are also characterized, under different assumptions of symmetry.
Received: April 1998/Revised version: February 2000 相似文献
8.
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
9.
Loss aversion equilibrium 总被引:1,自引:0,他引:1
Jonathan Shalev 《International Journal of Game Theory》2000,29(2):269-287
The Nash equilibrium solution concept for games is based on the assumption of expected utility maximization. Reference dependent
utility functions (in which utility is determined not only by an outcome, but also by the relationship of the outcome to a
reference point) are a better predictor of behavior than expected utility. In particular, loss aversion is an important element
of such utility functions.
We extend games to include loss aversion characteristics of the players. We define two types of loss-aversion equilibrium,
a solution concept endogenizing reference points. The two types reflect different procedures of updating reference points
during the game. Reference points emerge as expressions of anticipation which are fulfilled.
We show existence of myopic loss-aversion equilibrium for any extended game, and compare it to Nash equilibrium. Comparative
statics show that an increase in loss aversion of one player can affect her and other players' payoffs in different directions.
Received August 1998/Revised version February 2000 相似文献
10.
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
11.
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
12.
There exists a Nash equilibrium (ε-Nash equilibrium) for every n-person stochastic game with a finite (countable) state space and finite action sets for the players if the payoff to each
player i is one when the process of states remains in a given set of states G
i and is zero otherwise.
Received: December 2000 相似文献
13.
We consider a duopolistic industry where the current sales of each firm is proportional to its goodwill stock. The evolution
of the latter depends positively on own advertising effort and negatively on competitor’s advertising. A standard assumption
in the literature in differential games of advertising is that the players remain active throughout the whole (infinite) duration
of the game. We relax this assumption and characterize the circumstances under which a firm finds it optimal to remain or
exit the industry. Among other things, it is shown that, if both players are “strong”, then the unique Nash equilibrium is
the same that one would obtain in the absence of interference from competitor’s advertising.
Research supported by Ministry of University and Research of Italy, University of Padua and NSERC, Canada. 相似文献
14.
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
15.
《Applied Mathematics Letters》2003,16(5):683-687
A cooperative game engendered by a noncooperative n-person game (the master game) in which any subset of n players may form a coalition playing an antagonistic game against the residual players (the surrounding) that has a (Nash equilibrium) solution, is considered, along with another noncooperative game in which both a coalition and its surrounding try to maximize their gains that also possesses a Nash equilibrium solution. It is shown that if the master game is the one with constant sum, the sets of Nash equilibrium strategies in both above-mentioned noncooperative games (in which a coalition plays with (against) its surrounding) coincide. 相似文献
16.
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
17.
On computational complexity of membership test in flow games and linear production games 总被引:1,自引:0,他引:1
Qizhi Fang Shanfeng Zhu Maocheng Cai Xiaotie Deng 《International Journal of Game Theory》2002,31(1):39-45
Let Γ≡(N,v) be a cooperative game with the player set N and characteristic function v: 2N→R. An imputation of the game is in the core if no subset of players could gain advantage by splitting from the grand coalition
of all players. It is well known that, for the flow game (and equivalently, for the linear production game), the core is always
non-empty and a solution in the core can be found in polynomial time. In this paper, we show that, given an imputation x, it is NP-complete to decide x is not a member of the core, for the flow game. And because of the specific reduction we constructed, the result also holds
for the linear production game.
Received: October 2000/Final version: March 2002 相似文献
18.
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
19.
Joseph Y. Halpern 《International Journal of Game Theory》1999,28(3):315-330
Samet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction
solution in a game of perfect information. He argued that while hypothetical knowledge and the extended information structures used to model it bear some resemblance to the way philosophers have used conditional logic to model counterfactuals, hypothetical knowledge cannot be reduced to conditional logic together with epistemic logic. Here
it is shown that in fact hypothetical knowledge can be captured using the standard counterfactual operator “>” and the knowledge
operator “K”, provided that some assumptions are made regarding the interaction between the two. It is argued, however, that these assumptions
are unreasonable in general, as are the axioms that follow from them. Some implications for game theory are discussed. 相似文献
20.
It is well known that the set of correlated equilibrium distributions of an n-player noncooperative game is a convex polytope that includes all the Nash equilibrium distributions. We demonstrate an elementary yet surprising result: the Nash equilibria all lie on the boundary of the polytope.We are grateful to Francoise Forges, Dan Arce, the editors, and several anonymous referees for helpful comments. This research was supported by the National Science Foundation under grant 98–09225 and by the Fuqua School of Business.The use of correlated mixed strategies in 2-player games was discussed by Raiffa (1951), who noted: it is a useful concept since it serves to convexify certain regions [of expected payoffs] in the Euclidean plane. (p. 8)Received: April 2002 / Revised: November 2003 相似文献