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1.
Francesca Busetto Giulio Codognato Sayantan Ghosal 《International Journal of Game Theory》2008,37(3):371-386
In this paper, we investigate the problem of the strategic foundation of the Cournot–Walras equilibrium approach. To this
end, we respecify à la Cournot–Walras the mixed version of a model of simultaneous, noncooperative exchange, originally proposed
by Lloyd S. Shapley. We show, through an example, that the set of the Cournot–Walras equilibrium allocations of this respecification
does not coincide with the set of the Cournot–Nash equilibrium allocations of the mixed version of the original Shapley’s
model. As the nonequivalence, in a one-stage setting, can be explained by the intrinsic two-stage nature of the Cournot–Walras
equilibrium concept, we are led to consider a further reformulation of the Shapley’s model as a two-stage game, where the
atoms move in the first stage and the atomless sector moves in the second stage. Our main result shows that the set of the
Cournot–Walras equilibrium allocations coincides with a specific set of subgame perfect equilibrium allocations of this two-stage
game, which we call the set of the Pseudo–Markov perfect equilibrium allocations.
We would like to thank Pierpaolo Battigalli, Marcellino Gaudenzi, and an anonymous referee for their comments and suggestions. 相似文献
2.
Ankur A. Kulkarni Uday V. Shanbhag 《Journal of Optimization Theory and Applications》2012,154(1):175-186
Generalized Nash games with shared constraints represent an extension of Nash games in which strategy sets are coupled across players through a shared or common constraint. The equilibrium conditions of such a game can be compactly stated as a quasi-variational inequality (QVI), an extension of the variational inequality (VI). In (Eur. J. Oper. Res. 54(1):81–94, 1991), Harker proved that for any QVI, under certain conditions, a solution to an appropriately defined VI solves the QVI. This is a particularly important result, given that VIs are generally far more tractable than QVIs. However Facchinei et al. (Oper. Res. Lett. 35(2):159–164, 2007) suggested that the hypotheses of this result are difficult to satisfy in practice for QVIs arising from generalized Nash games with shared constraints. We investigate the applicability of Harker’s result for these games with the aim of formally establishing its reach. Specifically, we show that if Harker’s result is applied in a natural manner, its hypotheses are impossible to satisfy in most settings, thereby supporting the observations of Facchinei et al. But we also show that an indirect application of the result extends the realm of applicability of Harker’s result to all shared-constraint games. In particular, this avenue allows us to recover as a special case of Harker’s result, a result provided by Facchinei et al. (Oper. Res. Lett. 35(2):159–164, 2007), in which it is shown that a suitably defined VI provides a solution to the QVI of a shared-constraint game. 相似文献
3.
We present a method for the derivation of feedback Nash equi- libria in discrete-time finite-horizon nonstationary dynamic
games. A partic- ular motivation for such games stems from environmental economics, where problems of seasonal competition
for water levels occur frequently among heterogeneous economic agents. These agents are coupled through a state variable,
which is the water level. Actions are strategically chosen to max- imize the agents individual season-dependent utility functions.
We observe that, although a feedback Nash equilibrium exists, it does not satisfy the (exogenous) environmental watchdog expectations.
We devise an incentive scheme to help meeting those expectations and calculate a feedback Nash equilibrium for the new game
that uses the scheme. This solution is more environmentally friendly than the previous one. The water allocation game solutions
help us to draw some conclusions regarding the agents behavior and also about the existence of feedback Nash equilibria in
dynamic games.
The paper draws from Refs.1–2. Its earlier version was presented at the Victoria International Conference 2004, Victoria University
of Wellington, Wellington, New Zealand, February 9–13, 2004.
We thank the anonymous referee and Christophe Deissenberg for insightful comments, which have helped us to clarify its message.
We also thank our colleagues Sophie Thoyer, Robert Lifran, Odile Pourtalier, and Vladimir Petkov for helpful discussions on
the model and techniques used in this Paper.
Gratitude is expressed to the Kyoto Institute for Economic Research, Kyoto University, for this author's support in the final
stages of the paper preparation 相似文献
4.
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
5.
Bich Philippe 《International Journal of Game Theory》2009,38(3):395-410
In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with
possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny’s theorem can
be weakened: we introduce a measure allowing to localize the lack of quasiconcavity, which allows to refine the analysis of
equilibrium existence (I wish to thank P. J. Reny, two anonymous referees and the associated editor for corrections, suggestions
and remarks which led to improvements in the paper). 相似文献
6.
In this paper, we generalize the exitence result for pure strategy Nash equilibria in anonymous nonatomic games. By working directly on integrals of pure strategies, we also generalize, for the same class of games, the existence result for undominated pure strategy Nash equilibria even though, in general, the set of pure strategy Nash equilibria may fail to be weakly compact.
Received August 2001 相似文献
7.
Tasos Kalandrakis 《International Journal of Game Theory》2007,35(3):337-352
We analyze a class of two-candidate voter participation games under complete information that encompasses as special cases
certain public good provision games. We characterize the Nash equilibria of these games as stationary points of a non-linear
programming problem, the objective function of which is a Morse function (onethat does not admit degenerate critical points)
for almost all costs of participation. We use this fact to establish that, outside a closed set of measure zero of participation
costs, all equilibria of these games are regular (an alternative to the result of De Sinopoli and Iannantuoni in Econ Theory
25(2):477–486, 2005). One consequence of regularity is that the equilibria of these games are robust to the introduction of
(mild) incomplete information. Finally, we establish the existence of monotone Nash equilibria, such that players with higher
participation cost abstain with (weakly) higher probability.
相似文献
8.
Erik J Balder 《International Journal of Game Theory》1995,24(1):79-94
An approach initiated in [4] is shown to unify results about the existence of (i) Nash equilibria in games with at most countably many players, (ii) Cournot-Nash equilibrium distributions for large, anonymous games, and (iii) Nash equilibria (both mixed and pure) for continuum games. A new, central notion ofmixed externality is developed for this purpose. 相似文献
9.
On Coincidence of Feedback Nash Equilibria and Stackelberg Equilibria in Economic Applications of Differential Games 总被引:1,自引:0,他引:1
S. J. Rubio 《Journal of Optimization Theory and Applications》2006,128(1):203-220
The scope of the applicability of the feedback Stackelberg equilibrium concept in differential games is investigated. First,
conditions for obtaining the coincidence between the stationary feedback Nash equilibrium and the stationary feedback Stackelberg
equilibrium are given in terms of the instantaneous payoff functions of the players and the state equations of the game. Second,
a class of differential games representing the underlying structure of a good number of economic applications of differential
games is defined; for this class of differential games, it is shown that the stationary feedback Stackelberg equilibrium coincides
with the stationary feedback Nash equilibrium. The conclusion is that the feedback Stackelberg solution is generally not useful
to investigate leadership in the framework of a differential game, at least for a good number of economic applications
This paper was presented at the 8th Viennese Workshop on Optimal Control, Dynamic Games, and Nonlinear Dynamics: Theory and
Applications in Economics and OR/MS, Vienna, Austria, May 14–16, 2003, at the Seminar of the Instituto Complutense de Analisis
Economico, Madrid, Spain, June 20, 2003, and at the Sevilla Workshop on Dynamic Economics and the Environment, Sevilla, Spain,
July 2–3, 2003. The author is grateful to the participants in these sessions, in particular F.J. Andre and J. Ruiz, for their
comments. Five referees provided particularly helpful suggestions. Financial support from the Ministerio de Ciencia y Tecnologia
under Grant BEC2000-1432 is gratefully acknowledged. 相似文献
10.
Our aim is to present some limit theorems for capacities.We consider a sequence of pairwise negatively correlated random variables.We obtain laws of large numbers for upper probabilities and 2-alternating capacities,using some results in the classical probability theory and a non-additive version of Chebyshev’s inequality and Boral-Contelli lemma for capacities. 相似文献
11.
We consider a class of coalition formation games called hedonic games, i.e., games in which the utility of a player is completely determined by the coalition that the player belongs to. We first define the class of subset-additive hedonic games and show that they have the same representation power as the class of hedonic games. We then define a restriction of subset-additive hedonic games that we call subset-neutral hedonic games and generalize a result by Bogomolnaia and Jackson (2002) by showing the existence of a Nash stable partition and an individually stable partition in such games. We also consider neutrally anonymous hedonic games and show that they form a subclass of the subset-additive hedonic games. Finally, we show the existence of a core stable partition that is also individually stable in neutrally anonymous hedonic games by exhibiting an algorithm to compute such a partition. 相似文献
12.
D. W. K. Yeung 《Journal of Optimization Theory and Applications》1994,82(1):181-188
This note provides a lemma on differential games which possess a feedback Nash equilibrium (FNE). In particular, it shows that (i) a class of games with a degenerate FNE can be constructucted from every game which has a nondegenerate FNE and (ii) a class of games with a nondegenerate FNE can be constructed from every game which has a degenerate FNE.The author would like to thank an anonymous referee for invaluable comments and suggestions. 相似文献
13.
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
14.
Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games 总被引:1,自引:0,他引:1
The noncooperative multi-leader-follower game can be formulated as a generalized Nash equilibrium problem where each player solves a nonconvex mathematical program with equilibrium constraints. Two major deficiencies exist with such a formulation: One is that the resulting Nash equilibrium may not exist, due to the nonconvexity in each players problem; the other is that such a nonconvex Nash game is computationally intractable. In order to obtain a viable formulation that is amenable to practical solution, we introduce a class of remedial models for the multi-leader-follower game that can be formulated as generalized Nash games with convexified strategy sets. In turn, a game of the latter kind can be formulated as a quasi-variational inequality for whose solution we develop an iterative penalty method. We establish the convergence of the method, which involves solving a sequence of penalized variational inequalities, under a set of modest assumptions. We also discuss some oligopolistic competition models in electric power markets that lead to multi-leader-follower games.Jong-Shi Pang: The work of this authors research was partially supported by the National Science Foundation under grant CCR-0098013 and ECS-0080577 and by the Office of Naval Research under grant N00014-02-1-0286.Masao Fukushima: The work of this authors research was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Culture and Sports of Japan. 相似文献
15.
In this paper, we consider discrete-time \(N\) -person constrained stochastic games with discounted cost criteria. The state space is denumerable and the action space is a Borel set, while the cost functions are admitted to be unbounded from below and above. Under suitable conditions weaker than those in (Alvarez-Mena and Hernández-Lerma, Math Methods Oper Res 63:261–285, 2006) for bounded cost functions, we also show the existence of a Nash equilibrium for the constrained games by introducing two approximations. The first one, which is as in (Alvarez-Mena and Hernández-Lerma, Math Methods Oper Res 63:261–285, 2006), is to construct a sequence of finite games to approximate a (constrained) auxiliary game with an initial distribution that is concentrated on a finite set. However, without hypotheses of bounded costs as in (Alvarez-Mena and Hernández-Lerma, Math Methods Oper Res 63:261–285, 2006), we also establish the existence of a Nash equilibrium for the auxiliary game with unbounded costs by developing more shaper error bounds of the approximation. The second one, which is new, is to construct a sequence of the auxiliary-type games above and prove that the limit of the sequence of Nash equilibria for the auxiliary-type games is a Nash equilibrium for the original constrained games. Our results are illustrated by a controlled queueing system. 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.
B. Wernerfelt 《Journal of Optimization Theory and Applications》1987,53(1):133-138
The uniqueness of Nash equilibria is shown for a class of stochastic differential games where the dynamic constraints are linear in the control variables. The result is applied to an oligopoly.This paper benefitted from comments by two anonymous referees and by L. Blume and C. Simon. 相似文献
18.
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
19.
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
20.
Francesco Ciardiello 《Journal of Fixed Point Theory and Applications》2010,8(2):365-393
In this paper, we relax the classical quasi-concavity assumption for the existence of pure Nash equilibria in the setting
of constrained and unconstrained games in normal form. Multiconnected convexity (H. Ben-El-Mechaiekh et al., 1998) in spaces
without any linear structure is a keen point. We present two games in which we show how the generalized continuity and quasi-concavity
hypotheses are unrelated to each other as sufficient conditions for existence of Nash equilibria for games in normal form.
Then our results are applied to two non-zero-sum games lacking the classical quasi-concavity assumption (Nash, 1950) and the
more recent improvements (Ziad, 1999) and (Abalo and Kostreva, 2004). As minor results, we introduce new concept of convexity,
named a-convexity, and some counterexamples of the relationships between some continuity conditions on players’ payoffs imposed by
Lignola (1997), Reny (1999) and Simon (1987). 相似文献