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1.
This paper deals with a class of equilibria which are based on the use of memory strategies in the context of continuous-time stochastic differential games. In order to get interpretable results, we will focus the study on a stochastic differential game model of the exploitation of one species of fish by two competing fisheries. We explore the possibility of defining a so-called cooperative equilibrium, which will implement a fishing agreement. In order to obtain that equilibrium, one defines a monitoring variable and an associated retaliation scheme. Depending on the value of the monitoring variable, which provides some evidence of a deviation from the agreement, the probability increases that the mode of a game will change from a cooperative to a punitive one. Both the monitoring variable and the parameters of this jump process are design elements of the cooperative equilibrium. A cooperative equilibrium designed in this way is a solution concept for a switching diffusion game. We solve that game using the sufficient conditions for a feedback equilibrium which are given by a set of coupled HJB equations. A numerical analysis, approximating the solution of the HJB equations through an associated Markov game, enables us to show that there exist cooperative equilibria which dominate the classical feedback Nash equilibrium of the original diffusion game model.This research was supported by FNRS-Switzerland, NSERC-Canada, FCAR-Quebec. 相似文献
2.
B. Tolwinski 《Journal of Optimization Theory and Applications》1981,34(4):485-501
A new solution of a two-person, nonzero-sum Stackelberg game, with linear dynamics, quadratic performance criteion, and closed-loop information available to both players, is presented. This solution is applicable to all problems where the leader is able to influence the objective function of the follower, and this function is strictly convex with respect to the control variable handled by the follower. The resulting equilibrium strategies adapt to the possible nonoptimal behavior of players at some stages of the game. The strategy of the leader has a simple interpretation of a threat formulated by the leader toward the follower and, if necessary, carried out one stage after the follower has played inconsistently with the leader's wishes. 相似文献
3.
Piotr Więcek 《Mathematical Methods of Operations Research》2009,69(1):59-79
We present a discrete model of two-person constant-sum dynamic strategic market game. We show that for every value of discount
factor the game with discounted rewards possesses a pure stationary strategy equilibrium. Optimal strategies have some useful
properties, such as Lipschitz property and symmetry. We also show value of the game to be nondecreasing both in state and
discount factor. Further, for some values of discount factor, exact form of optimal strategies is found. For β less than , there is an equilibrium such that players make large bids. For β close to 1, there is an equilibrium with small bids. Similar result is obtained for the long run average reward game. 相似文献
4.
Mrinal K. Ghosh 《Journal of Mathematical Analysis and Applications》2003,283(1):167-179
We study a zero sum differential game of fixed duration in a separable Hilbert space. We prove a minimax principle and establish the equivalence between the dynamic programming principle and the existence of a saddle point equilibrium. We also prove sufficient conditions for optimality. 相似文献
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6.
S. E. Bukhtoyarov V. A. Emelichev 《Computational Mathematics and Mathematical Physics》2006,46(7):1193-1199
A finite cooperative game in normal form is considered. Its optimality principle is specified with the help of a parameter such that Pareto optimality and Nash equilibrium correspond to two extreme parameter values. The limiting level of perturbations in the coefficients of payoff functions that do not give rise to new efficient situations is studied. 相似文献
7.
This paper characterizes the stationary (subgame) perfect equilibria of an n-person noncooperative bargaining model with characteristic functions, and provides strategic foundations of some cooperative solution concepts such as the core, the bargaining set and the kernel. The contribution of this paper is twofold. First, we show that a linear programming formulation successfully characterizes the stationary (subgame) perfect equilibria of our bargaining game. We suggest a linear programming formulation as an algorithm for the stationary (subgame) perfect equilibria of a class of n-person noncooperative games. Second, utilizing the linear programming formulation, we show that stationary (subgame) perfect equilibria of n-person noncooperative games provide strategic foundations for the bargaining set and the kernel. 相似文献
8.
William Stanford 《Operations Research Letters》2010,38(2):94-96
We consider the set of all m×n bimatrix games with ordinal payoffs. We show that on the subset E of such games possessing at least one pure strategy Nash equilibrium, both players prefer the role of leader to that of follower in the corresponding Stackelberg games. This preference is in the sense of first-degree stochastic dominance by leader payoffs of follower payoffs. It follows easily that on the complement of E, the follower’s role is preferred in the same sense. Thus we see a tendency for leadership preference to obtain in the presence of multiple pure strategy Nash equilibria in the underlying game. 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.
Gerhard J. Woeginger 《Mathematical Methods of Operations Research》1995,41(3):313-324
We investigate a cooperative game with two types of players envolved: Every player of the first type owns a unit size bin, and every player of the second type owns an item of size at most one. The value of a coalition of players is defined to be the maximum overall size of packed items over all packings of the items owned by the coalition into the bins owned by the coalition.We prove that for=1/3 this cooperative bin packing game is-balanced in the taxation model of Faigle and Kern (1993).This research was supported by the Christian Doppler Laboratorium für Diskrete Optimierung. 相似文献
11.
The paper deals with a problem of optimal management of a common-property fishery, modelled as a two-player differential game. Under nonclassical assumptions on harvest rates and utilities, a feedback Nash equilibrium is determined, using a bionomic equilibrium concept. Later on, this assumption is relaxed and a feedback Nash equilibrium is established under minimal hypotheses. 相似文献
12.
This paper is a study of a general class of deterministic dynamic games with an atomless measure space of players and an arbitrary time space. The payoffs of the players depend on their own strategy, a trajectory of the system and a function with values being finite dimensional statistics of static profiles. The players' available decisions depend on trajectories of the system.The paper deals with relations between static and dynamic open-loop equilibria as well as their existence. An equivalence theorem is proven and theorems on the existence of a dynamic equilibrium are shown as consequences. 相似文献
13.
Recently, the concept of classical bargaining set given by Aumann and Maschler in 1964 has been extended to fuzzy bargaining set. In this paper, we give a modification to correct some weakness of this extension. We also extend the concept of the Mas-Colell's bargaining set (the other major type of bargaining sets) to its corresponding fuzzy bargaining set. Our main effort is to prove existence theorems for these two types of fuzzy bargaining sets. We will also give necessary and sufficient conditions for these bargaining sets to coincide with the Aubin Core in a continuous superadditive cooperative fuzzy game which has a crisp maximal coalition of maximum excess at each payoff vector. We show that both Aumann-Maschler and Mas-Colell fuzzy bargaining sets of a continuous convex cooperative fuzzy game coincide with its Aubin core. 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
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16.
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
17.
Kali P. Rath 《International Journal of Game Theory》1998,27(4):525-537
This paper examines Hotelling's model of location with linear transportation cost. Existence of pure strategy subgame perfect
equilibria in the infinitely repeated price game with fixed locations is proved. These subgame perfect equilibria have a stick
and carrot structure. Given firm locations, there are discount factors sufficiently high that there is a subgame perfect equilibrium
with a two-phase structure. Given the discount factors, there are stationary subgame perfect equilibria for a wide range of
locations. However, for some pairs of location, no symmetric simple penal code exists, all subgame perfect profiles are nonstationary,
and there is only one seller in the market in infinitely many periods.
Received July 1996/Final version May 1998 相似文献
18.
Pricing and Advertising of Private and National Brands in a Dynamic Marketing Channel 总被引:1,自引:0,他引:1
N. Amrouche G. Martín-Herrán G. Zaccour 《Journal of Optimization Theory and Applications》2008,137(3):465-483
We consider a marketing channel where a retailer sells, along the manufacturer’s brand, its own store brand. We assume that
each player invests in advertising in order to build the brand’s goodwill. One distinctive feature of this paper is the introduction
of the negative effect of own advertising on other player’s goodwill stock evolution. We characterize feedback-Nash pricing
and advertising strategies and assess the impact of the store brand and national brand’s goodwill stocks on these strategies
in different settings. The main findings suggest first that investing in building up some equity for each brand reduces the
price competition between them and propels the market power for both. Second, the retailer will pass to consumer an increase
in its purchasing cost of the national brand in all situations as no coordination is taken into account to counter the double
marginalization problem. Finally, the higher the brand equity of the store brand, the more the retailer invests in advertising. 相似文献
19.
In most of studies on multiobjective noncooperative games, games are represented in normal form and a solution concept of
Pareto equilibrium solutions which is an extension of Nash equilibrium solutions has been focused on. However, for analyzing
economic situations and modeling real world applications, we often see cases where the extensive form representation of games
is more appropriate than the normal form representation. In this paper, in a multiobjective two-person nonzero-sum game in
extensive form, we employ the sequence form of strategy representation to define a nondominated equilibrium solution which
is an extension of a Pareto equilibrium solution, and provide a necessary and sufficient condition that a pair of realization
plans, which are strategies of players in sequence form, is a nondominated equilibrium solution. Using the necessary and sufficient
condition, we formulate a mathematical programming problem yielding nondominated equilibrium solutions. Finally, giving a
numerical example, we demonstrate that nondominated equilibrium solutions can be obtained by solving the formulated mathematical
programming problem. 相似文献
20.
Though the prevalence of hepatitis B began to decline for the first time in 2010, it remains unclear whether this downward trend is permanent and the disease will be eradicated in mainland China under the current measures. Because a large number of hepatitis B virus (HBV) carriers and unknown HBV infections is characteristic of HBV infections in China, a mathematical model was designed and fitted to the reported hepatitis B data. The estimated basic reproduction number is 1.2861 (95\% confidence interval (CI) 1.2386-1.3302), which remains greater than one. Thus, the decline in 2010 may be part of the temporary benefits of public policy measures and should not be interpreted as indicative of successful intervention, although interventions do provide some benefits. To assess the effects of various interventions, the global uncertainty and sensitivity analyses revealed that the contribution of carriers is always greater than that of acute infections, and the prevalence of hepatitis B in China may be primarily a result of transmission by unknown patients. Therefore, strategies for controlling the HBV endemic, which target known patients, are unlikely to be highly effective. Additionally, three feasible strategies are proposed, although the benefits of these strategies may change radically over time. 相似文献