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1.
Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that: (i) the extension of the solution policy to a later starting time and to any possible state brought about by the prior optimal behavior of the players would remain optimal; (ii) all players do not have incentive to deviate from the initial plan. In this paper, we develop a mechanism for the derivation of the payoff distribution procedures of subgame consistent solutions in stochastic differential games with transferable payoffs. The payoff distribution procedure of the subgame consistent solution can be identified analytically under different optimality principles. Demonstration of the use of the technique for specific optimality principles is shown with an explicitly solvable game. For the first time, analytically tractable solutions of cooperative stochastic differential games with subgame consistency are derived. 相似文献
2.
The least square prenucleolus and the least square nucleolus. Two values for TU games based on the excess vector 总被引:1,自引:0,他引:1
Luis M. Ruiz Federico Valenciano Jose M. Zarzuelo 《International Journal of Game Theory》1996,25(1):113-134
The nucleolus and the prenucleolus are solution concepts for TU games based on the excess vector that can be associated to any payoff vector. Here we explore some solution concepts resulting from a payoff vector selection based also on the excess vector but by means of an assessment of their relative fairness different from that given by the lexicographical order. We take the departure consisting of choosing the payoff vector which minimizes the variance of the resulting excesses of the coalitions. This procedure yields two interesting solution concepts, both a prenucleolus-like and a nucleolus-like notion, depending on which set is chosen to set up the minimizing problem: the set of efficient payoff vectors or the set of inputations. These solution concepts, which, paralleling the prenucleolus and the nucleolus, we call least square prenucleolus and least square nucleolus, are easy to calculate and exhibit nice properties. Different axiomatic characterizations of the former are established, some of them by means of consistency for a reasonable reduced game concept. 相似文献
3.
K. Tadenuma 《International Journal of Game Theory》1992,20(4):325-334
This paper establishes an axiomatization of the core by means of an internal consistency property with respect to a new reduced game introduced by Moulin (1985). Given a payoff vector chosen by a solution for some game, and given a subgroup of agents, we define thereduced game as that in which each coalition in the subgroup could attain payoffs to its members only if they are compatible with the initial payoffs toall the members outside of the subgroup. The solution isconsistent if it selects the same payoff distribution for the reduced game as initially. We show that consistency together with individual rationality characterizes the core of both transferable and non-transferable utility games. 相似文献
4.
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
5.
The consistent Shapley value for hyperplane games 总被引:1,自引:0,他引:1
A new value is defined for n-person hyperplane games, i.e., non-sidepayment cooperative games, such that for each coalition, the Pareto optimal set is linear. This is a generalization of the Shapley value for side-payment games. It is shown that this value is consistent in the sense that the payoff in a given game is related to payoffs in reduced games (obtained by excluding some players) in such a way that corrections demanded by coalitions of a fixed size are cancelled out. Moreover, this is the only consistent value which satisfies Pareto optimality (for the grand coalition), symmetry and covariancy with respect to utility changes of scales. It can be reached by players who start from an arbitrary Pareto optimal payoff vector and make successive adjustments. 相似文献
6.
If two or more players agree to cooperate while playing a game, they help one another to minimize their respective costs as long as it is not to their individual disadvantages. This leads at once to the concept of undominated solutions to a game. Anundominated orPareto-optimal solution has the property that, compared to any other solution, at least one playerdoes worse or alldo the same if they use a solution other than the Pareto-optimal one.Closely related to the concept of a Pareto-optimal solution is theabsolutely cooperative solution. Such a solution has the property that, compared to any other permissible solution,every playerdoes no better if a solution other than the absolutely cooperative one is employed.This paper deals with control-space properties of Pareto-optimal and absolutely cooperative solutions for both static, continuous games and differential games. Conditions are given for cases in which solutions to the Pareto-optimal and absolutely cooperative games lie in the interior or on the boundary of the control set.The solution of a Pareto-optimal or absolutely cooperative game is related to the solution of a minimization problem with avector cost criterion. The question of whether or not a problem with a vector cost criterion can be reduced to a family of minimization problems with ascalar cost criterion is also discussed.An example is given to illustrate the theory.This research was supported in part by NASA Grant No. NGR-03-002-011 and ONR Contract No. N00014-69-A-0200-1020. 相似文献
7.
In cooperative games over time with uncertainty, a stringent condition (subgame consistency) is required for a dynamically
stable solution. In particular, a cooperative solution is subgame consistent if an extension of the solution policy to a situation
with a later starting time and any feasible state brought about by prior optimal behavior would remain optimal. This paper
derives an analytically tractable payoff distribution procedure leading to the realization of subgame consistent solutions
in cooperative stochastic dynamic games. This is the first time that subgame consistent solutions in discrete-time dynamic
games under uncertainty are provided. 相似文献
8.
《Operations Research Letters》2021,49(2):278-282
Dynamic process is an approach to cooperative games, and it can be defined as that which leads the players to a solution for cooperative games. Hwang et al. (2005) adopted Hamiache’s associated game (2001) to provide a dynamic process leading to the Shapley value. In this paper, we propose a dynamic transfer scheme on the basis of the dual similar associated game, to lead to any solution satisfying both the inessential game property and continuity, starting from an arbitrary efficient payoff vector. 相似文献
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10.
The payoff of each coalition has been assumed to be known precisely in the conventional cooperative games. However, we may come across situations where some coalitional values remain unknown. This paper treats cooperative games whose coalitional values are not known completely. In the cooperative games it is assumed that some of coalitional values are known precisely but others remain unknown. Some complete games associated with such incomplete games are proposed. Solution concepts are studied in a special case where only values of the grand coalition and singleton coalitions are known. Through the investigations of solutions of complete games associated with the given incomplete game, we show a focal point solution suggested commonly from different viewpoints. 相似文献
11.
We prove that the core on the set of all transferable utility games with players contained in a universe of at least five
members can be axiomatized by the zero inessential game property, covariance under strategic equivalence, anonymity, boundedness,
the weak reduced game property, the converse reduced game property, and the reconfirmation property. These properties also
characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced games,
and on the set of superadditive games. Suitable extensions of these properties yield an axiomatization of the core on sets
of nontransferable utility games.
Received September 1999/Final version December 2000 相似文献
12.
In the context of cooperative TU-games, we introduce a recursive procedure to distribute the surplus of cooperation when there is an exogenous ordering among the set of players N. In each step of the process, using a given notion of reduced games, an upper and a lower bound for the payoff to the player at issue are required. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. For a family of reduction operations, the behavior of this new solution concept is analyzed. For any ordering of N, the core of the game turns out to be the set of sequentially compatible payoffs when the Davis–Maschler reduced games are used. Finally, we study which reduction operations give an advantage to the first player in the ordering. 相似文献
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14.
M. Álvarez-Mozos R. van den Brink G. van der Laan O. Tejada 《International Journal of Game Theory》2017,46(4):1089-1113
Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict the players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the hierarchical structure relative to that player. To define each solution, we consider a certain mapping that transforms the hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley value to the class of games with levels structure. Such transformation mappings are studied by means of properties that relate a player’s position in both types of structure. 相似文献
15.
R. Branzei S. Z. Alparslan Gök O. Branzei 《Central European Journal of Operations Research》2011,19(4):523-532
Uncertainty is a daily presence in the real world. It affects our decision making and may have influence on cooperation. Often
uncertainty is so severe that we can only predict some upper and lower bounds for the outcome of our actions, i.e., payoffs
lie in some intervals. A suitable game theoretic model to support decision making in collaborative situations with interval
data is that of cooperative interval games. Solution concepts that associate with each cooperative interval game sets of interval
allocations with appealing properties provide a natural way to capture the uncertainty of coalition values into the players’
payoffs. This paper extends interval-type core solutions for cooperative interval games by discussing the set of undominated
core solutions which consists of the interval nondominated core, the square interval dominance core, and the interval dominance
core. The interval nondominated core is introduced and it is shown that it coincides with the interval core. A straightforward
consequence of this result is the convexity of the interval nondominated core of any cooperative interval game. A necessary
and sufficient condition for the convexity of the square interval dominance core of a cooperative interval game is also provided. 相似文献
16.
Francesc Carreras 《European Journal of Operational Research》2011,211(1):148-159
The notions of total power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of cooperative games on any given player set where the semivalue is defined. Several properties of these linear mappings are stated and the role of unanimity games as eigenvectors is described. We also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game. As a consequence, we derive a method to compute for any semivalue by means of multilinear extensions, in the original game and also in all its subgames, (a) the total power, (b) the potential, and (c) the allocation to each player given by the semivalue. 相似文献
17.
We propose two flexible game models to represent and analyze cases that cannot be modeled by current game models. One is called sharing creditability game (SCG) and the other is called bottomline game (BLG). The new models transform cooperative games into new games that incorporate auxiliary information (noncooperative in nature) usually neglected in previous theories. The new games will be solved only by traditional noncooperative game theory. When the new solutions are applied to the original games, the solutions can reflect the auxiliary information in addition to the original objectives of the decision makers or players. Generally, the new solutions are different from the cooperative and the noncooperative solutions of the original games. Existing transferable utility (TU) games and noncooperative games will coincide with special cases of the two new game models. Using SCG and BLG, the prisoner’s dilemma can be reformulated and a richer set of decisions can be considered for the players. The two new game models have potential applications in military and socioeconomic situations.This research was partly funded by the College Engineering, Ohio State University. 相似文献
18.
Koji Takamiya 《International Journal of Game Theory》2001,30(2):195-207
This paper examines the α-core of strategic games by means of the consistency principle. I provide a new definition of a
reduced game for strategic games. And I define consistency (CONS) and two forms of converse consistency (COCONS and COCONS*) under this definition of reduced games. Then I axiomatize the α-core for families of strategic games with bounded payoff
functions by the axioms CONS, COCONS*, weak Pareto optimality (WPO) and one person rationality (OPR). Furthermore, I show that these four axioms are logically
independent. In proving this, I also axiomatize the α-individually rational solution by CONS, COCONS and OPR for the same
families of games. Here the α-individually rational solution is a natural extension of the classical `maximin' solution.
Received: June 1998/Final version: 6 July 2001 相似文献
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