DYNAMIC COOPERATIVE GAMES

2000 ◽  
Vol 02 (01) ◽  
pp. 47-65 ◽  
Author(s):  
JERZY A. FILAR ◽  
LEON A. PETROSJAN
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Continuous Time ◽  
Cooperative Games ◽  
Solution Concept ◽  
Time Consistency ◽  
Standard Solution ◽  
Instantaneous Characteristic ◽  
Characteristic Function Form ◽  
Over Time

We consider dynamic cooperative games in characteristic function form in the sense that the characteristic function evolves over time in accordance with a difference or differential equation that is influenced not only by the current ("instantaneous") characteristic function but also by the solution concept used to allocate the benefits of cooperation among the players. The latter solution concept can be any one of a number of now standard solution concepts of cooperative game theory but, for demonstration purposes, we focus on the core and the Shapley value. In the process, we introduce some new mechanisms by which players may regard the evolution of cooperative game over time and analyse them with respect to the goal of attaining time consistency either in discrete or in continuous time setting. In discrete time, we illustrate the phenomena that can arise when an allocation according to a given solution concept is used to adapt the values of coalitions at successive time points. In continuous time, we introduce the notion of an "instantaneous" game and its integration over time.

Irrational-Behavior-Proof Conditions Based on Limit Characteristic Functions

2019 ◽  
Vol 7 (1) ◽  
pp. 1-16
Author(s):  
Cui Liu ◽  
Hongwei Gao ◽  
Ovanes Petrosian ◽  
Juan Xue ◽  
Lei Wang
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Games ◽  
Characteristic Functions ◽  
The Core ◽  
The Shapley Value ◽  
Irrational Behavior ◽  
The Individual

Abstract Irrational-behavior-proof (IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions. Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally, an illustrative example is given.

scholarly journals Computational Aspects of the Preference Cores of Supermodular Two-Scenario Cooperative Games

2018 ◽  
Author(s):  
Daisuke Hatano ◽  
Yuichi Yoshida
Keyword(s):  
Characteristic Function ◽  
Cooperative Games ◽  
Solution Concept ◽  
Multicast Tree ◽  
Characteristic Functions ◽  
Solution Concepts ◽  
Induced Subgraph ◽  
Computational Aspects ◽  
Tree Game ◽  
Multiple Scenarios

In a cooperative game, the utility of a coalition of players is given by the characteristic function, and the goal is to find a stable value division of the total utility to the players. In real-world applications, however, multiple scenarios could exist, each of which determines a characteristic function, and which scenario is more important is unknown. To handle such situations, the notion of multi-scenario cooperative games and several solution concepts have been proposed. However, computing the value divisions in those solution concepts is intractable in general. To resolve this issue, we focus on supermodular two-scenario cooperative games in which the number of scenarios is two and the characteristic functions are supermodular and study the computational aspects of a major solution concept called the preference core. First, we show that we can compute the value division in the preference core of a supermodular two-scenario game in polynomial time. Then, we reveal the relations among preference cores with different parameters. Finally, we provide more efficient algorithms for deciding the non-emptiness of the preference core for several specific supermodular two-scenario cooperative games such as the airport game, multicast tree game, and a special case of the generalized induced subgraph game.

scholarly journals Owen-stable coalition partitions in games with vector payoffs

2019 ◽  
Vol 10 (3) ◽  
pp. 3-23 ◽  
Author(s):  
Василий Гусев ◽  
Vasily Gusev ◽  
Владимир Мазалов ◽  
Vladimir Mazalov
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Owen Value ◽  
Stable Coalition ◽  
Vector Payoffs ◽  
Definition Of ◽  
Games With Vector Payoffs

The paper is devoted to the study of multicriteria cooperative games with vector payoffs and coalition partition. The imputation which is based on the concept of the Owen value is proposed. We use it for the definition of stable coalition partition for bicriteria games. In three person cooperative game with 0-1 characteristic function the conditions under which the coalition partition is stable are found.

VALUES FOR GAMES ON THE CYCLES OF A DIGRAPH

2012 ◽  
Vol 14 (02) ◽  
pp. 1250008
Author(s):  
WILLIAM OLVERA-LOPEZ ◽  
FRANCISCO SANCHEZ-SANCHEZ
Keyword(s):  
Mathematical Model ◽  
Characteristic Function ◽  
Shapley Value ◽  
Cooperative Games ◽  
Axiomatic Characterization ◽  
Efficient Solutions ◽  
Function Form ◽  
New Class ◽  
Characteristic Function Form

In this paper we introduce a new class of cooperative games. We define a characteristic function over the cycles of a digraph. We present a mathematical model for this situation and an axiomatic characterization of a solution for this class of cooperative games. This is introduced as a method to measure the importance of the nodes in a digraph, and can be related with the Shapley value of a game in characteristic function form. Also, we extend the modeling by applying coalitional structures for the nodes and r-efficient solutions, where the allocation amount is a real number r, showing axiomatic solutions in both cases.

MULTISTAGE COOPERATIVE GAMES AND PROBLEM OF TIME CONSISTENCY

2004 ◽  
Vol 06 (01) ◽  
pp. 157-170 ◽  
Author(s):  
VICTOR ZAKHAROV ◽  
MARIA DEMENTIEVA
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Time Consistency ◽  
Necessary And Sufficient Conditions ◽  
Dynamic Consistency ◽  
Problem Of Time ◽  
Reduced Game ◽  
Necessary And Sufficient

In this paper we consider the problem of time-consistency of the subcore in a multistage TU-cooperative game. We propose necessary and sufficient conditions for the time-consistency of an imputation from the subcore. Based on these conditions, we suggest an algorithm providing time-consistency of a selector of the subcore. Besides, we prove consistency of the subcore with respect to the MDM-reduction. Finally we introduce the notions of reduced game and dynamic consistency for multistage cooperative games. One of the main results of this paper is a theorem stating some properties of dynamic consistency of the subcore selectors. We focus particularly on the conditions of the dynamic consistency of the subcore with respect to the MDM-reduced game.

scholarly journals Wage bargaining as an optimal control problem: a dynamic version of the efficient bargaining model

2021 ◽  
Author(s):  
Marco Guerrazzi
Keyword(s):  
Optimal Control ◽  
Continuous Time ◽  
Bargaining Power ◽  
Wage Bargaining ◽  
Bargaining Model ◽  
Speed Of Convergence ◽  
Wage Setting ◽  
Dynamic Version ◽  
Efficient Bargaining ◽  
Over Time

AbstractIn this paper, I develop a dynamic version of the efficient bargaining model grounded on optimal control in which a firm and a union bargain over the wage in a continuous-time environment under the supervision of an infinitely lived mediator. Overturning the findings achieved by means of a companion right-to-manage framework, I demonstrate that when employment is assumed to adjust itself with some attrition in the direction of the contract curve implied by the preferences of the two bargainers, increases in the bargaining power of the firm (union) accelerate (delay) the speed of convergence towards the stationary solution. In addition, confirming the reversal of the results obtained when employment moves over time towards the firm’s labour demand, I show that the dynamic negotiation of wages tends to penalize unionized workers and favour the firm with respect to the bargaining outcomes retrieved with a similar static wage-setting model.

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