scholarly journals Cooperative optimality principals in differential games on networks

2020 ◽  
Vol 12 (4) ◽  
pp. 93-111
Author(s):  
Анна Тур ◽  
Anna Tur ◽  
Леон Аганесович Петросян ◽  
Leon Petrosyan
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Network Structure ◽  
Shapley Value ◽  
The Core ◽  
Investment Game ◽  
The Shapley Value ◽  
Research Investment ◽  
Optimality Principles

The paper describes a class of differential games on networks. The construction of cooperative optimality principles using a special type of characteristic function that takes into account the network structure of the game is investigated. The core, the Shapley value and the tau-value are used as cooperative optimality principles. The results are demonstrated on a model of a differential research investment game, where the Shapley value and the tau-value are explicitly constructed.

scholarly journals Strong Time-Consistent Solution for Cooperative Differential Games with Network Structure

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 755
Author(s):  
Anna Tur ◽  
Leon Petrosyan
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Network Structure ◽  
Shapley Value ◽  
Explicit Calculation ◽  
The Shapley Value ◽  
Consistent Solution ◽  
Optimality Principles ◽  
Cooperative Differential Games

One class of cooperative differential games on networks is considered. It is assumed that interaction on the network is possible not only between neighboring players, but also between players connected by paths. Various cooperative optimality principles and their properties for such games are investigated. The construction of the characteristic function is proposed, taking into account the network structure of the game and the ability of players to cut off connections. The conditions under which a strong time-consistent subcore is not empty are studied. The formula for explicit calculation of the Shapley value is derived. The results are illustrated by the example of one differential marketing game.

scholarly journals Feedback based strategies for autonomous linear quadratic cooperative differential games with continuous updating

2020 ◽  
Vol 13 ◽  
pp. 244-251
Author(s):  
Ildus Kuchkarov ◽  
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Shapley Value ◽  
Linear Quadratic ◽  
Cooperative Solution ◽  
Cooperative Strategies ◽  
The Shapley Value ◽  
Cooperative Differential Games

In the paper the class of linear quadratic cooperative differential games with continuous updating is considered. Here the case of feedback based strategies is used to construct cooperative strategies with continuous updating. Characteristic function with continuous updating, cooperative trajectory with continuous updating and cooperative solution are constructed. For the cooperative solution we use the Shapley value.

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.

COPING WITH UNCERTAINTY IN n-PERSON GAMES

2000 ◽  
Vol 08 (05) ◽  
pp. 503-523 ◽  
Author(s):  
SILVIU GUIASU
Keyword(s):  
Characteristic Function ◽  
Security Council ◽  
Shapley Value ◽  
Statistical Equilibrium ◽  
Individual Rationality ◽  
Von Neumann ◽  
Minimum Deviation ◽  
The Shapley Value ◽  
Un Security Council ◽  
Person Game

A solution of n-person games is proposed, based on the minimum deviation from statistical equilibrium subject to the constraints imposed by the group rationality and individual rationality. The new solution is compared with the Shapley value and von Neumann-Morgenstern's core of the game in the context of the 15-person game of passing and defeating resolutions in the UN Security Council involving five permanent members and ten nonpermanent members. A coalition classification, based on the minimum ramification cost induced by the characteristic function of the game, is also presented.

scholarly journals Hart–Mas-Colell consistency and the core in convex games

2021 ◽  
Author(s):  
Bas Dietzenbacher ◽  
Peter Sudhölter
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Individual Rationality ◽  
Transferable Utility ◽  
Convex Games ◽  
The Core ◽  
The Shapley Value ◽  
Scale Covariance

AbstractThis paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.

On Harsanyi Dividends and Asymmetric Values

2017 ◽  
Vol 19 (03) ◽  
pp. 1750012 ◽  
Author(s):  
Pierre Dehez
Keyword(s):  
Characteristic Function ◽  
Shapley Value ◽  
Transferable Utility ◽  
The Shapley Value ◽  
Transferable Utility Games ◽  
Harsanyi Dividends

The concept of dividend in transferable utility games was introduced by Harsanyi [1959], offering a unifying framework for studying various valuation concepts, from the Shapley value to the different notions of values introduced by Weber. Using the decomposition of the characteristic function used by Shapley to prove uniqueness of his value, the idea of Harsanyi was to associate to each coalition a dividend to be distributed among its members to define an allocation. Many authors have contributed to that question. We offer a synthesis of their work, with a particular attention to restrictions on dividend distributions, starting with the seminal contributions of Vasil’ev, Hammer, Peled and Sorensen and Derks, Haller and Peters, until the recent papers of van den Brink, van der Laan and Vasil’ev.

Multiplayer Allocations in the Presence of Diminishing Marginal Contributions: Cooperative Game Analysis and Applications in Management Science

2020 ◽  
Author(s):  
Mingming Leng ◽  
Chunlin Luo ◽  
Liping Liang
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
Extreme Points ◽  
Game Analysis ◽  
The Core ◽  
The Shapley Value ◽  
Code Sharing ◽  
Marginal Contributions ◽  
Least Core ◽  
Necessary And Sufficient

We use cooperative game theory to investigate multiplayer allocation problems under the almost diminishing marginal contributions (ADMC) property. This property indicates that a player’s marginal contribution to a non-empty coalition decreases as the size of the coalition increases. We develop ADMC games for such problems and derive a necessary and sufficient condition for the non-emptiness of the core. When the core is non-empty, at least one extreme point exists, and the maximum number of extreme points is the total number of players. The Shapley value may not be in the core, which depends on the gap of each coalition. A player can receive a higher allocation based on the Shapley value in the core than based on the nucleolus, if the gap of the player is no greater than the gap of the complementary coalition. We also investigate the least core value for ADMC games with an empty core. To illustrate the applications of our results, we analyze a code-sharing game, a group buying game, and a scheduling profit game. This paper was accepted by Chung Piaw Teo, optimization.

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