scholarly journals A Cooperative Network Packing Game with Simple Paths

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1683
Author(s):  
Sergei Dotsenko ◽  
Vladimir Mazalov
Keyword(s):  
Characteristic Function ◽  
Explicit Form ◽  
Cooperative Network ◽  
The Core ◽  
Fixed Length ◽  
Simple Paths

We consider a cooperative packing game in which the characteristic function is defined as the maximum number of independent simple paths of a fixed length included in a given coalition. The conditions under which the core exists in this game are established, and its form is obtained. For several particular graphs, the explicit form of the core is presented.

scholarly journals Dark matter from non-relativistic embedding gravity

2021 ◽  
pp. 2150101
Author(s):  
S. A. Paston
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Explicit Form ◽  
Equations Of Motion ◽  
Additional Contribution ◽  
Relativistic Limit ◽  
The Core ◽  
The Stability ◽  
Dimensional Surface

We study the possibility to explain the mystery of the dark matter (DM) through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple string-inspired geometrical principle: our spacetime is considered here as a four-dimensional surface in a flat bulk. We show that among the solutions of embedding gravity, there is a class of solutions equivalent to solutions of GR with an additional contribution of non-relativistic embedding matter, which can serve as cold DM. We prove the stability of such type of solutions and obtain an explicit form of the equations of motion of embedding matter in the non-relativistic limit. According to them, embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the [Formula: see text]CDM model.

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.

Research on Construction of the Mutually Supportive Network Using a Spring-Water Spots

2012 ◽  
Vol 524-527 ◽  
pp. 3853-3860
Author(s):  
Reiji Nanba ◽  
Masakazu Takahashi
Keyword(s):  
Spring Water ◽  
Elderly Persons ◽  
Cooperative Network ◽  
Cooperative Relationships ◽  
The Core

In this research, we have verified whether spring-water spots have what it takes to be the core of the mutually supportive network. Based on this verification, we have evaluated whether spring-water spots can become the foundation of a mutually supportive network. The above-mentioned findings show us that elderly persons visit spring-water spots at their own initiative, and they can build better and cooperative relationships with other visitors. Therefore, it is highly probable that spring-water spots have sufficient qualities to serve as the core for a mutually-cooperative network.

Component Acquisition Games

2015 ◽  
Vol 17 (04) ◽  
pp. 1550012
Author(s):  
Imma Curiel
Keyword(s):  
Integer Programming ◽  
Characteristic Function ◽  
Programming Formulation ◽  
Time Intervals ◽  
The Core ◽  
Integer Programming Formulation ◽  
A Company

This paper focuses on situations in several companies each of which has a set of jobs that it has to complete. Each job has a specific starting and ending time and a specific starting and ending point. In order to complete its jobs a company needs to acquire components. There are several types of components. Each job requires exactly one component but not all components are suitable for all jobs. By cooperating, the companies can reduce the costs of acquisition. A component can be used by several companies as long as there is no overlap in the time-intervals of usage by different companies and there is enough time to move the component from where a company has stopped using it to where the next company needs it. A cooperative component acquisition game is constructed to model the cooperation between the companies. This game need not be balanced. Additional properties are introduced that guarantee the game to be totally balanced. We construct an element of the core by using the integer programming formulation of the characteristic function. These games have some relationship with coloring games but we show that results that are valid for coloring games do not hold for them.

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.

The Core of Aggregative Cooperative Games with Externalities

2016 ◽  
Vol 16 (1) ◽  
pp. 389-410 ◽  
Author(s):  
Giorgos Stamatopoulos
Keyword(s):  
Normal Form ◽  
Characteristic Function ◽  
Coalition Formation ◽  
Cooperative Games ◽  
Grand Coalition ◽  
Normal Form Games ◽  
The Core ◽  
Aggregative Games ◽  
Games With Externalities

AbstractThis paper analyzes cooperative games with externalities generated by aggregative normal form games. We construct the characteristic function of a coalition S for various coalition formation rules and we examine the corresponding cores. We first show that the $$\gamma $$-core is non-empty provided each player’s payoff decreases in the sum of all players’ strategies. We generalize this result by showing that if S believes that the outside players form at least $$l(s) = n - s - (s - 1)$$ coalitions, then S has no incentive to deviate from the grand coalition and the corresponding core is non-empty (where n is the number of players in the game and s the number of members of S). We finally consider the class of linear aggregative games (Martimort and Stole 2010). In this case, if S believes that the outsiders form at least $$\widehat l(s) = {n \over s} - 1$$ coalitions [where $$\widehat l(s) \le l(s)$$] a core non-emptiness result holds again.

scholarly journals A direct approach to the stable distributions

2016 ◽  
Vol 48 (A) ◽  
pp. 261-282 ◽  
Author(s):  
E. J. G. Pitman ◽  
Jim Pitman
Keyword(s):  
Functional Equation ◽  
Characteristic Function ◽  
Integral Representation ◽  
Explicit Form ◽  
Regular Variation ◽  
Stable Distribution ◽  
Stable Distributions ◽  
Direct Approach ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible

AbstractThe explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying the theory of regular variation, without appeal to the general Lévy‒Khintchine integral representation of infinitely divisible distributions.

scholarly journals On a Simplified Method of Defining Characteristic Function in Stochastic Games

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1135
Author(s):  
Elena Parilina ◽  
Leon Petrosyan
Keyword(s):  
Characteristic Function ◽  
Stochastic Games ◽  
Stochastic Game ◽  
New Method ◽  
Characteristic Functions ◽  
Zero Sum Games ◽  
Subgame Consistency ◽  
The Core ◽  
Simplified Method ◽  
Zero Sum

In the paper, we propose a new method of constructing cooperative stochastic game in the form of characteristic function when initially non-cooperative stochastic game is given. The set of states and the set of actions for any player is finite. The construction of the characteristic function is based on a calculation of the maximin values of zero-sum games between a coalition and its anti-coalition for each state of the game. The proposed characteristic function has some advantages in comparison with previously defined characteristic functions for stochastic games. In particular, the advantages include computation simplicity and strong subgame consistency of the core calculated with the values of the new characteristic function.

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