Pairwise-Interaction Games

AbstractWe provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

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Branching processes with interactions: subcritical cooperative regime

Advances in Applied Probability ◽

10.1017/apr.2020.59 ◽

2021 ◽

Vol 53 (1) ◽

pp. 251-278

Author(s):

Adrián González Casanova ◽

Juan Carlos Pardo ◽

José Luis Pérez

Keyword(s):

Population Genetics ◽

Branching Processes ◽

Jump Diffusion ◽

Pairwise Interaction ◽

Pairwise Interactions ◽

Different Types ◽

Interesting Object ◽

The Moment ◽

Dynamics Of Populations

AbstractIn this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we consider include pairwise interactions, such as competition, annihilation, and cooperation; and interactions among several individuals that can be viewed as catastrophes. We call such families of processes branching processes with interactions. Our aim is to study their long-term behaviour under a specific regime of the pairwise interaction parameters that we introduce as the subcritical cooperative regime. Under such a regime, we prove that a process in this class comes down from infinity and has a moment dual which turns out to be a jump-diffusion that can be thought as the evolution of the frequency of a trait or phenotype, and whose parameters have a classical interpretation in terms of population genetics. The moment dual is an important tool for characterizing the stationary distribution of branching processes with interactions whenever such a distribution exists; it is also an interesting object in its own right.

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Parametric and non-parametric estimation for pairwise-interaction point processes

Probability Theory and Applications ◽

10.1515/9783112314227-010 ◽

1987 ◽

pp. 101-112

Keyword(s):

Point Processes ◽

Pairwise Interaction ◽

Parametric Estimation ◽

Interaction Point ◽

Non Parametric Estimation ◽

Non Parametric

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Numerical simulation of the pairwise interaction of deformable cells during migration in a microchannel

Physical Review E ◽

10.1103/physreve.90.012705 ◽

2014 ◽

Vol 90 (1) ◽

Cited By ~ 2

Author(s):

Hongzhi Lan ◽

Damir B. Khismatullin

Keyword(s):

Numerical Simulation ◽

Pairwise Interaction

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The Asymptotic Behavior of Nonextinction Probabilityof a Branching Process with Pairwise Interaction of Particles

Theory of Probability and Its Applications ◽

10.1137/s0040585x97975666 ◽

1997 ◽

Vol 41 (4) ◽

pp. 617-631

Author(s):

I. S. Badalbaev ◽

A. V. Dryakhlov

Keyword(s):

Asymptotic Behavior ◽

Branching Process ◽

Pairwise Interaction

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The Combination of Pairwise and Group Interactions Promotes Consensus in Opinion Dynamics

Complexity ◽

10.1155/2021/4382836 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Xiaoxuan Liu ◽

Changwei Huang ◽

Haihong Li ◽

Qionglin Dai ◽

Junzhong Yang

Keyword(s):

Complex Systems ◽

Numerical Simulations ◽

Complete Graph ◽

Group Interaction ◽

Opinion Dynamics ◽

Pairwise Interaction ◽

Network Structures ◽

Opinion Formation ◽

Group Interactions ◽

Bounded Confidence

In complex systems, agents often interact with others in two distinct types of interactions, pairwise interaction and group interaction. The Deffuant–Weisbuch model adopting pairwise interaction and the Hegselmann–Krause model adopting group interaction are the two most widely studied opinion dynamics. In this study, we propose a novel opinion dynamics by combining pairwise and group interactions for agents and study the effects of the combination on consensus in the population. In the model, we introduce a parameter α to control the weights of the two interactions in the dynamics. Through numerical simulations, we find that there exists an optimal α , which can lead to a highest probability of complete consensus and minimum critical bounded confidence for the formation of consensus. Furthermore, we show the effects of α on opinion formation by presenting the observations for opinion clusters. Moreover, we check the robustness of the results on different network structures and find the promotion of opinion consensus by α not limited to a complete graph.

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Cooperative n-person Prisoner's Dilemma on a Network

Contributions to Game Theory and Management ◽

10.21638/11701/spbu31.2021.11 ◽

2021 ◽

Vol 14 ◽

pp. 122-126

Author(s):

Aleksandra L. Grinikh ◽

◽

Leon A. Petrosyan ◽

Keyword(s):

Game Theory ◽

Cooperative Game ◽

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Pairwise Interaction ◽

Network Interaction ◽

The Game Theory

In the paper n-person prisoner's dilemma on the network is investigated. A cooperative game with the pairwise interaction of players is constructed. The model is a modification of the classic 2-person prisoner's dilemma problem in the game theory. Network interaction provide an ability to take into account the in uence only to the adjacent players from the whole set of players. The feature of the game is found that allows to make a decision about necessity of playing dominated strategy by a few players. This solution is based on the number of the adjacent players. The work is a continuation of the paper published earlier by Grinikh A.L. and Petrosyan L.A. in 2021.

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