Introduction to network theory and game theory as frameworks for the analysis of critical infrastructure

2013 ◽  
pp. 22-28 ◽  
Author(s):  
Urszula Kanturska ◽  
Panagiotis Angeloudis
Keyword(s):  
Game Theory ◽  
Network Theory ◽  
Critical Infrastructure

scholarly journals On the Existence of Pairwise Stable Weighted Networks

2020 ◽  
Vol 45 (4) ◽  
pp. 1393-1404 ◽  
Author(s):  
Philippe Bich ◽  
Lisa Morhaim
Keyword(s):  
Game Theory ◽  
Existence Theorem ◽  
Network Theory ◽  
Network Formation ◽  
Pairwise Stability ◽  
Weighted Networks ◽  
Standard Application ◽  
Unweighted Network ◽  
Game Theoretic

In network theory, Jackson and Wolinsky introduced a now widely used notion of stability for unweighted network formation called pairwise stability. We prove the existence of pairwise stable weighted networks under assumptions on payoffs that are similar to those in Nash's and Glicksberg’s existence theorem (continuity and quasi concavity). Then, we extend our result, allowing payoffs to depend not only on the network, but also on some game-theoretic strategies. The proof is not a standard application of tools from game theory, the difficulty coming from the fact that the pairwise stability notion has both cooperative and noncooperative features. Last, some examples are given and illustrate how our results may open new paths in the literature on network formation.

Combining evolutionary game theory and network theory to analyze human cooperation patterns

2016 ◽  
Vol 91 ◽  
pp. 17-24 ◽  
Author(s):  
Marialisa Scatà ◽  
Alessandro Di Stefano ◽  
Aurelio La Corte ◽  
Pietro Liò ◽  
Emanuele Catania ◽  
...  
Keyword(s):  
Game Theory ◽  
Evolutionary Game Theory ◽  
Network Theory ◽  
Evolutionary Game

scholarly journals Using chemical reaction network theory to show stability of distributional dynamics in game theory

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ross Cressman ◽  
Vlastimil Křivan
Keyword(s):  
Game Theory ◽  
Chemical Reaction ◽  
Network Theory ◽  
Group Formation ◽  
Evolutionary Game ◽  
Reaction Network ◽  
Chemical Reaction Network ◽  
Positive Equilibrium ◽  
Distributional Dynamics ◽  
Chemical Reaction Network Theory

<p style='text-indent:20px;'>This article shows how to apply results of chemical reaction network theory (CRNT) to prove uniqueness and stability of a positive equilibrium for pairs/groups distributional dynamics that arise in game theoretic models. Evolutionary game theory assumes that individuals accrue their fitness through interactions with other individuals. When there are two or more different strategies in the population, this theory assumes that pairs (groups) are formed instantaneously and randomly so that the corresponding pairs (groups) distribution is described by the Hardy–Weinberg (binomial) distribution. If interactions times are phenotype dependent the Hardy-Weinberg distribution does not apply. Even if it becomes impossible to calculate the pairs/groups distribution analytically we show that CRNT is a general tool that is very useful to prove not only existence of the equilibrium, but also its stability. In this article, we apply CRNT to pair formation model that arises in two player games (e.g., Hawk-Dove, Prisoner's Dilemma game), to group formation that arises, e.g., in Public Goods Game, and to distribution of a single population in patchy environments. We also show by generalizing the Battle of the Sexes game that the methodology does not always apply.</p>

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