Solutions of network games with pairwise interactions

Abstract

Работа посвящена кооперативным сетевым играм с попарным взаимодействием. Рассматривается двухшаговая игра, в первом состоянии которой происходит процесс формирования сети, а во втором -одновременные биматричные игры между соседями по сети. Построена характеристическая функция, доказана ее супермодулярность для случая одношаговой подыгры, начинающейся со второго состояния. Для особого класса сетей (сеть-звезда) найдена упрощенная формула вектора Шепли, не требующая вычисления значений характеристической функции по всем коалициям, а только лишь по коалициям размерностью не более двух.

Cooperative Solutions in Multi-Star Network Games

“…In (Petrosyan and Bulgakova, 2015) and (Bulgakova, 2019), the star model is proposed, and the Shapley value formula is given to study its distribution of income. (Petrosyan and Bulgakova, 2020) is dedicated to the study of multi-stage games with pairwise interactions under the consideration of complete graphs, constructing characteristic functions, and calculating Shapley values.…”

“…(Petrosyan and Bulgakova, 2020) is dedicated to the study of multi-stage games with pairwise interactions under the consideration of complete graphs, constructing characteristic functions, and calculating Shapley values. In (Bulgakova, 2019) and (Pankratova, 2018), studies on the construction of the characteristic function are carried out. (Hernandez, Munoz-Herrera and Sanchez, 2013) considered the interaction model between cooperation and coalition in network games.…”

The τ-value in Multistage Games with Pairwise Interactions

“…The principle of pairwise interaction in cooperative games was considered in (Bulgakova, 2019). This principle implies splitting the game into a family of simultaneous games between pairs of players -the vertices of the same edge in the network.…”

A note on cooperative differential games with pairwise interactions

“…In other words, the pairwise interaction games are proper subclass of the usual graphical or network game [2]. In the case of two strategies, pairwise interaction games on the complete graph can be modeled as congestion games [3].…”