Social Distancing as a Network Population Game in a Socially Connected World

TL;DR

This paper models social distancing as a network population game where individuals choose social sites to minimize contacts, identifying equilibrium strategies through maximal r-regular subnetworks, applicable to various network types and weighted networks.

Contribution

It introduces a novel game-theoretic framework for social distancing, linking equilibrium strategies to maximal r-regular subnetworks in social networks.

Findings

Equilibrium strategies correspond to maximal r-regular subnetworks.

Strategies can be adapted to weighted networks with different contact values.

The model applies to various network types, including disconnected and flexible social distancing scenarios.

Abstract

While social living is considered to be an indispensable part of human life in today's ever-connected world, social distancing has recently received much public attention on its importance since the outbreak of the coronavirus pandemic. In fact, social distancing has long been practiced in nature among solitary species, and been taken by human as an effective way of stopping or slowing down the spread of infectious diseases. Here we consider a social distancing problem for how a population, when in a world with a network of social sites, decides to visit or stay at some sites while avoiding or closing down some others so that the social contacts across the network can be minimized. We model this problem as a network population game, where every individual tries to find some network sites to visit or stay so that he/she can minimize all his/her social contacts. In the end, an optimal strategy can be found for every one, when the game reaches an equilibrium. We show that a large class of equilibrium strategies can be obtained by selecting a set of social sites that forms a so-called maximal r-regular subnetwork. The latter includes many well studied network types, which are easy to identify or construct, and can be completely disconnected (with r = 0) for the most strict isolation, or allow certain degree of connectivities (with r > 0) for more flexible distancing. We derive the equilibrium conditions of these strategies, and analyze their rigidity and flexibility on different types of r-regular subnetworks. We also extend our model to weighted networks, when different contact values are assigned to different network sites.