Individual Altruism Cannot Overcome Congestion Effects in a Global Pandemic Game

TL;DR

This paper models a global pandemic as a game where individuals choose locations based on infection and isolation costs, revealing that altruism can worsen outcomes and that selfish behavior can be near-optimal.

Contribution

It introduces a game-theoretic model of pandemic behavior, analyzing equilibria for selfish and altruistic populations, and highlights counterintuitive effects of altruism on social costs.

Findings

Selfish equilibria are generally not optimal but are within a constant factor of the best.

There are infinitely many stable altruistic equilibria, most worse than selfish ones.

Altruistic equilibria can have unbounded social costs, unlike in network congestion games.

Abstract

A key challenge in responding to public health crises such as COVID-19 is the difficulty of predicting the results of feedback interconnections between the disease and society. As a step towards understanding these interconnections, we pose a simple game-theoretic model of a global pandemic in which individuals can choose where to live, and we investigate the global behavior that may emerge as a result of individuals reacting locally to the competing costs of isolation and infection. We study the game-theoretic equilibria that emerge from this setup when the population is composed of either selfish or altruistic individuals. First, we demonstrate that as is typical in these types of games, selfish equilibria are in general not optimal, but that all stable selfish equilibria are within a constant factor of optimal. Second, there exist infinitely-many stable altruistic equilibria; all but finitely-many of these are worse than the worst selfish equilibrium, and the social cost of altruistic equilibria is unbounded. Our work is in sharp contrast to recent work in network congestion games in which all altruistic equilibria are socially optimal. This suggests that a population without central coordination may react very poorly to a pandemic, and that individual altruism could even exacerbate the problem.