Altruism Design in Networked Public Goods Games

TL;DR

This paper extends networked public goods games by incorporating altruism into agents' utility functions, analyzing how modifying altruism networks influences collective investment, with solutions ranging from linear programming to tractable special cases.

Contribution

Introduces a novel altruism-based extension to public goods games and studies the computational complexity of modifying altruism networks to promote the common good.

Findings

Linear programming solves the problem with fractional altruism modifications.

All-or-nothing altruism modifications are generally intractable.

Certain special cases of altruism network modifications are computationally tractable.

Abstract

Many collective decision-making settings feature a strategic tension between agents acting out of individual self-interest and promoting a common good. These include wearing face masks during a pandemic, voting, and vaccination. Networked public goods games capture this tension, with networks encoding strategic interdependence among agents. Conventional models of public goods games posit solely individual self-interest as a motivation, even though altruistic motivations have long been known to play a significant role in agents' decisions. We introduce a novel extension of public goods games to account for altruistic motivations by adding a term in the utility function that incorporates the perceived benefits an agent obtains from the welfare of others, mediated by an altruism graph. Most importantly, we view altruism not as immutable, but rather as a lever for promoting the common good. Our central algorithmic question then revolves around the computational complexity of modifying the altruism network to achieve desired public goods game investment profiles. We first show that the problem can be solved using linear programming when a principal can fractionally modify the altruism network. While the problem becomes in general intractable if the principal's actions are all-or-nothing, we exhibit several tractable special cases.