Cooperation in Threshold Public Projects with Binary Actions

TL;DR

This paper investigates the conditions under which cooperation can emerge in binary-action public projects, proves the computational complexity of finding cooperative equilibria, and proposes algorithms using external investments and matching funds to promote cooperation.

Contribution

It introduces the NP-completeness of identifying cooperative equilibria in threshold public projects and offers two algorithms to facilitate cooperation with near-optimal costs.

Findings

Deciding cooperative equilibria is NP-complete.

Matching funds are more cost-effective than external investments.

Algorithms can induce cooperation with near-optimal costs.

Abstract

When can cooperation arise from self-interested decisions in public goods games? And how can we help agents to act cooperatively? We examine these classical questions in a pivotal participation game, a variant of public good games, where heterogeneous agents make binary participation decisions on contributing their endowments, and the public project succeeds when it has enough contributions. We prove it is NP-complete to decide the existence of a cooperative Nash equilibrium such that the project succeeds. We also identify two natural special scenarios where this decision problem is tractable. We then propose two algorithms to help cooperation in the game. Our first algorithm adds an external investment to the public project, and our second algorithm uses matching funds. We show that the cost to induce a cooperative Nash equilibrium is near-optimal for both algorithms. Finally, the cost of matching funds can always be smaller than the cost of adding an external investment. Intuitively, matching funds provide a greater incentive for cooperation than adding an external investment does.