Investment in the common good: free rider effect and the stability of mixed strategy equilibria

TL;DR

This paper investigates the existence and stability of mixed strategy equilibria in a stochastic game of investment in the common good, highlighting the role of repeated opportunities and asymmetry among players.

Contribution

It demonstrates that mixed strategy equilibria can exist despite asymmetry if repeated investment opportunities are considered, challenging previous instability results.

Findings

Mixed strategy equilibrium exists with repeated investments despite asymmetry.

High asymmetry can eliminate the mixed strategy equilibrium.

Policymakers can prevent inefficient equilibria by promoting asymmetry.

Abstract

In the game of investment in the common good, the free rider problem can delay the stakeholders' actions in the form of a mixed strategy equilibrium. However, it has been recently shown that the mixed strategy equilibria of the stochastic war of attrition are destabilized by even the slightest degree of asymmetry between the players. Such extreme instability is contrary to the widely accepted notion that a mixed strategy equilibrium is the hallmark of the war of attrition. Motivated by this quandary, we search for a mixed strategy equilibrium in a stochastic game of investment in the common good. Our results show that, despite asymmetry, a mixed strategy equilibrium exists if the model takes into account the repeated investment opportunities. The mixed strategy equilibrium disappears only if the asymmetry is sufficiently high. Since the mixed strategy equilibrium is less efficient than pure strategy equilibria, it behooves policymakers to prevent it by promoting a sufficiently high degree of asymmetry between the stakeholders through, for example, asymmetric subsidy.