Directional learning and the provisioning of public goods

TL;DR

This paper demonstrates that public good provision can emerge from simple reinforcement learning dynamics without strategic information, by introducing the concept of k-strong equilibria to explain cooperative behavior.

Contribution

It introduces the concept of k-strong equilibria and shows how directional learning explains public good provision without social preferences.

Findings

Directional learning explains cooperation without strategic info.

Maximal k-strength of equilibrium influences stationary distribution.

Public goods can be provisioned under adverse conditions.

Abstract

We consider an environment where players are involved in a public goods game and must decide repeatedly whether to make an individual contribution or not. However, players lack strategically relevant information about the game and about the other players in the population. The resulting behavior of players is completely uncoupled from such information, and the individual strategy adjustment dynamics are driven only by reinforcement feedbacks from each player's own past. We show that the resulting "directional learning" is sufficient to explain cooperative deviations away from the Nash equilibrium. We introduce the concept of k-strong equilibria, which nest both the Nash equilibrium and the Aumann-strong equilibrium as two special cases, and we show that, together with the parameters of the learning model, the maximal k-strength of equilibrium determines the stationary distribution. The provisioning of public goods can be secured even under adverse conditions, as long as players are sufficiently responsive to the changes in their own payoffs and adjust their actions accordingly. Substantial levels of public cooperation can thus be explained without arguments involving selflessness or social preferences, solely on the basis of uncoordinated directional (mis)learning.