Fractional Punishment of Free Riders to Improve Cooperation in Optional Public Good Games

Abstract

Improving and maintaining cooperation are fundamental issues for any project to be time-persistent, and sanctioning free riders may be the most applied method to achieve it. However, the application of sanctions differs from one group (project or institution) to another. We propose an optional, public good game model where a randomly selected set of the free riders is punished. To this end, we introduce a parameter that establishes the portion of free riders sanctioned with the purpose to control the population state evolution in the game. This parameter modifies the phase portrait of the system, and we show that, when the parameter surpasses a threshold, the full cooperation equilibrium point becomes a stable global attractor. Hence, we demonstrate that the fractional approach improves cooperation while reducing the sanctioning cost.

Discipline and punishment in panoptical public goods games

“…This later analysis converges the proposal presented in Botta et al 72 , where fractional punishment emerges as a beneficial mechanism under resource-scarce conditions. Still, if defectors invade the population (Fig.…”

“…The penalized defector payoff becomes zero when is established. This condition restores the fractional punishment mechanism as suggested in 72 . Whereas, , the game is set as a public goods game with no incentives, as described by 18 .…”

“…In this context, in our prior study 72 , we have shown that imposing penalties on just a portion of the defectors in a compulsory PGG can induce a reevaluation of behavior among other potential free riders. This approach has been verified as effective for maintaining cooperation within a well-mixed population governed by replicator dynamics, under a framework of centralized punishment.…”

How many and how much should be punished?: A panoptical approach in analyzing cooperation in Public Goods Games.

“…A prevalent compromise identified in previous studies, such as the work of 20 , entails penalizing a smaller group of defectors, causing the remaining free-riders to adjust their tactics. This strategy, similar to random inspections, successfully enforces norms and rules.…”

“…A mechanism proposed in 20 paved the way in this sector by designing a "fractional punishment" mechanism in which chosen defectors had their payoffs completely erased, imitating a punitive service disconnect. However, this technique merely addressed the "how many" of the problem, leaving an intriguing gap in our understanding.…”