Prevention of the tragedy of the commons mediated by a noisy information channel

Synergy between evolutionary dynamics of cooperation and fluctuating states of a shared resource being consumed by the cooperators is essential for averting the tragedy of the commons. Not only in humans, but also in the cognitively limited organisms, this interplay between the resource and the cooperation is ubiquitously witnessed. The strategically interacting players engaged in such game-environment feedback scenarios naturally pick strategies based on their perception of the environmental state. Such perception invariably happens through some sensory information channels that the players are endowed with. The unfortunate reality is that any sensory channel must be noisy due to various factors; consequently, the perception of the environmental state becomes faulty, rendering the players incapable of adopting the strategy that they otherwise would. Intriguingly, the situation is not as bad as it sounds. Here we introduce the hitherto neglected information channel between players and the environment into the paradigm of stochastic evolutionary games with a view to bringing forward the counterintuitive possibility of emergence and sustenance of cooperation on account of the noise in the channel. Our primary study is in the simplest nontrivial setting of a two-state stochastically fluctuating resource harnessed by a large unstructured population of cooperators and defectors adopting either memory-1 strategies or reactive strategies while engaged in repeated two-player interactions. The effect of a noisy information channel in enhancing the cooperation in a reactive-strategied population is unprecedented. We find that the propensity of cooperation in the population is inversely related to the mutual information (normalized by the channel capacity) of the corresponding information channel.