Cooperation in the spatial prisoner's dilemma game with probabilistic abstention
This work addresses the evolution of cooperation in social dilemmas, offering a more realistic model of voluntary participation, though it is incremental in extending existing abstention frameworks.
The study introduced probabilistic abstention into the spatial prisoner's dilemma, showing that intermediate probabilities create a hybrid game that most effectively promotes cooperation, outperforming traditional optional games.
Research has shown that the addition of abstention as an option transforms social dilemmas to rock-paper-scissor type games, where defectors dominate cooperators, cooperators dominate abstainers (loners), and abstainers (loners), in turn, dominate defectors. In this way, abstention can sustain cooperation even under adverse conditions, although defection also persists due to cyclic dominance. However, to abstain or to act as a loner has, to date, always been considered as an independent, third strategy to complement traditional cooperation and defection. Here we consider probabilistic abstention, where each player is assigned a probability to abstain in a particular instance of the game. In the two limiting cases, the studied game reverts to the prisoner's dilemma game without loners or to the optional prisoner's dilemma game. For intermediate probabilities, we have a new hybrid game, which turns out to be most favorable for the successful evolution of cooperation. We hope this novel hybrid game provides a more realistic view of the dilemma of optional/voluntary participation.