Abstract
The problem of promoting the evolution of cooperative behaviour within populations of self-regarding individuals has been intensively investigated across diverse fields of behavioural, social and computational sciences. In most studies, cooperation is assumed to emerge from the combined actions of participating individuals within the populations, without taking into account the possibility of external interference and how it can be performed in a cost-efficient way. Here, we bridge this gap by studying a cost-efficient interference model based on evolutionary game theory, where an exogenous decision-maker aims to ensure high levels of cooperation from a population of individuals playing the one-shot Prisoner’s Dilemma, at a minimal cost. We derive analytical conditions for which an interference scheme or strategy can guarantee a given level of cooperation while at the same time minimising the total cost of investment (for rewarding cooperative behaviours), and show that the results are highly sensitive to the intensity of selection by interference. Interestingly, we show that a simple class of interference that makes investment decisions based on the population composition can lead to significantly more cost-efficient outcomes than standard institutional incentive strategies, especially in the case of weak selection.
Highlights
The study of the evolution of cooperation in populations of self-interested individuals has been given significant attention in a number of disciplines, ranging from Evolutionary Biology, Economics, Physics, Computer Science and Social Science
Under evolutionary dynamics of an eco-system, consisting of various stochastic effects such as those resulting from behavioural update and mutation, undesired behaviours can reoccur over time, if the interference was not sufficiently or efficiently carried out in the
The research question here is to determine when to make an investment at each time step, and by how much, in order to achieve our desired ratio of cooperation within the population such that the total cost of interference is minimised. We formalise this general problem of cost-efficient interference as a bi-objective optimisation problem, where the first objective is to provide a sequential interference scheme that maximises the frequency of cooperative behaviours within the population, while the second is to minimise the expected total cost of interference
Summary
The study of the evolution of cooperation in populations of self-interested individuals has been given significant attention in a number of disciplines, ranging from Evolutionary Biology, Economics, Physics, Computer Science and Social Science. They include kin and group selection[5,6], direct and indirect reciprocities[7,8,9,10,11], spatial networks[12,13,14,15,16,17,18,19], reward and punishment[20,21,22,23,24,25], and pre-commitments[26,27,28,29,30] In these works, the evolution of cooperation is typically originated from the emergence and stability of participating individuals’ strategic behaviours, which are cooperative in nature (e.g. direct reciprocity interactions are dominated by reciprocal strategies such as tit-for-tat like strategies, who tend to cooperate with alike individuals, leading to end populations with high levels of cooperation[8]). We formalise this general problem of cost-efficient interference as a bi-objective optimisation problem, where the first objective is to provide a sequential interference scheme (i.e., a sequence of interference decisions over time) that maximises the frequency of cooperative behaviours within the population, while the second is to minimise the expected total cost of interference
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