Prioritised Learning in Snowdrift-Type Games

Abstract

Cooperation is a ubiquitous and beneficial behavioural trait despite being prone to exploitation by free-riders. Hence, cooperative populations are prone to invasions by selfish individuals. However, a population consisting of only free-riders typically does not survive. Thus, cooperators and free-riders often coexist in some proportion. An evolutionary version of a Snowdrift Game proved its efficiency in analysing this phenomenon. However, what if the system has already reached its stable state but was perturbed due to a change in environmental conditions? Then, individuals may have to re-learn their effective strategies. To address this, we consider behavioural mistakes in strategic choice execution, which we refer to as incompetence. Parametrising the propensity to make such mistakes allows for a mathematical description of learning. We compare strategies based on their relative strategic advantage relying on both fitness and learning factors. When strategies are learned at distinct rates, allowing learning according to a prescribed order is optimal. Interestingly, the strategy with the lowest strategic advantage should be learnt first if we are to optimise fitness over the learning path. Then, the differences between strategies are balanced out in order to minimise the effect of behavioural uncertainty.

Where Do Mistakes Lead? A Survey of Games with Incompetent Players

“…The concept of incompetence was considered in biological settings when studying the evolution of social behaviour [36][37][38][39][40]. That is, incompetence now acts at the selection level rather than organisms themselves.…”

“…When allowing for learning after the stable equilibrium is reached, the focus of the analysis is the population's need to re-learn its effective strategies in an optimal manner. Hence, in [39] the learning under incompetence was considered with respect to maximising the fitness over the learning path.…”

“…Theorem 9 [39] The direction of the optimal learning path is determined by the sign of δ: for δ > 0 the direction of Strategy 2 is optimal and for δ < 0 the direction of Strategy 1 is optimal. If δ = 0, then there is no difference in the direction of optimal learning, that is,…”