The Role of Execution Errors in Populations of Ultimatum Bargaining Agents

The design of artificial intelligent agents is frequently accomplished by equipping individuals with mechanisms to choose actions that maximise a subjective utility function. This way, the implementation of behavioural errors, that systematically prevent agents from using optimal strategies, often seems baseless. In this paper, we employ an analytical framework to study a population of Proposers and Responders, with conflicting interests, that co-evolve by playing the prototypical Ultimatum Game. This framework allows to consider an arbitrary discretisation of the strategy space, and allows us to describe the dynamical impact of individual mistakes by Responders, on the collective success of this population. Conveniently, this method can be used to analyse other continuous strategy interactions. In the case of Ultimatum Game, we show analytically how seemingly disadvantageous errors empower Responders and become the source of individual and collective long-term success, leading to a fairer distribution of gains. This conclusion remains valid for a wide range of selection pressures, population sizes and mutation rates.