This paper addresses the problem of adaptively controlling the bias parameter in nonlinear opinion dynamics (NOD) to allocate agents into groups of arbitrary sizes for the purpose of maximizing collective rewards. In previous work, an algorithm based on the coupling of NOD with an multi-objective behavior optimization was successfully deployed as part of a multi-robot system in an autonomous task allocation field experiment. Motivated by the field results, in this paper we propose and analyze a new task allocation model that synthesizes NOD with an evolutionary game framework. We prove sufficient conditions under which it is possible to control the opinion state in the group to a desired allocation of agents between two tasks through an adaptive bias using decentralized feedback. We then verify the theoretical results with a simulation study of a collaborative evolutionary division of labor game.

The emergence of cooperative behavior, despite natural selection favoring rational self-interest, presents a significant evolutionary puzzle. Evolutionary game theory elucidates why cooperative behavior can be advantageous for survival. However, the impact of non-uniformity in the frequency of actions, particularly when actions are altered in the short term, has received little scholarly attention. To demonstrate the relationship between the non-uniformity in the frequency of actions and the evolution of cooperation, we conducted multi-agent simulations of evolutionary games. In our model, each agent performs actions in a chain-reaction, resulting in a non-uniform distribution of the number of actions. To achieve a variety of non-uniform action frequency, we introduced two types of chain-reaction rules: one where an agent's actions trigger subsequent actions, and another where an agent's actions depend on the actions of others. Our results revealed that cooperation evolves more effectively in scenarios with even slight non-uniformity in action frequency compared to completely uniform cases. In addition, scenarios where agents' actions are primarily triggered by their own previous actions more effectively support cooperation, whereas those triggered by others' actions are less effective. This implies that a few highly active individuals contribute positively to cooperation, while the tendency to follow others' actions can hinder it.

This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include i) the analysis of statistical properties of the number of (stable) equilibria in a random evolutionary game, and ii) the modelling of safety behaviours' evolution and the risk posed by advanced Artificial Intelligence technologies in a technology development race. Finally, it includes an outlook and some suggestions for future researchers.

Policy and guideline proposals for ethical artificial-intelligence research have proliferated in recent years. These are supposed to guide the socially-responsible development of AI for the common good. However, there typically exist incentives for non-cooperation (i.e., non-adherence to such policies and guidelines); and, these proposals often lack effective mechanisms to enforce their own normative claims. The situation just described constitutes a social dilemma---namely, a situation where no one has an individual incentive to cooperate, though mutual cooperation would lead to the best outcome for all involved. In this paper, we use stochastic evolutionary game dynamics to model this social dilemma in the context of the ethical development of artificial intelligence. This formalism allows us to isolate variables that may be intervened upon, thus providing actionable suggestions for increased cooperation amongst numerous stakeholders in AI. Our results show how stochastic effects can help make cooperation viable in such a scenario. They suggest that coordination for a common good should be attempted in smaller groups in which the cost for cooperation is low, and the perceived risk of failure is high. This provides insight into the conditions under which we should expect such ethics proposals to be successful with regard to their scope, scale, and content.