The Strategy Dynamics of Collective Systems

Abstract

The intricacies of collective decision-making in systems-of-systems design pose challenges stemming from localized incentives, incomplete information, and decentralized control. Traditional optimization methods offer limited effectiveness in addressing these complexities, resulting in strategic uncertainty that impacts system performance and decision-making. This study identifies a critical research gap in harnessing the potential of game theory to illuminate and navigate these complexities. To bridge this gap, we extend the concept of structural fear and greed strategy dynamics from two-player games to multi-player scenarios. We introduce the concept of "strategic hindrance," a method to facilitate the evaluation of stability in collective action by analyzing players' beliefs about the game and other players' strategies, particularly in contexts where exhaustive knowledge about the links between players is elusive. We quantify structural fear and greed by dissecting normal-form games into player-reduced games, visualizing strategic hindrance spaces that offer insights into strategic trade-offs amid ambiguity and uncertainty. We apply this framework to a graphical volunteer's dilemma, demonstrating the evolution of unfavorable strategy dynamics with increasing player numbers, paralleling real-world phenomena like the bystander effect. We further show that we can induce favorable strategy dynamics and reduce the prevalence of undesirable equilibrium conditions by judiciously altering player connectivity. The findings of this research can play a vital role in enhancing our understanding of strategy dynamics in complex decision-making processes. The insights gained from this study can help design effective incentive mechanisms within system-of-systems engineering, which can lead to socially efficient outcomes.