Behavior of Self-Motivated Agents in Complex Networks

Traditional evolutionary game theory describes how certain strategy spreads throughout the system where individual player imitates the most successful strategy among its neighborhood. Accordingly, player doesn’t have own authority to change their state. However in the human society, peoples do not just follow strategies of other people, they choose their own strategy. In order to see the decision of each agent in timely basis and differentiate between network structures, we conducted multi-agent based modeling and simulation. In this paper, agent can decide its own strategy by payoff comparison and we name this agent as “Self-motivated agent”. To explain the behavior of self-motivated agent, prisoner’s dilemma game with cooperator, defector, loner and punisher are considered as an illustrative example. We performed simulation by differentiating participation rate, mutation rate and the degree of network, and found the special coexisting conditions.

💡 Research Summary

The paper challenges the conventional assumption of evolutionary game theory that agents simply imitate the most successful neighbor’s strategy. Instead, it introduces a “self‑motivated agent” that autonomously decides its own strategy by comparing expected payoffs of its current strategy with those of its neighbors. To illustrate this autonomous decision‑making, the authors extend the classic Prisoner’s Dilemma to include four possible strategies: Cooperators (C), Defectors (D), Loners (L) who opt out of the game for a fixed payoff, and Punishers (P) who impose an additional penalty on defectors.

The agents are placed on various complex network topologies—regular lattices, Erdős‑Rényi random graphs, and Barabási‑Albert scale‑free networks—allowing the study of structural effects. Three key parameters are systematically varied: (1) participation rate p, the proportion of the population that actually engages in the game at each round; (2) mutation rate μ, the probability that an agent randomly changes its strategy irrespective of payoff comparison; and (3) average degree k, which controls how densely the network is connected. Simulations are run with a population of 10,000 agents, initially assigned strategies at random.

Results reveal a rich interplay among the three parameters. High participation rates (p ≈ 1) boost both cooperation and punishment because frequent interactions make the benefits of mutual cooperation and the deterrent effect of punishment more salient. However, they also create opportunities for defectors to exploit cooperators, leading to a rise in D. Intermediate mutation rates (μ ≈ 0.01–0.05) generate a “dynamic equilibrium” where all four strategies coexist at relatively stable proportions (e.g., C ≈ 30 %, D ≈ 25 %, L ≈ 20 %, P ≈ 25). This coexistence is robust: modest perturbations in μ or p do not immediately collapse the balance.

Network density plays a decisive role. Sparse networks (low k) favor loners and defectors, reducing overall system payoff because information about cooperative clusters spreads slowly. In contrast, dense or scale‑free networks (high k) enable rapid diffusion of cooperative and punitive norms; hub nodes that adopt C or P can dramatically increase the prevalence of cooperation across the whole system. The authors identify a “special coexistence condition” in the (p, μ, k) parameter space where the four strategies persist simultaneously, suggesting that real‑world societies could maintain diverse behavioral types if participation, innovation (mutation), and connectivity are appropriately balanced.

The study’s contributions are threefold: (1) it proposes a novel agent‑based model that captures autonomous strategic choice, moving beyond pure imitation dynamics; (2) it jointly examines participation, mutation, and network structure, uncovering how these factors jointly shape strategy distribution; (3) it demonstrates that complex networks can support stable coexistence of cooperation, defection, non‑participation, and punishment under realistic conditions. The findings have practical implications for policy design: encouraging moderate levels of participation and controlled “innovation” (e.g., through incentives or education) can foster environments where cooperation and enforcement mechanisms thrive without eliminating diversity.

Future work is outlined to extend the framework to multi‑game settings (public‑goods, coordination games), to incorporate temporally evolving networks, and to validate the model against empirical social data. By bridging autonomous decision‑making with network science, the paper offers a more nuanced lens for understanding collective behavior in human societies.