Unbiased third-party bots lead to a tradeoff between cooperation and social payoffs

TL;DR

This paper examines the impact of third-party bots--agents that do not directly participate in games but unbiasedly modify the payoffs of normal players engaged in prisoner's dilemma interactions--on the emergence of cooperation.

Abstract

The rise of artificial intelligence (AI) offers new opportunities to influence cooperative dynamics with greater applicability and control. In this paper, we examine the impact of third-party bots--agents that do not directly participate in games but unbiasedly modify the payoffs of normal players engaged in prisoner's dilemma interactions--on the emergence of cooperation. Using an evolutionary simulation model, we demonstrate that unbiased bots are unable to shift the defective equilibrium among normal players in well-mixed populations. However, in structured populations, despite their unbiased actions, the bots spontaneously generate distinct impacts on cooperators and defectors, leading to enhanced cooperation. Notably, bots that apply negative influences are more effective at promoting cooperation than those applying positive ones, as fewer bots are needed to catalyze cooperative behavior among normal players. However, as the number of bots increases, a trade-off emerges: while cooperation is maintained, overall social payoffs decline. These findings highlight the need for careful management of AI's role in social systems, as even well-intentioned bots can have unintended consequences on collective outcomes.

Figures (6)

• Figure 1: In structured populations, bots that impose negative effects are more effective at promoting cooperation than those impose positive effects. However, these bots introduce a trade-off: as their proportion increase, cooperation is further promoted, but at the cost of reduced social payoffs. Panel (A) illustrates the evolutionary dynamics of cooperation in a well-mixed population with $r = 0.2$, where neither positive nor negative influences from bots support the establishment of cooperation. The population converges to a state where $x=0$, i.e., pure defection. Results for the structured population depicted are the fraction of cooperation and average social payoffs among normal individuals as functions of the proportion of bots $\rho$ and influence of bot' action $\beta$ for (B) low-dilemma strength $r=0.05$ and (C) high-dilemma strength $r=0.14$ , respectively.
• Figure 2: Depiced are (A) the involvement of bots introduces both direct influences and crowding-out effect on individuals. The crowding-out effect arises when bots occupy the limited interaction space within a structured population, leading to a reduction in interactions between individuals and thereby diminishing individuals' potential maximum payoff by a $\Delta \pi$. Both cooperators and defectors are influenced by these effects, contingent upon the spatial arrangement of bots relative to the groups of cooperators and defectors. Both cooperators and defectors are impacted by these effects, but potential for cooperation to expand is contingent upon the spatial arrangement of bots with respect to the clusters of cooperators and defectors. (B) and (C) illustrate evolutionary snapshots under the influence of bots exerting positive (i.e., $\beta=1$) and negative impacts (i.e., $\beta=-1$), respectively, at $r = 0.05$. The evolution of cooperation in structured populations undergoes enduring period (END) of discrete cooperator extinction, cooperative clusters expanding period (EXP), and eventual stabilizationwang2013insight. We reveal the self-organizing characteristics during the evolutionary process by analyzing the temporal dynamics of the cooperator fraction ($F_C\in[0,1]$), cooperator assortativity ($\lambda_C \in[-1,1]$), calculated as the mean difference between the proportion of cooperative and defective neighbors for cooperator, and bot-cooperator assortativity ($\Delta \tau \in[-1,1]$), calculated as the mean difference in the proportion of cooperators and defectors surrounding the bots. The dashed line in left-most panels shows the steady-state fraction of cooperation $F_C^* = 0.58$ for traditional case without bots.
• Figure 3: An intermediate proportion of bots optimizes cooperation facilitation, as too few bots are insufficient to establish cooperative clusters, while too many bots isolate individuals and hinder cluster expansion. The spatial distribution at steady state under high dilemma strength $r = 0.14$ is shown for various bot proportions. Cooperators, defectors, and bots are depicted in blue, red, and white, respectively.
• Figure 4: Under strong imitation conditions where individuals rely strictly on payoff differences, bots can cultivate and enhance cooperation. Depicted are the fraction of cooperation as a function of imitation strength $\kappa$ for low dilemma strength $r=0.05$ and high dilemma strength $r=0.14$.
• Figure 5: In heterogeneous action distribution scenarios, bots that exert non-positive influences continue to enhance cooperation, while those exerting positive influences not only fail to support cooperation but also undermine the efficacy of bots applying non-positive influences. The results consider bot behaviors with mean values $\overline{\beta}=0$ follows uniform and normal distribution, and two skewed distributions ($\overline{\beta}=-0.25$) and ($\overline{\beta}=0.25$). (A) shows the frequency distributions of bot behaviors under normal and skewed distributions. Behaviors following a normal distribution are sampled from $\mathcal{N}(0,\ 0.15)$, while skewed distributions are sampled from beta distribution $\mathcal{B}(1.2,\ 9.6)$ and rescaled to $[-1,1]$. (B) and (C) illustrate the fraction of cooperation $(F_C)$ and average social payoffs as functions of the proportion of bots $(\rho)$ for low-dilemma strength $r=0.05$ and high-dilemma strength $r=0.14$, respectively.