Evolution of fairness in hybrid populations with specialised AI agents

TL;DR

We address fairness in hybrid human\u2013AI societies using a bipartite Ultimatum Game, placing humans and AI into separate proposer and receiver populations. The authors compare unconditional Samaritan AI agents (always offering or accepting fairness) with a Discriminatory AI proposer that conditions offers on predicted receiver behavior, within finite well-mixed Moran dynamics and a Markov-chain fixation framework. Key findings show AI receivers robustly promote population-wide fairness, while AI proposers are ineffective under strong selection; Discriminatory AI proposer outperforms both Samaritan variants and reduces the required AI count, especially when selection is strong, indicating targeted enforcement beats unconditional generosity. The work provides design principles for deploying asymmetric AI interventions in increasingly hybrid environments, highlighting trade-offs between intervention costs and social welfare and suggesting extensions to networks, learning-enabled agents, and noisy information.

Abstract

Fairness in hybrid societies hinges on a simple choice: should AI be a generous host or a strict gatekeeper? Moving beyond symmetric models, we show that asymmetric social structures--like those in hiring, regulation, and negotiation--AI that guards fairness outperforms AI that gifts it. We bridge this gap with a bipartite hybrid population model of the Ultimatum Game, separating humans and AI into distinct proposer and receiver groups. We first introduce Samaritan AI agents, which act as either unconditional fair proposers or strict receivers. Our results reveal a striking asymmetry: Samaritan AI receivers drive population-wide fairness far more effectively than Samaritan AI proposers. To overcome the limitations of the Samaritan AI proposer, we design the Discriminatory AI proposer, which predicts co-players' expectations and only offers fair portions to those with high acceptance thresholds. Our results demonstrate that this Discriminatory AI outperforms both types of Samaritan AI, especially in strong selection scenarios. It not only sustains fairness across both populations but also significantly lowers the critical mass of agents required to reach an equitable steady state. By transitioning from unconditional modelling to strategic enforcement, our work provides a pivotal framework for deploying asymmetric AIs in the increasingly hybrid society.

Figures (12)

• Figure 1: Schematic of the Ultimatum Game in hybrid human-AI populations. The model consists of two populations: the proposer population, where players choose between a high ($h$) and a low ($l$) offer, the and receiver population, where players have either a high ($h$) or low ($l$) acceptance threshold. Each population can be a hybrid population consisting of human players and AI agents. AI agents are pre-designed with a strategic rule. Human players update their strategy following social learning to learn the successful strategy within their population.
• Figure 2: AI receivers outperform AI proposers in enhancing fairness in both populations. Panels in the top row show the fraction of $H$-proposers and $H$-receivers among human players as a function of the number of AI proposers with different selection intensities, respectively. Panels in the bottom row show the fraction of $H$-proposers and $H$-receivers as a function of the number of AI receivers with different selection intensities, respectively. Parameters are set as $h=0.5$, $l=0.1$, $\beta \in \{0.1, 1, 10, 100\}$ from left to the right column, respectively, $M_R=0$ in the top row and $M_P=0$ in the bottom row.
• Figure 3: AI receivers effectively alter the evolutionary direction to enhance fairness. The percentages indicate the stationary distribution of each state. The arrows represent the transition direction between paired strategies, highlighting the transition probabilities and the stronger direction of transitions. Dashed lines represent neutral transitions. Horizontal (vertical) lines represent transition within the receiver (proposer) population. Parameters are set as $h=0.5$, $l=0.1$, (a) $M_P=M_R=0$, $\beta=0.1$, (b) $M_P=1$, $M_R=0$, $\beta=0.1$, (c) $M_P=0$, $M_R=1$, $\beta=0.1$, (d) $M_P=M_R=0$, $\beta=1$, (e) $M_P=14, M_R=0$, $\beta=1$, and (f) $M_P=0, M_R=1$, $\beta=1$.
• Figure 4: The interplay of AI proposer and receiver shows better effectiveness at large selection intensity. Panels in the top (bottom) row show the stationary distributions of $HH$ ($LL$) as a function of the numbers of AI receivers and AI proposers with different selection intensities, respectively. The solid line in panel (m) represents the sum of AI agents, $M_R+M_P=58$. Parameters are set as $h=0.5$, $l=0.1$, $\beta=0.1$ in the first column, $\beta=1$ in the second column, $\beta=10$ in the third column, and $\beta=100$ in the last column.
• Figure 5: AI agents robustly sustain mutual fairness across a wide range of game payoffs and selection intensities. Shown are the frequencies of each stationary distribution. Numerical calculations results are obtained using $M_P \in [0,100]$ with step 5, $M_R \in [0,100]$ with step 5, $h \in[0.4,0.6]$ with step 0.01, $l \in[0.1,0.3]$ with step 0.01, and $\beta \in \{0.1, 1, 10, 100\}$.