Perceptual Rationality: An Evolutionary Game Theory of Perceptually Rational Decision-Making

TL;DR

The paper introduces perceptual rationality, where decision-making in N-person games is guided by evolvable perceptions of payoffs and modulated by social information use. It shows that perceptual diversity naturally emerges and can follow power-law distributions, with no evolutionary stable strategy in binary trait settings, leading to a coexistence of context-dependent rational personalities. Through replicator-mutator dynamics in both well-mixed and structured populations, the work reveals non-monotonic evolution, cyclic dominance in small groups, and strong links between perception, sociality, and cooperation. It also connects micro-level perceptual evolution to macro-scale eco-evolutionary patterns, demonstrating how social structure can modify exponents and spectral properties of ecological time series. Collectively, these findings suggest that rational decision-making can be a driver of behavioral diversity and complex social dynamics in cooperation, with testable predictions for empirical systems.

Abstract

Understanding how biological organisms make decisions is of fundamental importance in understanding behavior. Such an understanding within evolutionary game theory so far has been sought by appealing to bounded rationality. Here, we present a perceptual rationality framework in the context of group cooperative interactions, where individuals make rational decisions based on their evolvable perception of the environment. We show that a simple public goods game accounts for power law distributed perceptual diversity. Incorporating the evolution of social information use into the framework reveals that rational decision-making is a natural root of the evolution of consistent personality differences and power-law distributed behavioral diversity. The behavioral diversity, core to the perceptual rationality approach, can lead to ever-shifting polymorphism or cyclic dynamics, through which different rational personality types coexist and engage in mutualistic, complementary, or competitive and exploitative relationships. This polymorphism can lead to non-monotonic evolution as external environmental conditions change. The framework provides predictions consistent with some large-scale eco-evolutionary patterns and illustrates how the evolution of social structure can modify large-scale eco-evolutionary patterns. Furthermore, consistent with most empirical evidence and in contrast to most theoretical predictions, our work suggests diversity is often detrimental to public good provision, especially in strong social dilemmas.

Figures (11)

• Figure 1: Perceptual public goods game. A: In a simple perceptual public goods game, rational individuals play a public goods game. Individuals are rational and play the Nash equilibrium of their game based on their perception of public good cost and benefit, which may or may not coincide with objective reality. B: In a social perceptual public goods game, in addition to their perception of public goods cost and benefit, individuals have a social trait that determines how susceptible they are to social information. Individuals play the Nash equilibrium of the game based on the socially perceived payoffs, defined as $\hat{p}^s_i=(1-s_i)\hat{p_i}+s_i\hat{p}_{-i}$, where, $\hat{p}_{-i}=\sum_{j\neq i}\hat{p}_j/(g-1)$, $i$ stands for the focal individual, $s$ is the sociality of the individual, $\hat{p}$ stands for the perception of individuals of the public good cost, $\hat{c}$, and benefit $\hat{b}$ and $g$ is the number of individuals playing the game. C: A rational individual cooperate if the difference between socially perceived payoffs of cooperation and defection, $(1-s_i)A+s_iB$, where $A=\hat{b}_i-\hat{c}_i$ and $B=\hat{b}_{-i}-\hat{c}_{-i}$, is positive and defect otherwise. Defining, the personal value of cooperation $\hat{\pi}_C=(1-s)A+sB$. Individuals can be decomposed into those with prosocial private economic perceptions, $A>0$ (green), and anti-social economic perceptions, $A<0$ (red). Increasing sociality may only lead to defection in the former, in groups with too low a perception of public goods benefit. By contrast, increasing sociality can only lead to cooperation in those with antisocial economic perception, when they are in groups with high economic perception. The value of sociality where individuals switch, $s^*$ depends on both the individual's perception, $A$, and their group's collective perception, $B$, leading to the flexibility of individuals' behavior. Besides, because others' perception depends on the focal individual's perception, individuals may develop complex strategies to adapt to, and affect, their group's behavior.
• Figure 2: The evolution of perceptual diversity in a simple perceptual public goods game. A: Cooperation in a simple perceptual public goods game in both well-mixed and structured populations is compared with cooperation in boundedly rational agents. In both boundedly rational and perceptually rational agents, cooperation does not evolve (in the public good regime, $1<r<5$, where a social dilemma exists) in a simple public goods game. B: The logarithm of the frequency perceived benefit-to-cost ratio is plotted as a function of enhancement fact. Despite the lack of cooperation and behavioral simplicity, individuals exhibit a broad distribution of perceptions. C: The logarithm of the frequency of perceived benefit-to-cost ratio as a function of the logarithm of benefit-to-cost ratio is plotted. The perceived benefit-to-cost ratio exhibits a nearly symmetric power law with an exponent equal to $2$. Parameter values: $\nu=10^{-3}$ and $N=10000$.
• Figure 3: The evolution of cooperation, sociality, and diversity in a social perceptual public goods game. A and B: Cooperation (A), payoffs and perceptions of payoffs ("happiness") (B) in a social perceptual public goods game in both well-mixed and structured population as a function of enhancement factor are plotted. C and D: Perceived net benefit of the public good (benefit minus cost) and average sociality in a well-mixed and structured population are plotted. While the perceptions do not show high differences, or even higher in a well-mixed population, individuals evolve to be more social in a structured population, leading to higher cooperation. E: The distribution of the logarithm of benefit-to-cost ratio and sociality is plotted in logarithmic scale. High social and perceptual diversity exists in the system. However, the distribution of sociality exhibits two modes for too-small and too-large sociality. F: The connected correlation function of sociality and perceived net benefit of the public good, $\langle (\hat{b}-\hat{c})s\rangle-\langle s\rangle \langle (\hat{b}-\hat{c})\rangle$, where, $\langle$.$\rangle$ represents an average over the population, as a function of the enhancement factor is plotted. For intermediate values of enhancement factors, where the population is behaviorally heterogeneous, a strong correlation between perceptions and sociality is observed. Parameter values: $\nu=10^{-3}$ and $N=10000$.
• Figure 4: Social information use and perception of cooperating and defecting individuals. Sociality (A) and the perception of net public good benefit per individual, $\hat{b}-\hat{c}$, (A) separately for cooperating and defecting individuals in a well-mixed population as a function of enhancement factor is plotted. Cooperating individuals exhibit higher sociality and a more positive economic perception. Parameter values: $\nu=10^{-3}$ and $N=10000$.
• Figure 5: The structure and function of diversity. A: The logarithm of the frequency of perceived benefit-to-cost ratio as a function of the logarithm of benefit-to-cost ratio is plotted. The perceived benefit-to-cost ratio exhibits an asymmetric power law with an exponent between $-1$ and $-2$, depending on the enhancement factor. B: Inverse sociality exhibits a power law tail, with separate laws for personal ($b>c$) and anti-social ($c<b$) perceptions, with exponents close to $-1$. C and D: The inverse perceived benefit and perceived cost exhibit a power law tail with an exponent between $-1$ and $-2$. Social information use and perception of cooperating and defecting individuals. Sociality (A) and the perception of net public good benefit per individual, $\hat{b}-\hat{c}$, (A) separately for cooperating and defecting individuals in a well-mixed population as a function of enhancement factor is plotted. Cooperating individuals exhibit higher sociality and a more positive economic perception. Parameter values: $\nu=10^{-3}$ and $N=10000$.