The Less Intelligent the Elements, the More Intelligent the Whole. Or, Possibly Not?

TL;DR

The paper investigates how varying levels of individual intelligence in an agent-based Lotka–Volterra system influence emergent collective dynamics. By endowing predators and preys with categories of rules—from KISS to KIDS and including linear extrapolation predictions and meta-cognition—the study analyzes transitions among $E_1$ (extinction), $E_2$ (prey-only growth), and $E_3$ (predator–prey coexistence) under different basins of attraction, with $x$ and $y$ denoting prey and predator densities and the continuous-time dynamics given by $\dot{x}=a x - b x y$ and $\dot{y}=-c y + d x y$. Results show that simple extrapolation-based predictions most reliably generate coexistence or explosive growth regimes, while perfectly foresighted or highly metacognitive strategies often fail to sustain $E_3$; predators with meta-cognitive, cooperative rules can promote coexistence, whereas prey-focused strategies may lead to dominance or extinction. The work highlights a nuanced view of the KISS–KIDS debate in ABMs and demonstrates that modest, first-order predictive capabilities can drive rich, sometimes unbounded, collective dynamics with implications for ecological and socio-economic interpretations. The analysis relies on Lyapunov-based stability considerations and sensitivity analyses to map how coefficients and rule-sets shape the system’s attractors and long-run behavior, reinforcing that heterogeneous interactions and simple local rules can underpin complex global phenomena.

Abstract

The agent-based modelling community has a debate on how ``intelligent'' artificial agents should be, and in what ways their local intelligence relates to the emergence of a collective intelligence. I approach this debate by endowing the preys and predators of the Lotka-Volterra model with behavioral algorithms characterized by different levels of sophistication. The main finding is that by endowing both preys and predators with the capability of making predictions based on linear extrapolation a novel sort of dynamic equilibrium appears, where both species co-exist while both populations grow indefinitely. While this broadly confirms that, in general, relatively simple agents favor the emergence of complex collective behavior, it also suggests that one fundamental mechanism is that the capability of individuals to take first-order derivatives of one other's behavior can allow the collective computation of derivatives of any order.

Figures (3)

• Figure 1: Three Lyapunov functions. Left (a), a saddle with equilibria at its extremes. Center (b), a stable limit cycle along which the two populations oscillate. Right (c), a stable equilibrium point to which the two populations converge. By courtesy of © Rong Ge.
• Figure 2: The most common outcome of case \ref{['cond:wolvesSheepPredict']}. Both populations grow while predators (black wolves) are chasing preys (white sheep).
• Figure 3: The oscillations of the population of predators, averaged over the 797 time series where $E_3$ obtains (thick red line) plotted against one single time series selected for being closest to the mean (thin black line). The oscillations of the population of preys, averaged over the 797 time series where $E_3$ obtains (thick blue line) plotted against one single time series selected for being closest to the mean (gray thin line). On average, the population of predators grows from 50 to 49,530.68 individuals whereas the population of preys grows from 100 to 7,453.59 individuals.

Theorems & Definitions (6)

• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 3.1
• Proposition 3.2
• Proposition 3.3