Noncooperatively Optimized Tolerance: Decentralized Strategic Optimization in Complex Systems

TL;DR

This paper introduces noncooperatively optimized tolerance (NOT), a game-theoretic extension of HOT, demonstrating how strategic interactions influence robustness, landscape structure, and criticality in complex systems like forest fire models.

Contribution

It develops a new model, NOT, that generalizes HOT by incorporating strategic interactions, revealing complex behaviors including features of self-organized criticality and robustness.

Findings

Model retains HOT features like robustness and high yield.

Emergence of self-organized criticality with many players.

Robustness persists despite increased system fragmentation.

Abstract

We introduce noncooperatively optimized tolerance (NOT), a generalization of highly optimized tolerance (HOT) that involves strategic (game theoretic) interactions between parties in a complex system. We illustrate our model in the forest fire (percolation) framework. As the number of players increases, our model retains features of HOT, such as robustness, high yield combined with high density, and self-dissimilar landscapes, but also develops features of self-organized criticality (SOC) when the number of players is large enough. For example, the forest landscape becomes increasingly homogeneous and protection from adverse events (lightning strikes) becomes less closely correlated with the spatial distribution of these events. While HOT is a special case of our model, the resemblance to SOC is only partial; for example, the distribution of cascades, while becoming increasingly heavy-tailed as the number of players increases, also deviates more significantly from a power law in this regime. Surprisingly, the system retains considerable robustness even as it becomes fractured, due in part to emergent cooperation between neighboring players. At the same time, increasing homogeneity promotes resilience against changes in the lightning distribution, giving rise to intermediate regimes where the system is robust to a particular distribution of adverse events, yet not very fragile to changes.