Taking a shower in Youth Hostels: risks and delights of heterogeneity

TL;DR

This paper models the coordination challenges of shower temperature control in youth hostels, revealing the instability of homogeneous strategies and the emergence of heterogeneity due to imperfect information and finite options.

Contribution

It introduces an evolutionary game-theoretic model to analyze how heterogeneity in strategies arises in a coordination problem with limited options and imperfect information.

Findings

Homogeneous strategies are evolutionarily unstable.

Heterogeneity emerges as a stable strategy.

Finite tap positions limit agents' ability to reach preferred temperatures.

Abstract

Tuning one's shower in some hotels may turn into a challenging coordination game with imperfect information. The temperature sensitivity increases with the number of agents, making the problem possibly unlearnable. Because there is in practice a finite number of possible tap positions, identical agents are unlikely to reach even approximately their favorite water temperature. We show that a population of agents with homogeneous strategies is evolutionary unstable, which gives insights into the emergence of heterogeneity, the latter being tempting but risky.