“Taking a Shower in Youth Hostels: Risks and Delights of Heterogeneity,” Christina Matzke and Damien Challet, Bonn Graduate School of Economics Discussion paper, January 2008. (Thanks to Peter Buch for bringing this to our attention.)
The authors, affiliated variously with the University of Bonn, Germany; the Institute for Scientific Interchange, in Torino, Italy; and the University of Fribourg, Switzerland, report [AIR 16:1]:
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. Heterogeneity allows some agents to reach much better temperatures, at the cost of higher risk.