Abstract
Most mutually beneficial social interactions (cooperation within species, mutualism between species) involve some degree of partner choice. In an analogy to economic theory as applied to human trading practices, biological market theory (BMT) focuses on how partner choice affects payoff distributions among non-human traders. BMT has inspired a great diversity of research, including research on the mutualism between cleaner fish Labroides dimidiatus and other marine fish, their 'clients'. In this mutualism, clients have ectoparasites removed and cleaners obtain food in return. We use the available data on L. dimidiatus cleaner-client interactions to identify avenues for future expansion of BMT. We focus on three main topics, namely how partner quality interacts with supply-to-demand ratios to affect service quality, the role of threats and forms of forceful intervention, and the potential role of cognition. We consider it essential to identify the specifics of each biological market as a basis for the development of more sophisticated BMT models. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.