Mutualism, market effects and partner control

Intraspecific cooperation and interspecific mutualism often feature a marked asymmetry in the scope for exploitation. Cooperation may nevertheless persist despite one-sided opportunities for cheating, provided that the partner vulnerable to exploitation has sufficient control over the duration of interaction. The effectiveness of the threat of terminating an encounter, however, depends upon the ease with which both the potential victim and the potential exploiter can find replacement partners. Here, we extend a simple, game-theoretical model of this form of partner control to incorporate variation in the relative abundance of potential victims and exploiters, which leads to variation in the time required for individuals of each type to find a new partner. We show that such market effects have a dramatic influence on the stable level of exploitation (and consequent duration of interaction). As the relative abundance of victims decreases, they become less tolerant to exploitation, terminating encounters earlier (for a given level of exploitation), whereas exploiters behave in a more cooperative manner. As a result, the stable duration of interaction actually increases, despite the decreasing tolerance of the victims. Below a critical level of relative victim abundance, the model suggests that the cost of finding a replacement partner becomes so great that it does not pay to exploit at all.