Endogenous timing in competitive interactions among relatives

Most evolutionary game theory models solve for equilibrium levels of some behaviour on the restrictive assumptions that players choose their actions simultaneously, and that a player cannot change its action after observing that of its opponent. An alternative framework is provided by sequential or 'Stackelberg' games in which one player commits to a 'first move' and the other has an opportunity to observe this move before choosing its response. Recent interest in the economic literature has focused on Stackelberg games which exhibit 'endogenous timing', i.e. games in which a leader and a follower arise spontaneously as a consequence of each player attempting to maximize its reward. Here, we provide the first demonstration of endogenous timing in an evolutionary context using a simple model of resource competition (the 'tug-of-war' model). We show that whenever two related individuals compete for a share of communal resources, both do best to adopt distinct roles in a sequential game rather than engage in simultaneous competition. Somewhat counterintuitively, the stable solution is for the weaker individual to act as leader and commit to a first move, because this arrangement leads to a lower total effort invested in competition. Endogenous timing offers a new explanation for the spontaneous emergence of leaders and followers in social groups, and highlights the benefits of commitment in social interaction.