Endogenous timing in competitive interactions among relatives

Abstract

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 'tugof-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.

Individual Variation in Social Aggression and the Probability of Inheritance: Theory and a Field Test

“…For example, the transactional model of Reeve and Keller (1997) shows that it will always pay a dominant individual to appease a potential challenger by offering it a share of reproduction. By contrast, the tug-of-war model assumes that the distribution of reproduction is the outcome of a scramble competition in which the dominant individual exerts a stronger "tug" (Reeve et al 1998;Cant and Shen 2006). In either case, the contested resource is current reproduction, and future benefits of group membership are explicitly excluded.…”

Pathogen evolution under host avoidance plasticity

“…The end result is resistance plasticity drives a superior outcome for both the pathogen and the host, and delivers an evolutionary result more akin to the classic prediction of pathogens evolving towards avirulence. Indeed, this represents an example of a Stackelberg game exhibiting endogeneous timing [43,44]. Endogeneous timing occurs when both players achieve higher fitness by playing their strategies in a particular sequence, rather than simultaneously.…”

Peer Review #2 of "Intergenerational conflicts may help explain parental absence effects on reproductive timing: a model of age at first birth in humans (v0.1)"

“…We model independent sequential decision-making in Section 3.2, rather than synchronous decision-making that is blind to the other's behavior. This is because parents and adolescents are likely able to detect each other's reproductive effort and adjust their decisions accordingly, and because they have some incentive to communicate their intentions to coordinate their reproduction in this game (Cant and Shen, 2006). We further assume that actors have equal competitive abilities such that those who are willing to expend more competitive effort are more likely to assure themselves the right to reproduce first.…”

“…This explains the negative "losses" to going 2nd for the adolescent, who prefers to decide not to reproduce after having seen the parent reproduce, than to reproduce herself first and then have the parent add a 2nd child to the household. Under these circumstances (and whenever one actor suffers negative losses from going second in Figure 2) the model exhibits endogenous timing, meaning that both players agree about who should act first (Cant and Shen, 2006). Given the costs to pregnancy termination and the mutual interests of kin, such contexts should favor signaling reproductive intent.…”