Foresight in a Game of Leadership

Abstract

Leadership can be effective in promoting cooperation within a group, but as the saying goes “heavy is the head that wears the crown.” A lot of debate still surrounds exactly what motivates individuals to expend the effort necessary to lead their groupmates. Evolutionary game theoretic models represent individual’s thought processes by strategy update protocols. The most common of these are random mutation, individual learning, selective imitation, and myopic optimization. Recently we introduced a new strategy update protocol - foresight - which takes into account future payoffs, and how groupmates respond to one’s own strategies. Here we apply our approach to a new 2x2 game, where one player, a leader, ensures via inspection and punishment that the other player, a subordinate, produces collective good. We compare the levels of inspection and production predicted by Nash Equilibrium, Quantal Response Equilibrium, level-k cognition, fictitious play, reinforcement learning, selective imitation, and foresight. We show that only foresight and selective imitation are effective at promoting contribution by the subordinate and inspection and punishment by the leader. The role of selective imitation in cultural and social evolution is well appreciated. In line with our prior findings, foresight is a viable alternative route to cooperation.

Coevolution of actions, personal norms and beliefs about others in social dilemmas

“…Nevertheless several approaches successfully capturing certain aspects of human decision-making have been developed. These include classical (Fudenberg and Tirole, 1992), evolutionary (Sandholm, 2010), mean-field (Tembine, 2017) and quantum (Piotrowski and Sladkowski, 2003; Siopsis et al, 2018) game theories focusing on the effects of material payoffs, social influence models focusing on the dynamics of consensus formation (or fragmentation) in social networks as a result of social learning and imitation (DeGroot, 1974; Watts, 2002; Friedkin et al, 2016; Redner, 2019; Galesic and Stein, 2019; Zino et al, 2020; Kashima et al, 2021), models of strategic deliberation (Golman et al, 2020), models of normative behaviour (Azar, 2004; S. Gavrilets and Richerson, 2017; S. Gavrilets, 2020) and models of foresight (Perry et al, 2018; Perry and Gavrilets, 2020). Each of these approaches concentrates on specific forces shaping human behaviour and beliefs while neglecting many other important factors.…”

The dynamics of cooperation, power, and inequality in a group-structured society

“…These include reputation, punishment (Brandt et al, 2003;Boyd et al, 2003;Fowler, 2005;Boyd et al, 2010;De Weerd & Verbrugge, 2011;Przepiorka & Diekmann, 2013;Perry et al, 2018), between-individual differences, social norms and institutions (Axelrod, 1986;Nyborg & Rege, 2003;Asheim, 2010;Gavrilets & Richerson, 2017;Michaeli & Spiro, 2017;Gavrilets et al, 2020). Certain types of free-riding can be mitigated if individuals update their strategies by using imitation or foresight rather than the myopic best response we used here (Perry et al, 2018;Gavrilets & Shrestha, 2019;Perry & Gavrilets, 2020). Moreover, we anticipate that some equilibria would not occur with foresight.…”

“…Inequality also negatively affect the well-being of citizens in different ways especially when it becomes institutionalized (e.g., as studied in the Social Dominance Theory, Sidanius & Pratto 2001). To better understand these processes, we need to consider the dynamics of collective action (Olson, 1965;Hardin, 1982;Boyd et al, 2003;Brandt et al, 2003;Rand & Nowak, 2013;Medina, 2013;Gavrilets, 2015b;Perry et al, 2018;Gavrilets & Shrestha, 2019;Perry & Gavrilets, 2020) in cooperation and conflict at multiple levels (Boyd et al, 2003;Gavrilets & Fortunato, 2014).…”

The dynamics of injunctive social norms

“…My approach for defining the utility function effectively (a) postulates that it depends on both immediate and future costs and benefits (both material and normative) and (b) implies that individuals are able to predict the reaction of their groupmates to their own action. Viewed this way, my approach can be interpreted as an example of application of a recently introduced strategy revision protocol called foresight (Perry et al, 2018; Perry & Gavrilets, 2020; Gavrilets, 2021)). Foresight aims to capture in game theoretic models the ability of humans and some non-human animals to foresee the future (Szpunar et al, 2014) and make intertemporal choices (Frederick et al, 2002) as well as their ‘theory of mind’, i.e.…”

“…the ability to reason about the knowledge and thought processes of others in the social context (Premack & Wodruff, 1979; Krupenye et al, 2016; de Waal, 2016). Our earlier work has shown that foresight can solve the first- and second-order free-rider problems in the presence of punishment (Perry et al, 2018; Perry & Gavrilets, 2020), can lead to the evolution of social institutions by the route of self-interested design (Gavrilets & Shrestha, 2020) or undermine cooperation via tactical deception (Gavrilets, 2021)). The models and behaviours studied here provide an additional illustration of the power of foresight.…”