Compliance with Social Norms as an Evolutionary Stable Equilibrium

Abstract

This paper analyzes the compliance with social norms optimally established by a benevolent central planner. Since compliance is costly, agents have an incentive to free-ride on others, in a public good game. We distinguish two types of agents: standard pro-self agents (Sanchos) whose payoffs are defined by a prisoner's dilemma game dominated by the non-compliance strategy, and pro-social Quixotes, who still have an incentive to free-ride, although prefer compliance over mutual defection (as in a snowdrift game). Compliance is analyzed in a two-population evolutionary game considering an imitative revision protocol. Individuals from one population play against and imitate agents within their own but also the other population. Inter-population interaction and imitation allow us to investigate under which circumstances some Sanchos might imitate compliant Quixotes, so escaping the non-compliance equilibrium characteristic of an isolated population of Sanchos.Correspondingly, we analyze the conditions under which the interaction with the population of selfish Sanchos increases or decreases the compliance rate among altruistic Quixotes.

Interaction and imitation with heterogeneous agents: A misleading evolutionary equilibrium

“…For each of the four scenarios i), ii), iii), iv), one can analytically compute the five equilibria M EE O , M EE y M EE 01 , M EE x and M EE I . Within each interval it is easy although tedious to compute the system of differential equations defined in ( 8) and ( 9), together with ( 5), (7) and ( 10)- (11). Given this system, if ẏ > 0 within a particular interval, then the only possible stable equilibrium requires y * = 1.…”

“…The system of differential equations given in ( 8) and ( 9), with conditional imitation rates in ( 5), (7) and switching probabilities in ( 10)- (11), presents five different MEE depending on the parameter values.…”

“…We do not present the proof here, although the phase diagrams in Figure 2 show that, for each particular parameters constellation, the corresponding M EE e is asymptotically stable. 11 Note that (0, 0) and (1, 1) are always steady-state equilibria of the system of differential equations ( 8)-( 11), although typically unstable, except under conditions ( 14) and ( 18), respectively. The equilibria in Proposition 2 are represented in Figure 2 as round solid black points when stable, and as round blank red points if unstable.…”

Formation of crowdshipping habits in public transport: Leveraging anticipated positive emotions through feedback framing

“…Such positive emotional outcomes may entail psychological rewards for living up to ideals of 'doing the right thing', such as undertaking environmentally friendly behaviour (Venhoeven et al, 2013). These feelings have been shown to take the form of a 'warm glow', which may also encompass a social dimension of belonging or living up to social norms (Cabo, García-González, & Molpeceres-Abella, 2020;IJzerman et al, 2012;Taufik, Bolderdijk, & Steg, 2015). The question then becomes if and how the motivational potential of anticipated emotional outcomes may be deployed to induce and guide environmentally friendly behaviour in situational contexts that leave little room for conscious deliberation.…”

Variance, norms and cooperative behavior in public goods games

“…In order to enhance and sustain cooperation, scholars seek to explore explanatory mechanisms for cooperative behavior. Social norms have been recognized as an important causal mechanism for cooperative behavior in social dilemmas ( Fehr and Fischbacher, 2004 ; Reuben and Riedl, 2013 ; Fehr and Schurtenberger, 2018 ; Cabo et al, 2020 ; Quan et al, 2020 ; Kölle and Quercia, 2021 ). Based on the previous literature, by directly assuming the existence of a cooperation norm that a significant proportion of individuals have an intrinsic desire to follow, most of the regularities that violate the rationality assumption can be explained by social norms ( Lindbeck et al, 1999 ; Ostrom, 2000 ; Krupka and Weber, 2013 ; Kimbrough and Vostroknutov, 2016 ; Fehr and Schurtenberger, 2018 ).…”