We propose a model to investigate the dynamics of fashion traits purely driven by social interactions. We assume that people adapt their style to maximize social success and we describe the interaction as a repeated group game in which the payoffs reflect the social norms dictated by fashion. On one hand, the tendency to imitate the trendy stereotypes opposed to the tendency to diverge from them to proclaim identity; on the other hand, the exploitation of sex appeal for dating success opposed to the moral principles of the society. These opposing forces promote diversity in fashion traits, as predicted by the modeling framework of Adaptive Dynamics. Our results link the so-called horizontal dynamics-the primary driver of fashion evolution, compared with the vertical dynamics accounting for inter-class and economic drivers-to style variety.Keywords: Adaptive Dynamics, diversity, game theory, evolutionary branching, fashion, replicator equation, social interactions.
IntroductionThe dynamics of fashion traits has attracted much attention in the last century [Blumer, 1969, Simmel, 2 1904, Sproles, 1979, Veblen, 1894. The several driving forces of fashion are best described by Sproles [1985]: "Psychologists speak of fashion as the seeking of individuality; sociologists see class competition and 4 social conformity to norms of dress; economists see a pursuit of the scarce; aestheticians view the artistic components and ideals of beauty; historians offer evolutionary explanations for changes in design. Literally 6 hundreds of viewpoints unfold, from a literature more immense than for any phenomenon of consumer behavior." Changes in fashion traits have been documented since the XVIII century [Lowe and Lowe, 1990, 8 Richardson and Kroeber, 1940, Robinson, 1976, Sproles, 1981, Weeden, 1977, Young, 1937 and many studies tried to formally interpret and model fashion dynamics, from both the empirical [Lowe, 1993, Lowe and 10 Lowe, 1982 and conceptual points of view [Caulkins et al., 2007, Miller et al., 1993, Pesendorfer, 1995. But "The current state of fashion theory includes a loosely organized array of descriptive principles 12 and propositions but is not formalized in that it does not specify a detailed structure of concepts, variables, and relations" [Sproles, 1981].14 We focus on the evolution of fashion traits that emerges from pure personal choice driven by social interactions, the so-called horizontal dynamics in the trickle-across [Field, 1970, Robinson, 1976 1904] and trickle-up theories-"It now appears that some fashions, as well as some analogous nonfashion phenomena, climb the status pyramid from below, trickling up, as it were" [Field, 1970]. We intentionally
18do not consider all vertical drivers of fashion, related to social class differences among consumers and the tendency to emulate stereotypes from higher classes (investigated in the trickle-down theory [Simmel, 1904, 20 Veblen, 1894]) and to economic aspects from both the production (business, marketing, design, and manufacturi...