Game Theory Applications in Trend Adoption of Local Clothing Stores

The Economics of FashionTrend emergence following fashion weeks trickle down to markets, creating new fashions, styles and interpretations. Before individuals can dress themselves in the latest vogue, however, clothing houses must decide which trends to incorporate into their collections, thus we apply Game Theory into inquiry. How do local fashion brands Bayo and Plains&Prints face the challenge of trend adoption?

Everyone wears clothing and thus, partakes in fashion, even if they don’t follow it. It is an important creative industry, a global business posting billions of output and sales. Fashion in the Philippines is a growing phenomenon, with many of the youth’s self-confessed fashionistas making the country a hodgepodge of fashion. Looking to be at the cutting edge of style, the most affluent buy designer jeans, shirts, bags and shoes, while the middle class fuse designer and imitation, and the less affluent create trends all their own. Consumers concerned with their fashion being up-to-date with global trends now offer opportunities and pressure the clothing retail industry to strengthen demand for their products amid the expected decrease in value sales by 2% between 2009 and 2014, following the 3% decrease in 2009.

Furthermore, in the heart of a social life—whether in arts, sciences, politics, academia, law, entertainment or business—fashion is exemplified in different ways. People are constantly in motion to one idea from another, to one style from a previous one, whichever has emerged generally new, more fascinating and exciting at a certain point in time. Our society greatly values innovation, partaking in new, original, “fresh” and “hot” practices. Thus, we recognize fashion. In The Law, Culture and Economics of Fashion, Hemphill and Suk say, “The desire to be “in fashion”—most visibly manifested in the practice of dress—captures a significant aspect of social life, characterized by both the pull of continuity with others and the push of innovation toward the new.” Fashion has provided the humanities meanings that express social and individual significance, and the field of economics cases to explain theories of consumption and conformity.

Thus local clothing retailers, faced with this challenge which, done properly, would mean high profits, must adapt a strategy in their adoption of global fashion trends into their collections. This paper fuses the concepts of Game Theory to give reason to the strategies of trend adoption of local clothing stores. How do local brands Bayo and Plains & Prints create their styles for the season in relation to global fashion trends? How much of an “in” ensemble do they adopt into their own collections, and how do they determine which trends to adopt? Whose strategy is most effective in terms of revenues and public appeal? Do these stores move according to coordination with each other? In the end, Game Theory will rationalize the actions of these players into a synthesized plan of strategy that yields high profits and public feedback.

Game Theory as a branch of mathematical analysis is used by economists to study the interaction of firms in their decision-making, and to predict the outcomes for the agents whose actions affect the payoffs and other players involved. In the theoretical framework of Game Theory, players choose among a set of actions in which each action has a corresponding payoff to the player and a consequence to the other agents. A player is thus faced with a set of moves he can play and will form a strategy, his best response to his environment, by which he will play. A “Nash Equilibrium” is reached when each player’s actions causes a reaction by all other agents which, ultimately, results in the same initial action. In this equilibrium, the best responses of all players are in accordance with each other.

Bayo and Plains & Prints play a game of strategy in order to capture the demand for trendy fashions and earn high profits. The decisions the firms make altogether influence the local fashion landscape that is growing to follow international vogue, and work for the players to take consumer demand and offer them what they want in fashion to wear.

Data collated through participant observation will determine the strategies set by the players, with the set of actions from which they choose coming from the global fashion industry. In this study, the 2010 collections of the respective brands have been reviewed, such that the trends that have trickled down from international fashion designers have been determined as the set of possible decisions whether or not the player will adapt the trend. Finally, the set of a player’s actions has been determined by observation of the collections that appear on the racks available for consumers to purchase.

Payoffs are limited to the amount of public interest achieved by each player, which may be assumed directly proportional to revenues generated upon the decision made.

Game TheoryIn basic strategic games, it is assumed that each player holds the correct belief about the other players’ actions. There is the assumption of complete information about the game being played, which, in many cases and most relevantly in fashion trend adoption of local fashion houses, is not realistic. Players are rarely ever perfectly informed about their opponents’ characteristics.

Modeling this situation of imperfect information thus requires the use of Bayesian games—generalized strategic games in which players can be uncertain about the aspects of their environment that are relevant to their actions.

Bayesian Game

In a game of complete information, the players’ payoffs are common knowledge. In contrast, in games of incomplete information, also called Bayesian games, at least one player is uncertain about another player’s payoff function. Bayesian games are a combination of game theory and probability theory that allow taking incomplete information into account. In Bayesian games, each player is allowed to have some private information that affects the overall game play, but which is not known by the others. However, others are assumed to have beliefs about the private information. A common example of a static Bayesian game is a sealed-bid auction: each bidder knows his or her own valuation for the good being sold but does not know any other bidder’s valuation; the moves can be thought of as simultaneous, as bids are submitted in sealed envelopes.

In a Bayesian game, a state is a possible scenario that may be realized in the game. When there are multiple states, types are used to summarize the degree to which each player can differentiate between the states. For instance, in a Bayesian game with two states, a player with two types can distinguish between the states while a player with one type cannot. Each type of each player in a Bayesian game holds a belief about the likelihood of the states consistent with that type. This means that if a type is associated with several states but cannot distinguish between the states, it assigns a probability distribution over the set of types. If a type is associated with only one state, then that type believes with certainty that it is in that state. Given that each player can have multiple types with different beliefs, players in a Bayesian game can adopt strategies that are conditioned on their types. The payoffs for a strategy profile are calculated as the expected values of that strategy profile across all states.

A Bayesian game may result to a Nash Equilibrium, as in Normal Form static games. In a Nash equilibrium of Bayesian game, the action chosen by each type of each player is optimal given the actions of every type of every other player. At the same time, the actions of one type of player i do not affect the choice of actions for other types of player i. Vanberg defines a Nash equilibrium of a Bayesian game as being a Nash equilibrium of a corresponding normal form game in which (1) the set of players is equal to all of the types in the Bayesian game and (2) the payoffs to player i are equal to the players expected payoffs given her beliefs.

Normal-Form Representation of Static Bayesian Games

To define the normal-form representation of a simultaneous-move game of incomplete information (a static Bayesian game), the first step is to represent the idea that each player

knows his or her own payoff function but may be uncertain about other agents’ payoff functions. A set ui(a1,…,an; ti) is determined as player i’s payoff function, where ti is called player i’s type, belonging to a set of possible types Ti called a type space. Each type ti corresponds to a different payoff function that player i might have. In this study, the type represents trend adoption while payoffs stand for revenues.

Suppose player i has two possible payoff functions. Thus that player has two types: ti1 and ti2 and has the type space Ti = {ti1ti2} with the payoff functions being ui(a1,…,an; ti1) and ui(a1,…,an; ti2).

The game further assumes that each of a player’s types corresponds to a different payoff function the player might have to represent the possibility that the player might have different set of feasible actions as follows. This is the player’s belief, which describes the player’s uncertainty about the other players’ possible types (denoted by t-i) given its own type ti, from T-i which is the set of all possible values of t-i. The probability distribution pi (t-i | ti) is player i’s belief about the other players’ types, t-i, given his knowledge of his own type ti.

In most cases, the players’ types are independent, in which case pi (t-i | ti) does not depend on ti, thus we can rewrite player i’s belief as pi (t-i).

The existence of beliefs is true for fashion producers, as trend adoption is greatly related to the brand’s payoffs. Thus we suppose that player i’s set of feasible actions is {a, b} with probability q and {a, b, c} with probability 1-q. Then we can define that i has two types, which are ti1 and ti2, where the probability of ti is q, and i’s set of feasible actions is {a, b, c}, thus the payoff from taking action c is -∞ for type ti.

The timing of a Bayesian game, following Harsanyi, is as follows:1. Nature draws a type vector t = (ti, …, tn), where ti is drawn from the set of

possible types Ti

2. Nature reveals ti to player i but not to any other player3. The players simultaneously choose actions, with player i choosing ai from

the feasible set Ai

4. Payoffs ui(a1,…,an; ti1) are received

Bayesian Nash Equilibrium

Given the timing of a static Bayesian game in which nature begins the game (in trend adoption, international trend takeoff represents “nature”) by drawing the players’ types, a pure strategy for player i specifies a feasible action for each of player i’s possible types. The strategy for player i is a function si(ti), where for each type ti in Ti, si(ti) represents the action from the feasible set Ai that type ti would choose if drawn by nature. This strategy space is constructed from the type and action spaces, rather than given by the normal-form presentation of the game.

A Nash equilibrium in a static game of imperfect information is in its simplest idea is that each player’s strategy must be a best response to the other players’ strategies. Thus, in a Bayesian Nash equilibrium, a Nash equilibrium in a Bayesian game, no player wants to change his or her strategy, even if the change involves only one action by one type.

Application

We can revisit the Battle of the Sexes game in which Ross and Rachel must decide to go to either a basketball game or a concert for their date. We recall that there are two pure-strategy Nash equilibria (Basketball, Basketball) and (Concert, Concert). The payoff matrix is as follows:

RachelRachelRachel

Ross CONCERT BASKETBALLRoss

CONCERT 2, 1 0, 0

Ross

BASKETBALL 0, 0 1, 2

Suppose that although Ross and Rachel are not quite sure of each other’s payoffs: Ross’ payoff if both attend the Concert is 2 + ts, where ts is privately known by Ross; Rachel’s payoff if both attend Basketball is 2 + tc, where tc is privately known by Rachel. All other payoffs are the same.

In terms of the static Bayesian game in normal form, the action spaces are As = Ac = {Concert, Basketball}, the type spaces are Ts = Tc = [0, x] (because ts and tc are independent draws from a uniform distribution on [0, x]), the beliefs are ps(tc) = pc(ts) = 1/x for all ts and tc

and the payoff matrix is as follows:

RachelRachelRachel

Ross CONCERT BASKETBALLRoss

CONCERT 2 + ts, 1 0, 0

Ross

BASKETBALL 0, 0 1, 2 + tc

The Bayesian Nash equilibrium is constructed as follows: Ross plays Concert if ts exceeds a critical value, s, and plays Basketball otherwise and Rachel plays Basketball if tc exceeds a critical value c, and plays Concert otherwise. In that equilibrium, Ross plays Concert with probability (x - s)/x and Rachel plays Basketball with probability (x - c)/x. The Bayesian Nash equilibrium, in the end, approaches their behavior in the original Nash equilibrium in the simpler game of complete information: if both (x - s)/x and (x - c)/x approach 2/3 as x approaches zero.

For simplicity’s sake, we take the proof as true, thus, we arrive at the conclusion that:Ross playing Concert is optimal iff ts ≥ (x/p) - 3 = s

Rachel playing Basketball is optimal iff tc ≥ (x/p) - 3 = c

The players, then, in this pure-strategy Bayesian Nash equilibrium of the incomplete-information game approaches their behavior in the mixed-strategy Nash equilibrium in the original game of complete information.

Fashion Trend Sequence

The Emergence of VogueHow do fashion trends come about? How does Fashion Week dictate the emergence of the minimalist look, the neutral color palette for the season? Do these designers connive to showcase a common piece to create a trend? Is there a secret group of fashion editors who meet to discuss the silhouette for spring? How do fashion trends emerge? If it takes 6-12 months to form a collection, how do designers know what to place on the catwalks come Fashion Week?

Trendbooks and Catalogues

Jumpstarting the emergence of fashion trends worldwide are Promostyl and Nelly Rodi, two well-known Trendbook firms. For 12 to 18 months before a season, researchers for these firms travel all over the world looking at fashion hubs to study what is happening, from political to economic and social conditions. What are they wearing now? What is happening now? They then predict, from all the data they have collated, “what will they wear in the future?” Nelly Rodi and Promostyl produce with Trendbooks and Catalogues chock-full of themes, silhouettes, colors, fabrics and designs that they predict will be the trend in the coming season.

Trade Shows

The backbone of fashion trends, Trade Shows are conventions inviting fashion buyers and designers to introduce the themes, colors, fabrics, shapes and trends of an upcoming season. Several Trade Shows are held in different countries. PURE is prominent in the UK, Plitti Filati in Italy, GDS in Germany for shoes, Bread & Butter in Spain, and the most important, Premier Vision in Paris.

Worth Global Style Network (WGSN) and Fashion Weeks

If designers don’t buy Trendbooks or don’t attend Trade Shows, they look to WGSN for the trends of the season. Worth Global Style Network compiles the essentials to define trends and is in fact most used by fashion designers and buyers. In six to twelve months, designers’ creations are showcased on the runways of Fashion Week, most notable of which are held in New York, Paris and Milan every season.

Directional Shopping and the Search for Suppliers

Directional Shopping is done by fashion buyers to give the direction of the season. Buyers, given a budget, travel to collect inspiration for creating their own pieces. Fashion buyers explore key locations for fashion goods such as Portobello Road, Camden Town, Spita Field Market and other unique areas to find inspirations for their next hit pieces. At this point, buyers begin sourcing fabrics, buttons, beads and other material to supply for their collections.

Fashion Magazines

Finally, trends come to grace the covers and contents of fashion magazines, available for purchase by consumers and thus take on the trends that have successfully taken off.

2010 Trends

Differentiation and FlockingThrough fashion, people communicate and express themselves. Fashionable individuals’ personal style is often described as distinctive or “unique.” If consumers use fashion to express themselves as distinctive individuals, then it follows that there is available a large range of different identifiers. Fashion goods provide a vocabulary for expression and interpretation.

What consumers might value in fashion, then, is the availability of a variety of goods to choose from, a production of the number of interpretations that can be made. The availability of a variety of different goods enlarges the vocabulary and the meanings that can be communicated.

A key feature of the consumption and production of fashion is thus differentiation, given that as consumers use fashion as an expression of their individuality, they desire an identifiable feature in fashionable goods. But there is also a collective trait in fashion, as even if individuals strive for differentiation in their fashion choices, there continues to be a pursuit of participation in common movement—flocking, a second key feature of fashion. Consumers, after all, engage in flocking in purchasing new clothes, not by necessity but more due to the fact that their existing wardrobe appear outdated.

Differentiation and flocking simultaneously take place in fashion as people partake in fashion dressing: while they create looks to express a coined idea of themselves, they also move in a common direction and interpret a same trend. People engage in flocking in the manner that allows for individual differentiation. The interaction between the two is desirable, and as Anna Wintour of Vogue notes, what is admirable in fashionable people is at once “looking on-trend and beyond trend and totally themselves.” Moreover, tastes for differentiation and flocking vary for consumers and one could posit herself at the very extreme, valuing differentiation to the utmost and avoiding trendiness altogether for the similarity it retains with others. In contrast, another could assert herself as one wishing to appear exactly as others in a certain point in time, adhering to the season’s trends as they emerge. Majority of individuals, however, find themselves hovering in the midrange instead of the extremes,

expressing measures of both differentiation and flocking. Consumer utility from differentiation and flocking also depend on the particular item of fashion and the trend, requiring further complex analysis on the key dynamics of the features of fashion consumption and production.

Flocking, Differentiation and Innovation

In flocking and differentiation is the creative impulse in fashion for producers. Hemphill and Suk note that “The impulse to flock in fashion is expressed in the aspects of fashion that draw on and sometimes copy existing works, but what makes the field a creative endeavor is the drive to differentiate—to reinterpret, change, remix, and transform, and as such, resist the sheer replication of existing works even while incorporating them.” Differentiation constitutes innovation in fashion, such that without it fashion itself would not be recognized a form of innovation. In favoring differentiation, we come to the side of the producers, the clothing firms themselves, to identify their strategies of production.

The Demand Side: Trend AdoptionThe process of trend adoption reflects differentiation and flocking. On the demand side, we think of a fashion piece as having two kinds of attributes: a trend feature around which customers flock and several distinctive features. These distinctive, differentiating features are design elements apart from the trend feature, those that make the pieces within the trend still different from each other.

The trend feature is some shared, recognizable design element, such as a bright red color, a distinctive 1950’s full skirt, a leopard print or a cutout dress. Consumers are able to identify and distinguish trend features from other features of a good, from mere observation of the trend feature in stores, on the street, or as seen on media; advertising and magazine articles further enhance recognition of the trend feature. Many consumers prefer new items that are part of a trend, that is to say, pieces that are trendy. Individuals have tastes for differentiation in the item’s other features, varying preferences that consider body shape, aesthetics and personal style. Fashion-conscious people are generally not seeking to wear the precise same outfit as someone else, rather they seek goods that contain the identified trend feature but are differentiated.

How does a trend catch on? If in one season, a designer produces an unusually large number of designs in a nude palette and consumers begin to recognize the color as the feature that is part of the potential trend, the trend takes off—provided that enough consumers recognize that enough other people are buying items with the trend feature (thus a trend will occur), and that the consumer’s preferences are served well enough by the particular item that she buys it. Individuals buy if others are buying or can be expected to buy—pieces with the same trend feature also appear in many shops at the same time. A trend must offer something sufficiently new to take off, for in the context of clothing, the new trend is competing with the consumer’s closet full of existing clothes. If multiple brands offer the same new trend feature at the same time, incorporated with differentiating details to satisfy consumer demand for this feature of differentiation, a trend is more likely to successfully emerge.

The Supply Side: Trend AdoptionDesigners, too, engage in a process of differentiation and flocking. In any given season, they flock to similar dress shapes, hemlines, and tailoring. They converge on similar or related styles and motifs. The precise result reached by each producer, however, is different.

In part, flocking results from a sharing of influences. If images of disco fill the news, seventies-inspired styles may enter multiple collections. If a new film gains acclaim for a distinctive style, that style may be incorporated into the work of different designers, particularly, the followers. Forecasting services provided by Trendbooks firms furnish a common input to some designers, leading to a “convergent evolution” of derived similar innovations. New technological possibilities, such as a new way to create pleats, can produce commonalities in collections as well.

Flocking also results from mutual influences and inspiration among designers. They and their assistants attend fabric and other trade shows, where they learn from suppliers what other designers have planned—sometimes with the suppliers’ active encouragement. Stylists, magazine editors, and buyers travel from designer to designer, cross-pollinating as they move. The shows are not quite simultaneous, extending across several weeks and cities, and last- minute tinkering can incorporate the influence of designers who have had earlier shows. These shared influences promote convergence around a trend, but not identical articles. For one thing, the shared influences are usually too general to produce identical articles. Moreover, each producer has substantial incentives to produce a differentiated product. A producer, faced with differentiated demand, will tend to seek out a differentiated niche to satisfy, rather than occupy the exact same space as another producer. Some producers are better suited for some niches than others—they may understand one segment of the market (teenagers, say, or Californians) better than another, and focus accordingly. Offering an on-trend, distinctive good may be a source of benefit to some producers, since it offers the opportunity to work with and be in communication with others on a similar problem. And choosing a differentiated product, rather than the exact same good offered by another producer, raises the probability that a trend supported by differentiation within flocking will get off the ground in the first place.

The economic imperative to both differentiate and flock resembles the innovative production of more technologically intensive goods. Similar limited cooperation takes place in the development of a new computer operating system or DVD player, in which producers jointly struggle to get a new “standard” or “platform” off the ground. There, too, it is a variety of differentiated products—“launch titles”—that contribute to the success of the shared feature, by providing confidence about sufficient adoption that the platform will be a success.

The Game of Trend AdoptionWe thus define the game of trend adoption, a static Bayesian game with Bayo and Plains&Prints as players. We assume that unlike regular international brands that follow the fashion trend cycle, Bayo and Plains&Prints rely on innovation following the trends that have already taken off globally. Thus, the game begins upon the takeoff of a trend, determined by internationally-acclaimed fashion websites Style.com and WhoWhatWear.com, and the decision point is now which of the trends in the type space will be produced by the players, with each action corresponding to a different payoff function the players may have.

The set uB(a1,…,an; tB) represents Bayo’s payoff function, from the type space TB and the set uP(a1,…,an; tP) represents Plains&Prints’ type from the type space TP. Note that the type spaces TB and TP are essentially the same, however differently defined by the players themselves; there are after all only few trends that take off, and interpretations only differ upon the perceptions of innovations the brands can make if it adopted the trend.

The Payoff Matrix

We sketch the payoff matrix for the two players regarding one trend, say, incorporating full skirts into their collection. Bayo and Plains&Prints are faced with the decision of adopting or not adopting the trend, but each has its own payoffs for every action. In the case of perfect information and the brands know perfectly each other’s payoffs, the matrix is as follows:

Plains&PrintsPlains&PrintsPlains&Prints

Bayo ADOPT NOT ADOPTBayo

ADOPT 5, 5 10, 0

Bayo

NOT ADOPT 0, 10 1, 1

In this game, we assume that by adopting the trend, Bayo will have a payoff of 5 if Plains&Prints also adopts the trend. For the reason that if both firms adopt, two brands in the market will then be offering the same style. This will not be a dominant strategy, as a fashion house would like to retain its market as well as its exclusivity by being the only seller for full skirts in the market, therefore a payoff of only 5.

The payoff for Bayo if it adopted the trend while Plains&Prints does not adopt the trend is even higher at 10, thus the dominant strategy for Bayo is to adopt the trend. The same goes for Plains&Prints, whose dominant strategy will also be to adopt the trend.

However, the true representation of the game follows the Bayesian theory and Bayo has a payoff 5 + tB, where tB is privately known by Bayo; Plains&Prints’ payoff if both do not adopt the trend is 1 + tP, where tP is privately known by Plains&Prints. In this regard, we may assume tB to include Bayo’s style as a brand itself: Bayo has been seen as a preppy, middle-class brand and this proposition greatly affects the styles of the collections released. Plains&Prints, on the other hand, evokes a more classic style, a factor in determining tP. These ideas come into play as they affect the strategies of the brands in trend adoption, aside from revenues and positive consumer feedback.

Thus we have the Bayesian game with the payoff matrix:

Plains&PrintsPlains&PrintsPlains&Prints

Bayo ADOPT NOT ADOPTBayo

ADOPT 5 + tB, 5 10, 0

Bayo

NOT ADOPT 0, 10 1, 1 + tP

Our theoretical framework tells us that the Nash equilibrium in this Bayesian game of incomplete information approaches the Nash equilibrium in the original game of complete information.

Bayo playing Adopt is optimal iff tB ≥ (x/p) - 3 = B

Plains&Prints playing Not Adopt is optimal iff tP ≥ (x/p) - 3 = P

The following cases illustrate the concrete outcome of different trend adoptions.

Trend Report: Red

Trend Adoption: Red as seen in Plains&Prints

Trend Report: Nude Tones

Trend Adoption: Nude Tones as seen in Bayo

Trend Report: Minimalism

Trend Adoption: Minimalism in Bayo and

Plains&Prints

Trend Report: Fifties Dressing

ConclusionEven though fashion is not widely regarded as one of the “fine arts,” it is undeniably a creative good that has expressive features. It is a means of individual expression through which people partake in collective movement and the spirit of the times. Fashion enables this expressive process, and as such has benefits much like those associated with other consumptive goods that are also expressive.

Some may view fashion consumption as a product of social pressure and therefore unable to confer meaningful welfare gains on its consumers. Participation in fashion seems to be freely chosen by consumers. The desire to be “in fashion” involves more than signals about status, and the trend adoption of fashion producers provides individuals with the option for participation, a chance to express themselves through outfits, by producing fashion innovations.

The amount and kind of innovation in fashion is directly connected to its meaning-making function. The trend adoption of fashion houses may be interpreted as a Bayesian game of strategy, where there is incomplete information, and the strategies of fashion producers may or may not exhibit the theoretical framework of the game. However, we have shown that the types take into account many different factors that result into an innovation desired by producers themselves, for several payoffs.

Ann Jillian V. Adona 4 - AB Management Economics, Ateneo de Manila University

BibliographyHemphill, C. S., & Suk, J. (n.d.). The Law, Culture and Economics of Fashion. Retrieved November 12, 2010, from http://ssrn.com/abstract=1323487

Gibbons, R. (1992). A Primer in Game Theory. Hertfordshire: Harvester Wheatsheaf.

Danforth, B. (2009, August 24). Game Theory: Bayesian Games. Retrieved January 20, 2011