Why are Americans addicted to baseball? An empirical analysis of fandom in Korea and the United States

Contemporary Economic Policy, Jan, 2008 by Young H. Lee, Trenton G. Smith

C. Fandom as a Signaling Game

There are many reasons to expect spectator sports to be habit forming: the longer one follows a team, the more he/she learns about the strategy of the game, the particular talents and personalities of the players, and the culture and nature of other sports fans. In the naturalistic counterpart of spectator sports, these accumulated bits of information would all have served an adaptive purpose, enabling the "fan" to better predict competitive outcomes and make judgments about when (and how) to offer assistance to fellow group members. But perhaps more importantly, participation as a fan would serve the purpose of cementing one's reputation as a loyal member of the group, worthy of trust and mutual aid. To see how concerns about reputation might lead to habit formation, consider the following decision problem.

An individual (i.e., a fan) is periodically presented with opportunities to participate in ("attend") a group activity. Other members of the group have incomplete information about the true degree of the fan's allegiance: a steadfast fan ("member") will attend any given event with probability [[pi].sub.M], while a lesser fan ("nonmember") will attend with probability [[pi].sub.N], where [[pi].sub.N] < [[pi].sub.M]. In period t, the probability of the fan being a member (given prior beliefs [[pi].sub.t-1] and current attendance [att.sub.t]) is denoted [[pi].sub.t]. The fan receives periodic income m, which can be spent on attendance at price p or on a composite numeraire good [c.sub.t]. Fan utility in period t is a linear function (17) of [[pi].sub.t] and [c.sub.t], yielding the optimization problem:

[max.[[att.sub.t],[c.sub.t]]][[pi].sub.t]([att.sub.t]) [c.sub.t]

subject to

m [greater than or equal to] [att.sub.t]p [c.sub.t],

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and the resulting (myopic) decision rule is "attend if and only if p [less than or equal to] f([[pi].sub.t - 1])," where f([[pi].sub.t-1]) = [[pi].sub.t](1) - [[pi].sub.t](0) = (1 - [[pi].sub.t-1])([[pi].sub.M] - [[pi].sub.N])/{([[pi].sub.t-1]([[pi].sub.M] - [[pi].sub.N]) [[pi].sub.N]) - ([[pi].sub.t-1]([[pi].sub.M] - [[pi].sub.N]) [[pi].sub.N])[.sup.2]} is the marginal increase (i.e., the increase attributable to period t attendance) in the fan's posterior probability of being a member. This decision rule is myopic in the sense that it excludes long-term dynamic considerations but underscores the importance of the function f([[pi].sub.t-1]), which is concave and (for low values of [[pi].sub.t-1]) increasing in [[pi].sub.t-1]. In other words, concerns about reputation generate marginal utilities that are increasing in attendance for new fans. This is, of course, the central behavioral postulate in the theory of rational addiction.

For our purposes, the value in considering the natural origins of fan behavior stems from the rich descriptive theory that results. Modeling fan behavior as a signaling problem is consistent not only with the evidence from anthropology and behavioral endocrinology reviewed above, but it also fits well with many of the idiosyncratic aspects of fan behavior, such as the tendency of fans to congregate in social settings (i.e., stadiums, bars, or living rooms) when viewing games and to make their allegiances known via both verbal proclamation and the prominent display of team apparel. The importance of habit formation among fans is implicitly acknowledged by team owners not only in their pricing strategies (as suggested by the evidence presented in Section III) but also in such widely used promotional strategies as product giveaways and group or organizational discounts. If habit formation among fans is in part a function of reputational considerations, and we can identify the determinants of reputation (or their psychological analogues in the modern world), we can make predictions about the circumstances most conducive to habit formation. The next section considers some of the differences between the baseball cultures of the United States and Korea, how they might explain the divergent findings reported in Section III, and how they may point the way to an endogenous theory of baseball addiction.