TOO COOL FOR SCHOOL?SIGNALING AND COUNTERSIGNALINGNICK FELTOVICH, RICK HARBAUGH, AND TED TOAbstract. In signaling environments ranging from consumption to ed-ucation, high quality senders often shun the standard signals that shouldseparate them from lower quality senders. We find that allowing for ad-ditional, noisy information on sender quality permits equilibria wheremedium types signal to separate themselves from low types, but hightypes then choose to not signal or countersignal. High types not onlysave costs by relying on the additional information to stochastically sep-arate them from low types, but countersignaling itself is a signal of con-fidence which separates high types from medium types. Experimentalresults confirm that subjects can learn to countersignal.Journal of Economic Literature Classification Categories: C72, D82,D83.Date: March 2001.We thank Chris Avery, Bruno Broseta, William Hamilton, Robin Hanson, JohnHardman-Mo ore, John Kagel, Barry Nalebuff, Al Roth, Karl Schlag and seminar par-ticipants at various conferences and departments. Harbaugh thanks the Yale School ofManagement for post-doctoral support. Claremont Colleges working papers in economicsClaremont Graduate University • Claremont Institute for Economic Policy Studies • Claremont McKenna College • Drucker Graduate School of Management • Harvey Mudd College • Lowe Institute • Pitzer College • Pomona College • Scripps CollegeTOO COOL FOR SCHOOL? 1“For Nash to deviate from convention is not as shocking asyou might think. They were all prima donnas. If a mathe-matician was mediocre he had to toe the line and be conven-tional. If he was good, anything went.”– Z. Levinson from A Beautiful Mind(Nasar, 1998, p. 144)1. IntroductionFollowing in the tradition of Veblen’s (1899) analysis of conspicuous con-sumption and Akerlof’s (1970) model of adverse selection, Spence’s (1973a;1974) signaling model of overeducation showed how seemingly wasteful ac-tions can be valued as evidence of unobservable quality. Signaling modelshave since been applied to economic phenomena from advertising (Nelson,1974) to financial structure (Ross, 1977), social phenomena from courtship(Spence, 1973b) to gift exchange (Camerer, 1988), and biological phenom-ena from a peacock’s plumage (Zahavi, 1975) to a tree’s autumn foliage(Brown and Hamilton, 1996). These models conclude that in a separatingequilibrium “high” types (high in productivity, wealth, fecundity, or someother valued attribute) send a costly signal to differentiate themselves fromlower types.Contrary to this standard implication, high types sometimes avoid thesignals that should separate them from lower types, while intermediate typesoften appear the most anxious to send the “right” signals. The nouveauriche flaunt their wealth, but the old rich scorn such gauche displays. Minorofficials prove their status with petty displays of authority, while the trulypowerful show their strength through gestures of magnanimity. People ofaverage education show off the studied regularity of their script, but the well–educated often scribble illegibly. Medio cre students answer a teacher’s easyquestions, but the best students are embarrassed to prove their knowledge oftrivial points. Acquaintances show their good intentions by politely ignoringone’s flaws, while close friends show intimacy by teasingly highlighting them.People of moderate ability seek formal credentials to impress employers andsociety, but the talented often downplay their credentials even if they havebothered to obtain them. A person of average reputation defensively refutesaccusations against his character, while a highly-respected person finds itdemeaning to dignify accusations with a response.How can high types be so understated in their signals without diminish-ing their perceived quality? Most signaling models assume that the onlyinformation available on types is the signal, implying that high types willbe confused with lower types if they do not signal. But in many cases otherinformation is also available. For instance, wealth is inferred not just fromconspicuous consumption, but also from information about occupation andfamily background. This extra information is likely to be noisy in that thesender cannot be sure what the receiver has learned, implying that types of2 NICK FELTOVICH, RICK HARBAUGH, AND TED TOmedium quality may still feel compelled to signal so as to separate them-selves from low types. But even noisy information will often be sufficientto adequately separate high types from low typ es, leaving high types moreconcerned with separating themselves from medium types. Since mediumtypes are signaling to differentiate themselves from low types, high typesmay choose to not signal, or “countersignal,” to differentiate themselvesfrom medium types.We investigate such countersignaling behavior formally with a model thatincorporates extra, noisy information on type into a signaling game. We findthat countersignaling can emerge as part of a standard sequential equilib-rium in which all players are forming rational beliefs and are acting ratio-nally given these beliefs. Countersignaling is naturally interpreted as a signof confidence.1While signaling proves the sender is not a low type, it canalso reveal the sender’s insecurity. Since medium types have good reasonto fear that the extra information on type will not differentiate them fromlow types, they must signal to clearly separate themselves. In contrast, hightypes can demonstrate by countersignaling that they are confident of notbeing confused with low types.The extra information on type in our model can be seen as a second signalfollowing the literature on multidimensional signals (Quinzii and Rochet,1985; Engers, 1987). This literature is primarily concerned with whethersuch signals can ensure complete separation when sender type varies in mul-tiple dimensions. We assume that sender type varies in only one dimensionand concentrate instead on the opposite problem of how the extra informa-tion can encourage partial pooling rather than complete separation.2Giventhe noisy nature of the extra information, it might seem that high typesshould signal to further emphasize their quality. Instead, we find that theinformation asymmetry arising from the noisy extra information can giveperverse incentives. Pooling with low types can become a signal in itself—away for high types to show their confidence that the