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TOO COOL FOR SCHOOL? SIGNALING AND COUNTERSIGNALING



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Claremont Colleges working papers in economics Claremont 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 College TOO COOL FOR SCHOOL SIGNALING AND COUNTERSIGNALING NICK FELTOVICH RICK HARBAUGH AND TED TO Abstract In signaling environments ranging from consumption to education high quality senders often shun the standard signals that should separate them from lower quality senders We find that allowing for additional noisy information on sender quality permits equilibria where medium types signal to separate themselves from low types but high types then choose to not signal or countersignal High types not only save costs by relying on the additional information to stochastically separate them from low types but countersignaling itself is a signal of confidence which separates high types from medium types Experimental results 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 John Hardman Moore John Kagel Barry Nalebuff Al Roth Karl Schlag and seminar participants at various conferences and departments Harbaugh thanks the Yale School of Management for post doctoral support TOO COOL FOR SCHOOL 1 For Nash to deviate from convention is not as shocking as you might think They were all prima donnas If a mathematician was mediocre he had to toe the line and be conventional If he was good anything went Z Levinson from A Beautiful Mind Nasar 1998 p 144 1 Introduction Following in the tradition of Veblen s 1899 analysis of conspicuous consumption and Akerlof s 1970 model of adverse selection Spence s 1973a 1974 signaling model of overeducation showed how seemingly wasteful actions can be valued as evidence of unobservable quality Signaling models have 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 phenomena from a peacock s plumage Zahavi 1975 to a tree s autumn foliage Brown and Hamilton 1996 These models conclude that in a separating equilibrium high types high in productivity wealth fecundity or some other valued attribute send a costly signal to differentiate themselves from lower types Contrary to this standard implication high types sometimes avoid the signals that should separate them from lower types while intermediate types often appear the most anxious to send the right signals The nouveau riche flaunt their wealth but the old rich scorn such gauche displays Minor officials prove their status with petty displays of authority while the truly powerful show their strength through gestures of magnanimity People of average education show off the studied regularity of their script but the well educated often scribble illegibly Mediocre students answer a teacher s easy questions but the best students are embarrassed to prove their knowledge of trivial points Acquaintances show their good intentions by politely ignoring one s flaws while close friends show intimacy by teasingly highlighting them People of moderate ability seek formal credentials to impress employers and society but the talented often downplay their credentials even if they have bothered to obtain them A person of average reputation defensively refutes accusations against his character while a highly respected person finds it demeaning to dignify accusations with a response How can high types be so understated in their signals without diminishing their perceived quality Most signaling models assume that the only information available on types is the signal implying that high types will be confused with lower types if they do not signal But in many cases other information is also available For instance wealth is inferred not just from conspicuous consumption but also from information about occupation and family background This extra information is likely to be noisy in that the sender cannot be sure what the receiver has learned implying that types of 2 NICK FELTOVICH RICK HARBAUGH AND TED TO medium quality may still feel compelled to signal so as to separate themselves from low types But even noisy information will often be sufficient to adequately separate high types from low types leaving high types more concerned with separating themselves from medium types Since medium types are signaling to differentiate themselves from low types high types may choose to not signal or countersignal to differentiate themselves from medium types We investigate such countersignaling behavior formally with a model that incorporates extra noisy information on type into a signaling game We find that countersignaling can emerge as part of a standard sequential equilibrium in which all players are forming rational beliefs and are acting rationally given these beliefs Countersignaling is naturally interpreted as a sign of confidence 1 While signaling proves the sender is not a low type it can also reveal the sender s insecurity Since medium types have good reason to fear that the extra information on type will not differentiate them from low types they must signal to clearly separate themselves In contrast high types can demonstrate by countersignaling that they are confident of not being confused with low types The extra information on type in our model can be seen as a second signal following the literature on multidimensional signals Quinzii and Rochet 1985 Engers 1987 This literature is primarily concerned with whether such signals can ensure complete separation when sender type varies in multiple dimensions We assume that sender type varies in only one dimension and concentrate instead on the opposite problem of how the extra information can encourage partial pooling rather than complete separation 2 Given the noisy nature of the extra information it might seem that high types should signal to further emphasize their quality Instead we find that the information asymmetry arising from the noisy extra information can give perverse incentives Pooling with low types can become a signal in itself a way for high types to show their confidence that the extra information is favorable to them by taking an action that is too risky for medium types Because countersignaling serves as a signal of confidence


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