Imperfect Signaling and the Local Credibility Test
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Imperfect Signaling and the Local Credibility Test
Imperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Testnement in signaling models. We propose a Local Credibility Test (LCT) that is somewhat stronger than the Cho and Kreps Intuitive Criterion but weaker than the “strong Intuitive Criterion” of Grossman and Perry. Allowing deviations by a pool of “nearby” types, the LCT gives consistent solutions for a Imperfect Signaling and the Local Credibility Testny positive, though not necessarily perfect, correlation between the signal sender’s true types (e.g., signaling cost) and the value to the signal recImperfect Signaling and the Local Credibility Test
eiver (e.g., marginal product). It also avoids ruling out reasonable pooling equilibria when separating equilibria do not make sense. We identify condImperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Testntical as we take the limit of the finite type case. We then apply the characterization results to the Spence education signaling model and the Milgrom and Roberts advertising signaling model. Intuitively, the conditions for a separating equilibrium to survive our LCT test require that a measure of Imperfect Signaling and the Local Credibility Testsignaling “effectiveness” is sufficiently high for even' type and that the type distribution is not lilted upwards loo much.♦UCLA, UCLA, and Ohio StatImperfect Signaling and the Local Credibility Test
e University. We would like to thank In-Koo Cho, David Cooper, Massimo Morelli, James Peck, and seminar participants at Arizona University, Illinois WImperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Test University, for helpful comments and suggestions. All remaining errors are our own.1. IntroductionSince (he seminal work of Cho and Kreps (1987), various refinement concepts have been proposed (0 rank different equilibria in signaling games in terms of their “reasonableness”. However, the mission i Imperfect Signaling and the Local Credibility Tests still far from being completed. In many applications, signals are "imperfect” in the sense that there is a positive yet imperfect correlation betweeImperfect Signaling and the Local Credibility Test
n the signal sender’s true type (e.g., signaling cost) and the signal receiver’s expected value (which then determines her response), see Riley (2001,Imperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Tests do not observe their values to the receiver, they are effectively the same type, so the existing refinement concepts, such as the Cho and Kreps Intuitive Criterion, apply in the usual way. However, if these two types do observe their different values to the receiver, then the Intuitive Criterion i Imperfect Signaling and the Local Credibility Tests unable to rank equilibria. The reason is that if one of the two types likes a deviation, the other also likes it, hence no deviation is credible byImperfect Signaling and the Local Credibility Test
a single type. This is highly unsatisfactory because the two cases are observationally equivalent.The reason for the inconsistent solutions in the aboImperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Testman and Perry (1986a,b), in a bargaining context, propose an equilibrium refinement concept strengthening the Cho-Kreps Intuitive criterion to allow pooling deviations. In this paper, in a general signaling model, we weaken slightly the Grossman-Perry Strong Intuitive Criterion, and propose a “Local Imperfect Signaling and the Local Credibility Test Credibility Test” (LCT) in which a possible deviation is interpreted as coming from one or more types whose equilibrium actions are nearby. We considImperfect Signaling and the Local Credibility Test
er only local pooling deviations, first because they seem to US more natural, second because they have much of the power of global pooling deviations,Imperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Testng equilibria. We will argue that in some situations separating equilibria seem unreasonable while pooling equilibria can be rather appealing. By allowing pooling deviations, the LCT avoids ruling out pooling equilibria in such situations. Consider a simple two type education-signaling model, in whi Imperfect Signaling and the Local Credibility Testch the high type must take a quite costly signal (e.g., several years of unproductive education) to separate from the low2type. Now suppose there is oImperfect Signaling and the Local Credibility Test
nly one low type agent in every' 5 million high type agents. In such a situation separation seems highly unreasonable, because without taking the costImperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Testequilibrium a pooling deviation to some sufficiently low cost level of the signal is profitable to both types, so no separating equilibrium satisfies the LCT.rhe thrust of our analysis is to derive conditions under which there exist equilibria satisfying the LCT. Wo study a family of continuous tyrp Imperfect Signaling and the Local Credibility Testc models of which the Spence education signaling and the Milgrom and Roberts advertising signaling are both members. We begin by formulating the conceImperfect Signaling and the Local Credibility Test
pt of the I .CT for the finite type models first, sine e the intuition is easier to present. Then we consider a discretization of the continuous type Imperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Teste model satisfies the LCT. The required conditions are intuitive. As long as a measure of signaling •‘effectiveness” is sufficiently high for every' type and the type distribution is not lilted upwards too much, the separating equilibrium can survive our LCT lest.In the continuous type case, the set Imperfect Signaling and the Local Credibility Test of equilibrium signals is dense so that out-of-equilibrium signals can be only found outside the set of equilibrium signals. However, thinking of theImperfect Signaling and the Local Credibility Test
continuous type case as the limiting case of the finite type case with many close types, it is natural to generalize the concept of the LCT to the coImperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Teston- or off-equilibrium), if it is interpreted as from types of a small neighborhood of the immediate equilibrium type, it is profitable for the types in this neighborhood Io deviate Io this signal, but unprofitable for types out of this neighborhood to do so. Another way of Ihinking about ihis credi Imperfect Signaling and the Local Credibility Testbility lest in the continuous type case is the following. If, lor an on-equilibrium signal, there is such a deviation-perc eption pair, then those neaImperfect Signaling and the Local Credibility Test
rby types can c redibly deviate to the partic ular on-equilibrium signal by throwing away £ amount of money.Wc derive conditions under which the LCT iImperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Test because models with continuous types and models with finitely3many types are theoretical tools for analyzing the same kind of real world problems. Put differently, it would be highly unsatisfactory if an equilibrium refinement concept applies to one case but not the other, or gives different answer Imperfect Signaling and the Local Credibility Tests for the two cases.The paper is structured as follows. The next section uses simple examples to illustrate the basic idea of the LCT. Then Section 3Imperfect Signaling and the Local Credibility Test
presents the general signaling model. In Section 4, we formulate the concept of the LCT for the finite type case. Then we derive conditions under whicImperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Teston 5 generalizes the formulation of the LCT to the continuous type case, and shows that the conditions for the LCT are exactly- the same as in the discrete type case. We discuss an issue of robustness in Section 6. Concluding remarks are in Section 7.2. ExamplesA consultant (Sj.Vj) has a signaling c Imperfect Signaling and the Local Credibility Testost type s, and a marginal product of Vj, where 5, < s2 <... < sa and Vj < V, <... < vm. She can signal at level z at a cost of C(z,Sj).deWe suppose tImperfect Signaling and the Local Credibility Test
hat —-(z, s) < 0 so that a higher type has a lower signaling cost. If paid a ỞSwage w her payoff isư(z, w,Sị) = w - C(z,s.). In a competitive labor maImperfect Signaling and the Local Credibility TestHongbin Cai, John Riley and Lixin Ye* November, 2004AbstractIn this paper we study equilibrium refin Imperfect Signaling and the Local Credibility Testignaling.15 a decreasingfunction of Sf . The set of signaling cost types is s = {Sj.sj, and the set of possibleproductivity levels is V = ...vm). The probability of each type, nfSj.Vj), is commonknowledge.* 11If rr(s , V ) = 0 for all 1 * J. (he model reduces to the usual Spence model in which (he n Imperfect Signaling and the Local Credibility Testegative correlation between signaling cost and value to receivers is perfect. While we assume Hs , V,) > 0 foi alli and i , the analysis applies generImperfect Signaling and the Local Credibility Test
ally.4Initially we assume that each consultant observes her own signaling cost type but not her productivity. We define v(S|) = E(v| S(1, and assume tGọi ngay
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