Unformatted text preview: Ec o no m ic s 6 1 1 H and o ut # 7
T HE E C ONOMIC S OF A SY MMET RIC INF ORMAT ION
Signaling (action taken by the more-informed agent) At cost c(e,è), workers of type è display level e that is reliably observable by all firms. c(0,è) = 0 Partials: ce(e,è) > 0, cee(e,è) > 0
cè(e,è) < 0, ceè(e,è) < 0 r(èL) = r(èH) = 0 < èL < èH ; and beliefs depend on e: ì(e) for firm 1 and ì(e)ó1*(w|e) for firm 2
Here we are able to strengthen from weak perfect Bayesian equilibrium to perfect
Bayesian equilibrium by adding the condition:
The firms' wage offers following each choice e constitute a Nash equilibrium of the
simultaneous-move wage offer game in which the probability that the worker is of high ability is
611.07 - 1 Worker (with u(w,e(è)) = w – c(e,è) : last decision: A worker of type è and education e accepts
employment only at one of the highest wage firms and does so only if r(è) w(e).
Here, r(èL) = r(èH) = 0 (Outcome in absence of signaling) Firms: Offer wage: w*(e) = ì(e)èH + (1 – ì(e))èL . 611.07 - 2 Worker: Education decision: e*(è). “Single-crossing” There are many PBE
Pooling equilibria vs. Separating equilibria
I. Separating equilibria e*(èL) e*(èH) At separating equilibria: w*(e*(èL)) = èL and w*(e*(èH)) = èH
Also: e*(èL) = 0 Example 1. Define ê by u(èL, 0) = u(èH, ê) 611.07 - 3 Firms: Solve offer wage equation to determine beliefs: w*(e) as in the diagram: Here w*(0) = èL and w*(ê) = èH. Workers: e*(èL) = 0 and e*(èH) = ê. 611.07 - 4 Example 2. w*(e) = èH if e e and w*(e) = èL if e < e.
Example 3. 611.07 - 5 Pooling equilibria: e*(èL) = e*(èH) = e*
w*(e*) = E(è) = ëèH + (1 – ë)èL
Define e by u(èL, 0) = u(ëèH + (1 – ë)èL , e)
Example 4. 611.07 - 6 Another example of pooling: 611.07 - 7 ...
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