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Tadelis (2001) - The Market For Reputations As An Incentive Mechanism (view source)
Revision as of 20:43, 28 April 2010
, 20:43, 28 April 2010no edit summary
*Only names have track records
*There is a competitive market of buyers so that prices are bid up to their expected surplus
*There is no discounting
In addition there are the following driving assumptions:
*Shifts of name ownership are not observable
*Name changes are costless
*With probability <math>\epsilon \ge 0\,</math> a seller can not change his name (note that this is a technical assumptionto rule out some 'bad' equilibria from costless name changes)
The model uses a rational expectations equilibrium.
#Success or failure realized
#Retiring agent can sell his name/continuing agent can change their name
===Benchmark: No Reputations Markets===
Here we assume that names can not be traded and restrict attention to two periods with three generations as depicted below.
<math>
\vskip 5pt
\hskip 200pt$t=1$\hskip 57pt$t=2$
\hskip 80ptGeneration 0:\hskip 10pt\TEXTsymbol{\vert}\_\_\_\_\_\_\_\_\_\_%
\TEXTsymbol{\vert}
\vskip 2pt
\hskip 80ptGeneration 1:\hskip 10pt\TEXTsymbol{\vert}\_\_\_\_\_\_\_\_\_\_%
\TEXTsymbol{\vert}\_\_\_\_\_\_\_\_\_\_\TEXTsymbol{\vert}
\vskip 2pt
\hskip 80ptGeneration 2:\hskip 105pt\TEXTsymbol{\vert}\_\_\_\_\_\_\_\_\_\_%
\TEXTsymbol{\vert}
\,</math>
In period 1 there is one wage as everyone has a new name. In period 2 there are three wages depending on the <math>h\,</math> (histories) observed which are either <math>S\,</math> (success), <math>F\,</math> (failure), or <math>N\,</math> (new name). <math>F\,</math> histories are irrelevant as sellers who failed are better off costly changing their name.
<math>O\,</math> types will exert zero effort in the second period (as it is costly and contracts are made in advance) so <math>w_{2}(h)\,</math> only depends on clients' beliefs about the likelihood of <math>h\,</math> belonging to a <math>G\,</math> type.
Expected period 2 utility of an <math>O\,</math> type is:
:<math>\mathbb{E}u_{O} =w_{1}+eP_{G}w_{2}(S)+(1-eP_{G})w_{2}(N)-c(e) =w_{1}+eP_{G}\Delta w+w_{2}(N)-c(e)\,</math>
where <math>\Delta w\equiv w_{2}(S)-w_{2}(N)\,</math>
The equilibrium is characterized by the tuple <math>\left\langle w_{1},w_{2}(S),w_{2}(N),e\right\rangle\,</math> such that <math>e\,</math> is a best response given <math>w_{2}(S)\,</math> and <math>w_{2}(N)\,</math>, and all wages are correct given rational expectations about <math>e\,</math>
Equilibrium beliefs imply:
:<math>\Pr \{G|S\}=\frac{\gamma P_{G}}{\gamma P_{G}+(1-\gamma )eP_{G}}\,</math>
:<math>\Pr \{G|N\} =\frac{\gamma (1-P_{G})+\gamma }{\gamma (1-P_{G})+(1-\gamma)(1-eP_{G})+1} =\frac{2\gamma -\gamma P_{G}}{2-P_{G}[\gamma +(1-\gamma )e]}\,</math>
Equilibrium wages are:
:<math>w_{2}(h)=\Pr \{G|h\}\cdot P_{G}\,</math>
Fixing <math>\Delta w\,</math> the equilibrium <math>e\,</math> solves the FOC:
:<math>P_{G}\Delta w=c^{\prime}(e)\,</math>
However, optimal effort must solve:
:<math>P_{G} \ge c^{\prime }(e)\,</math>
<math> \,</math>
