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Baron (2001) - Theories of Strategic Nonmarket Participation (view source)
Revision as of 03:16, 31 October 2009
, 03:16, 31 October 2009no edit summary
The first order conditions of (b) and (c) taken together imply:
:<math>c_J^*'\prime(x^*) = u_J^*'\prime(x^*)\quad</math>and therefore that the contribution schedules are locally truthful around <math>x^*</math>.
The contribution schedules are constructed as linear functions of the utility of the principals, specifically:
Using (d) we can note that if player <math>i</math> doesn't contribute then the agent choses:
:<math>x_j \in \arg \max u_e(x) + u_j(x)\quad</math>
Comparing this to the equilibrium where both players contribute and noting that for the agent <math>x* \succsim x_g\,</math> and <math>x* \succsim x_h\;</math> it must be the case that <math>x_g , x_h\,</math> are off the equilibrium path.
