|Has page=Baron (2001) - Theories of Strategic Nonmarket Participation
|Has bibtex key=
|Has article title=Theories of Strategic Nonmarket Participation
|Has author=Baron
|Has year=2001
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|In volume=
|In number=
|Has pages=
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*This page is part of a series under [[PHDBA279A]]
*This page is referenced in [[BPP Field Exam Papers]]
==Reference(s)==
:Case 1: <math>z \le y: \quad r_x=\alpha (x-y)</math> obtained by noting that <math>x \ge y</math> and that both of the absolute values are positive and rearranging.
:Case 2: <math>y \le z \le x: \quad r_x= 2 \alpha \left (\frac{x+y}{2} + - z \right )</math> obtained by noting that the LHS absolute value in equation (1) is positive, whereas the RHS value is negative.
:Case 3: <math>x \le z: \quad r_x=-\alpha (x-y)</math> obtained by noting that both of the absolute values are negative and rearranging.
Bernheim and Whinston (1984) provide four necessary and sufficient conditions for a sub-game perfect Nash equilibrium in this model. In the notion of the model, these are:
<math>\{c_Jc_j^*(x),x\}</math> is an SPNE iff: :a) <math>c_Jc_j^*(x)\,</math> is feasible
And so the we have both that (as As <math>\widehat{U_e^\hat}(x) = u_e(x) + u_g(x) + u_h(x) \quad</math>) , the principal's problem is to maximize the joint surplus and that the contribution schedules are truthful.
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> , and so it must be the case that <math>x_g , x_h\,</math> are off the equilibrium path.
Therefore the agent will choose <math>x^*\,</math> iff: