Difference between revisions of "VC Bargaining"
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imported>Ed |
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:<math>V_0=0, f(0)=0, f'>0, f''<0, k>0 \,</math> | :<math>V_0=0, f(0)=0, f'>0, f''<0, k>0 \,</math> | ||
| − | should do us just fine. Having <math>k>0\,</math> will force a finite number of rounds as the optimal solution providing there is a stopping constraint on < | + | should do us just fine. Having <math>k>0\,</math> will force a finite number of rounds as the optimal solution providing there is a stopping constraint on <math>V_t\,</math> (so players don't invest forever). |
There are two simple methods that come to mind: | There are two simple methods that come to mind: | ||
| − | :< | + | :<math>f'(0) >0, f''<0, \exist z* s.t. \forall z > z* f'(z)<0\,</math> |
Or we could force and exit once | Or we could force and exit once | ||
| − | :<math\sum_t (x_t) \ge \overline{x}\,</math> | + | :<math>\sum_t (x_t) \ge \overline{x}\,</math> |
In each period there is Rubenstein finite bargaining, with potentially different patience, and one player designated as last. This will give a single period equilibrium outcome with the parties having different bargaining strength. | In each period there is Rubenstein finite bargaining, with potentially different patience, and one player designated as last. This will give a single period equilibrium outcome with the parties having different bargaining strength. | ||
Revision as of 15:43, 24 May 2011
This page is for Ed and Ron to share their thoughts on VC Bargaining. Access is restricted to those with "Trusted" access.
Thoughts
- We shouldn't include effort from the entrep. - we want a model that has no contract theory, just bargaining.
A Basic Model
- [math]V_t=V_{t-1} + f(x_t) - k \,[/math]
with
- [math]V_0=0, f(0)=0, f'\gt 0, f''\lt 0, k\gt 0 \,[/math]
should do us just fine. Having [math]k\gt 0\,[/math] will force a finite number of rounds as the optimal solution providing there is a stopping constraint on [math]V_t\,[/math] (so players don't invest forever).
There are two simple methods that come to mind:
- [math]f'(0) \gt 0, f''\lt 0, \exist z* s.t. \forall z \gt z* f'(z)\lt 0\,[/math]
Or we could force and exit once
- [math]\sum_t (x_t) \ge \overline{x}\,[/math]
In each period there is Rubenstein finite bargaining, with potentially different patience, and one player designated as last. This will give a single period equilibrium outcome with the parties having different bargaining strength.
