Difference between revisions of "VC Bargaining"
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==A Basic Model== | ==A Basic Model== | ||
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| + | ===The Value Function=== | ||
:<math>V_t=V_{t-1} + f(x_t) - k \,</math> | :<math>V_t=V_{t-1} + f(x_t) - k \,</math> | ||
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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). | 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 | + | There are some methods that come to mind: |
| + | |||
| + | we could force and exit once | ||
| + | |||
| + | :<math>\sum_t (x_t) \ge \overline{x}\,</math> | ||
| + | |||
| + | of once | ||
| + | |||
| + | :<math>V_t \ge \overline{V_t}\,</math> | ||
| + | |||
| + | or we could try to induce an optimum value | ||
:<math>f'(0) >0, f''<0, \exist z^* s.t. \forall z > z^* f'(z)<0\,</math> | :<math>f'(0) >0, f''<0, \exist z^* s.t. \forall z > z^* f'(z)<0\,</math> | ||
| − | + | though now that I look at this I realize it isn't going to work using just investment... | |
| + | |||
| + | or we could just fix <math>t\,</math>, but it would be nice to have it endogenous, otherwise we would need to justify discrete rounds seperately (as we did yesterday evening with the state-tree perhaps). | ||
| − | + | ===Bargaining=== | |
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 15:49, 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
The Value Function
- [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 some methods that come to mind:
we could force and exit once
- [math]\sum_t (x_t) \ge \overline{x}\,[/math]
of once
- [math]V_t \ge \overline{V_t}\,[/math]
or we could try to induce an optimum value
- [math]f'(0) \gt 0, f''\lt 0, \exist z^* s.t. \forall z \gt z^* f'(z)\lt 0\,[/math]
though now that I look at this I realize it isn't going to work using just investment...
or we could just fix [math]t\,[/math], but it would be nice to have it endogenous, otherwise we would need to justify discrete rounds seperately (as we did yesterday evening with the state-tree perhaps).
Bargaining
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.
