Difference between revisions of "VC Bargaining"
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imported>Ed m (Protected "VC Bargaining" [edit=trusted:move=trusted:read=trusted]) |
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This page is for Ed and Ron to share their thoughts on VC Bargaining. Access is restricted to those with "Trusted" access. | This page is for Ed and Ron to share their thoughts on VC Bargaining. Access is restricted to those with "Trusted" access. | ||
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| + | ==Thoughts== | ||
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| + | *We shouldn't include effort from the entrep. - we want a model that has no contract theory, just bargaining. | ||
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| + | ==A Basic Model== | ||
| + | |||
| + | :<math>V_t=V_{t-1} + f(x_t) - k \,</math> | ||
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| + | with | ||
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| + | :<math>V_0=0, f(0)=0, f'>0, f''<0, k>0 \,</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 <mathV_t\,</math> (so players don't invest forever). | ||
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| + | There are two simple methods that come to mind: | ||
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| + | :<mathf'(0) >0, f''<0, \exist z* s.t. \forall z > z* f'(z)<0\,</math> | ||
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| + | Or we could force and exit once | ||
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| + | :<math\sum_t (x_t) \ge \overline{x}\,</math> | ||
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| + | 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 16:43, 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 <mathV_t\,</math> (so players don't invest forever).
There are two simple methods that come to mind:
- <mathf'(0) >0, f<0, \exist z* s.t. \forall z > z* f'(z)<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.
