VC Bargaining

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 an exit once

[math]\sum_t (x_t) \ge \overline{x}\,[/math]

or 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.