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Or though now that I look at this I realize it isn't going to work using just investment... or we could force and exit once 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).
:<math>\sum_t (x_t) \ge \overline{x}\,</math>===Bargaining===
no edit summary
==A Basic Model==
===The Value Function===
:<math>V_t=V_{t-1} + f(x_t) - k \,</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 <math>V_t\,</math> (so players don't invest forever).
There are two simple 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>
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.
