Changes

The model then solves out for a feasible consumption path, and computes the flow utility before a stabilization (which is the income effect of taxes plus the welfare loss from the tax distortion). With constant consumption after the stabilization (which was shown to be feasible), one can then compute the different in present discounted value of the excess taxes that the loser must pay relative to the winner and loser lifetime utilities from stabilization forward:

:<math>V^W(T) - V^L(T) = (2 \alpha -1)\overline(bar{b) } e^{(1-\gamma)rT}\,</math>  This is the present value of the excess taxes that the loser must pay relative to the winner.

*<math>\underline{\theta} > \alpha - \frac{1}{2}\,</math> : This prevents a groups group's optimum concession time from being infinite, as otherwise a group may prefer to wait indefinatelyindefinitely, as the cost of living in the unstable economy and bearing half of the tax burden is less than the cost of being the loser.

*Ignoring the equilibria in which one group concedes immediately, as the paper wants to examine delay.*Looking and thus looking for a symmetric equilibriaNash equilibrium.*Lemma 1 in the paper give <math>t_iT_i'(\theta_i) < 0\,</math> : The optimal concession time is monotonically decreasing in <math>\theta_i \,</math>

:<math>\underbrace{\underbrace{\left(-\frac{f(\theta)}{F(\theta)}\frac{1}{tT'(\theta)}\right)}_{\mbox{A1}}\underbrace{\frac{2 \alpha -1}{r}}_{\mbox{A2}}}_{\mbox{A}}= \underbrace{\gamma (\theta + \frac{1}{2} - \alpha)}_{\mbox{B}}\,</math> and the initial boundary condition <math>\T(\bar{\theta})=0\,</math>