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Proposition 1 states that there exists a symmetric Nash equilbirum with each group's concession function described by <math>T(\theta)\,</math> where <math>T(\theta)\,</math> is implicitly defined by:
 :<math>\underbrace{\underbrace{\left(-\frac{f(\theta)}{F(\theta)}\frac{1}{t'(\theta)}\right) }{mbox{conditional probability that opponent concedes}}\underbrace{\frac{2 \alpha -1}{r}}{mbox{gain if opponent concedes}}}{\mbox{benefit of waiting another instant to concede}}= \underbrace{\gamma (\theta + \frac{1}{2} - \alpha)}{mbox{cost of waiting another instant to concede}}\,</math>
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