= Turnout equilibria with two supporters and one opponent
Suppose turnout costs $3c>0$, each supporter gains $4c$ on passage, and the opponent loses $8c$. The symmetric-supporter <Nash equilibria> $(\alpha,\beta,\gamma)$ are $(0,1/4,1/4)$ and $(1,3/4,3/4)$. Allowing different supporter probabilities adds $(1/4,0,3/8)$ and $(1/4,3/8,0)$. These follow by comparing the <pivotal voting probabilities> with the turnout cost; no player benefits by changing their mixed strategy.
// Target: mathematical-optimization.bigb
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