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Run the continuous replicator equation on the resulting eight-strategy zero-sum game: = - , where = \, U(i,j) is species i ’s expected payoff against the current population mix and = is the population’s average payoff. Starting from a uniform mix across all eight and integrating to convergence, the system does not settle into anything resembling the real ladder’s spread. It collapses toward a near-monopoly: Great Tusk at 87.71% of the stationary mix, Dragonite at 6.50%, Kingambit at 5.76%, and the other five species asymptoting toward zero, Gholdengo included, despite Gholdengo sitting in second place on the…
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Equation 15 · Pokémon Formal Machinery
The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Run the continuous replicator equation on the resulting eight-strategy zero-sum game: = - , where = \, U(i,j) is species i ’s expected payoff against the current population mix and = is the population’s average payoff. Starting from a uniform mix across all eight and integrating to convergence, the system does not settle into anything resembling the real ladder’s spread. It collapses toward a near-monopoly: Great Tusk at 87.71% of the stationary mix, Dragonite at 6.50%, Kingambit at 5.76%, and the other five species asymptoting toward zero, Gholdengo included, despite Gholdengo sitting in second place on the…