Equation 16 · Part 1 · The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It

Symbol i

i

i

What this part means

i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol iArticle meaning

The passage around this formula

Run the continuous replicator equation on the resulting eight-strategy zero-sum game: $\dot{x}_i$ = $x_i$ $\big($ $f_i(x)$ - $\phi(x)$ $\big)$ , where $f_i(x)$ = $\sum_j$ $x_j$ \, U(i,j) is species i ’s expected payoff against the current population mix and $\phi(x)$ = $\sum_i$ $x_i$ $f_i(x)$ 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…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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