Equation 14 · Part 5 · The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It

Symbol phi

\dot{x}_i = x_i\big(f_i(x) - \phi(x)\big)

\phi

What this part means

phi is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

phi is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol phiArticle 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…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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See this notation across published equations →

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