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Equation 7 · Part 5 · The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It

=

U(i,j)=log⁡2 ⁣(E(i,j)/E(j,i))U(i,j) = \log_2\!\big(E(i,j)/E(j,i)\big)
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

A matrix of pairwise advantages is an invitation to ask what a population that only cared about that matrix would converge on. Convert E into a genuine zero-sum payoff by taking a log-ratio: U(i,j) = log⁡2\log_2\!(\big(E(i,j)/E(j,i))\big) , which is antisymmetric by construction ( U(i,j) = -U(j,i) ) and reads in doublings of relative advantage — U(i,j)=2 means i ’s best attack into j outclasses j ’s best attack into i by a factor of four. This is a standard move in evolutionary game theory, and this piece does not pretend to invent the tool: this house has already used replicator dynamics to model real market selection and a matched null-model discipline to test claims of selection against chance,…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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The article lists its research sources here.