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Equation 7 · Part 6 · The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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