if you maximize the product of utilities (nash phrased as product, or as area), you’re invariant to scaling (because multiplying either by a constant just rescales all possibilities).
=>
if you maximize the log of utilities (nash phrased as log), you’re invariant to scaling (because multiplying either by a constant just shifts all logs, because addition in log space is multiplication in linear space).
sure, makes sense.
I am bouncing off the proof of existence, but aaalmost see how this property implies it. I remember understanding it in CoCo.
if you maximize the product of utilities (nash phrased as product, or as area), you’re invariant to scaling (because multiplying either by a constant just rescales all possibilities).
=>
if you maximize the log of utilities (nash phrased as log), you’re invariant to scaling (because multiplying either by a constant just shifts all logs, because addition in log space is multiplication in linear space).
sure, makes sense.
I am bouncing off the proof of existence, but aaalmost see how this property implies it. I remember understanding it in CoCo.