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Ten short pieces, in order. Each one ends with what it changes about a decision — if it does not change one, it is not worth your time. Number nine is the strongest argument against this whole approach.
1 · Softmax and λ — where the randomness comes from
Stop asking whether your rival is rational and start asking how sharply they chase their best option. It is one number, you can estimate it from their past moves, and it is the difference between planning against one price and planning against four.
022 · The fixed point — everyone's noise responds to everyone's noise
Your best move depends on theirs, and theirs on yours. Any planning process that fixes their behaviour first and optimises against it is answering a different question than the one you have.
033 · QRE vs mixed Nash — sensitivity, not indifference
Assuming the other side is perfect is not the conservative choice — it is a specific, usually wrong, forecast. Price the difference before you adopt it.
044 · MaxEnt — the softmax is not an assumption
When you genuinely do not know what they will do, the honest forecast is the most spread-out one consistent with what you do know. Anything sharper is you adding information you do not have.
055 · Gibbs and potential games — where the physics is exact
Some situations have a hill everyone is climbing; in those, a change you make moves things where you expect and comparative statics can be trusted. Find out which kind you are in before trusting a sensitivity table.
066 · Detailed balance and currents — the visual heart
If your market cycles rather than settling, waiting for it to stabilise is not a strategy — it will not. Time your moves against the cycle instead of trying to end it.
077 · Reciprocity — the same number both ways
Measure how much your price moves theirs and how much theirs moves yours. When the two are different sizes, one of you structurally leads — and that asymmetry, not the average elasticity, is the thing to act on.
088 · Elasticity vs λ — two dials that people conflate
A demand elasticity and a rival's decisiveness look the same in a regression and mean opposite things for what you should do. Separate them before you set a price on either.
099 · The one-price objection — the strongest case against all of this
If your rival really does set one price and never move, none of this buys you anything and you should say so. Check that first; it takes a minute and it is the cheapest way to avoid a wrong model.
1010 · The same machinery everywhere — the point of the whole exercise
The pricing answer, the bidding answer and the routing answer come out of one piece of arithmetic. If you have solved one of these decisions well, you already know how to set up the others.