Should you hold your price, or cut first?
Your best price depends on what your rival does, and theirs depends on you. That is a game, not a forecast, and this template solves it: dominant strategies, the equilibrium you will actually land on, and exactly what a truce is worth to each side.
Operations Intermediate Game Theory Pro engine
After you install, this is the model to open.
Price War: Hold or Cut?
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
This one runs on a Pro engine, and every free install includes five full-quality runs on your own numbers, shared across all five Pro engines rather than five for each. After that, Pro is $199/year.
The answer
What rational play looks like:
- Equilibrium
- Both cut $4M each
- The truce
- Both hold $8M each
- Temptation
- $2M per side
- Verdict
- Prisoner's dilemma
Cutting is each side's dominant strategy, so the game settles at both cut, $4M each, even though both holding pays $8M each. The report prices the temptation to break a truce at $2M a side: that is the number any agreement, repetition, or reputation has to outweigh. Edit the four cells to match your market and see whether the dilemma survives.
The model
A 2x2 payoff grid in $M of margin. Each cell holds both payoffs, yours then theirs, for one combination of moves.
| Both hold | You $8M · Rival $8M |
| You hold, they cut | You $2M · Rival $10M |
| You cut, they hold | You $10M · Rival $2M |
| Both cut | You $4M · Rival $4M |
| Equilibrium | solved |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
Next question
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Every model like this one, and the method behind them: Decision trees.