Common Grounds doesn't read your team chat, but it does see the prices on your street. Every price you post is a move in a game, and the other players move too.
Learning objectives. After this week you can (1) find a best response and a Nash equilibrium in a 2×2 payoff table; (2) explain why a price war is a prisoner's dilemma; and (3) explain how repeated play makes tacit cooperation possible.
Remember this: your best move depends on theirs. A stable outcome is not always a good one.
1) Games and best responses
A game has players (the shops on your street and Common Grounds), strategies (price high, cut) and payoffs (daily profit). A best response is your most profitable move given what the others chose. A dominant strategy is your best response whatever they choose. A Nash equilibrium is a set of moves where everyone is best-responding at once, so nobody gains by changing alone.
2) The price war as a prisoner's dilemma
| They price HIGH | They CUT | |
|---|---|---|
| You price HIGH | ($240, $240) | ($150, $300) |
| You CUT | ($300, $150) | ($180, $180) |
If they price high, cutting pays you $300, not $240. If they cut, cutting pays $180, not $150. Cutting is dominant for both, so the Nash equilibrium is (CUT, CUT) at $180 each, though (HIGH, HIGH) would pay each shop $60 more a day. Stable, and bad for both: the prisoner's dilemma.
3) Playing every day
You play this game every day of the season: a repeated game. If shops expect a cut today to be answered tomorrow (a trigger strategy: cooperate until someone cuts, then cut too), the one-day gain from cutting can cost many days of lower prices. Holding prices up with no agreement is tacit collusion. Actually agreeing on prices with competitors is explicit collusion, and it is illegal in real markets.
A war has a floor, too. At a $1.40 latte with a $1.20 MC latte, each cup adds $0.20. Covering a $480 wage bill (three baristas, 10 hours, $16 an hour) would take 480 ÷ 0.20 = 2,400 cups, far more than a day brings.
4) Reading your street
- Interdependence. Customers compare every shop on the street, so a classmate's price cut can lower your sales when you changed nothing.
- The rival moves too. Common Grounds' latte price on your report shifts as the prices around it shift. PROMO today means the rival ran a sale: a substitute got cheaper, so your customers dip that day, a cross-price effect. It is not a war.
- Customers can skip coffee. If every shop raises prices together, some customers leave the market altogether. Even perfect cooperation can't escape the demand curve.
Quick self-check
(a) In the table, if they cut, what is your best response? (b) Is (CUT, CUT) the best outcome for the two shops? (Answers: cut, because $180 beats $150; no, both earn $60 more at (HIGH, HIGH), but it isn't stable.)
Common mistakes
- Thinking Nash means best for everyone. The one-shot war's Nash is the bad outcome.
- Reading a promo-day dip as an attack. Check the PROMO flag first.
- Winning share below cost. Each cup sold below your MC latte loses money.
This week in the arena
On each Daily Report this week, write down your latte price, Common Grounds' latte price and your Market share, and mark any PROMO day. Is your street drifting toward a price war or holding steady? Check the leaderboard to see who that drift is paying.