Spark & Anvil Privacy

Teach & case

Help a near-peer reason through the idea — when you explain it, you understand it best — then read the real decision it comes from.

A case · you decide

Elena and the two food trucks in a price war

Elena — a student modeling two rival food trucks that both keep cutting prices until neither will move

The idea in play: a Nash equilibrium is STABLE (no one gains by switching alone) — not necessarily best for both.

Two food trucks share a corner. Each keeps undercutting the other until both sit at rock-bottom prices, each barely breaking even. Neither will raise first. Elena's friend says "well, that's the equilibrium, so it must be the best they can do." Is it?

At the low-low prices, if either truck alone raises its price, it loses all its customers to the rival — so neither wants to move. That's what "equilibrium" means: no player gains by unilaterally switching. It's STABLE.

But both-keep-prices-high would earn each of them MORE. It's better for both — yet it isn't an equilibrium, because from there either truck gains by secretly undercutting. Stable and best-for-both are different questions.

Both trucks are at rock-bottom prices, neither willing to move. Is this the best outcome they could reach?

Elena says "the high-price outcome is better for both, so THAT must be the real equilibrium." Does better-for-both make it an equilibrium?

Find the equilibrium yourself →

When two ideas meet: 2 cases with two people

A case · you decide

Cai and Dex: the stable outcome nobody wants

Cai & Dex — a player who wants to cooperate, and one who sees what defecting earns

The idea in play: in a one-shot prisoner’s dilemma, defecting is each player’s best reply whatever the other does, so mutual defection is the equilibrium even though both would prefer mutual cooperation.

One round, no talking. Both cooperate: 3 points each. Both defect: 1 each. If one defects and the other cooperates, the defector gets 5 and the cooperator 0.

Dex checks each case: what does defecting earn him if Cai cooperates, and what does it earn if Cai defects?

Cai sees the same numbers from the other side.

Where does this one-shot game settle?

Open the Strategy Lab →

A case · you decide

Tao and Ines: the last round

Tao & Ines — a tit-for-tat player in a repeated game, and a friend who reasons back from the end

The idea in play: repetition supports cooperation because tomorrow can reward or punish today; in the known last round there is no tomorrow, so the one-shot logic returns.

The same dilemma, played ten times, and both players know round ten is the last. Tao has been copying the other player's last move, and it has kept both cooperating.

Ines asks what could reward cooperation in round ten. No round eleven exists.

What does backward induction predict for round ten?

Open the Strategy Lab →