Two friends agreed to meet tonight but lost signal before deciding where. You would rather go to the gig. Your friend would rather go to the match. Both of you would far rather be together than alone at either.
Neither can reach the other, so each has to guess where the other will go.
Together at the gig: 2 for you, 1 for your friend. Together at the match: 1 for you, 2 for your friend. Apart: 0 each.
You are Friend A
Watch one round, or choose now.
Friend A
or
You
Friend A
?
You
Friend B
or
Your friend
Friend B
?
Your friend
Your friend picks at random here, like a coin toss.
The whole game on one grid
Every pair of choices and what each side gets: yours first, then theirs. Each number is a payoff.
Step 0 of 3
The cards are face down. Turn them, then step through which squares are stable.
What do you think they'll do?
Your best move depends on what you expect from your friend. Drag to set how likely you think it is they pick The gig.
What it teaches
Agreeing matters more than what you agree on, but the two of you disagree about which to agree on.
The usual mistakeReading it as a game about communication, so concluding that a single phone call solves it, when the two of you would still be arguing about which answer to give and the person who concedes does worse.
The checkTalk settles coordination only once something outside the payoffs breaks the tie. Ask what asymmetry, habit or precedent decides which equilibrium gets played, because nothing inside the matrix does.
In the real world
Real world
Blu-ray against HD DVD
Both camps wanted a single high definition disc standard, because a split market left buyers unwilling to commit to either player, but each preferred the standard built on its own patents and plant. Talks on a unified format failed and the two launched against each other from 2006, with studios, retailers and console makers taking sides, and Sony putting a Blu-ray drive in every PlayStation 3. Warner Bros. declared for Blu-ray in January 2008 and Toshiba abandoned HD DVD the following month.
Both sides ranked any single standard above a split market but ranked the two candidate standards in opposite orders, which makes it a battle of the sexes rather than a driving convention, where the players do not care which of the two they match on. The inference is that each camp was optimising for the royalty stream and the hardware position that came with owning the standard rather than for the disc itself, which is why the fight was settled by buying the studios' commitment rather than on technical merit.
Fiction: Succession
The Roy siblings' united front
The Roy siblings repeatedly need to act as one bloc, because a united front is the only thing with any weight against their father and later against the buyer of the company. Every attempt founders on which of them is to lead it: they agree on the need for a pact and not on its terms, and it collapses at the moment it has to be named. The company ends up in the hands of someone none of them wanted.
Either leadership arrangement beats no arrangement for both of them, but they rank the two arrangements oppositely, so the obstacle is distribution rather than doubt about the other's nerve; in a stag hunt they would agree on which outcome is best and fear only that the other will not turn up. The inference the series keeps pressing is that what each sibling is actually optimising for is their father's verdict rather than control or money, which is why no side payment ever closes the deal: the prize is indivisible by construction.
Committee voting gameA third equilibrium exists on the outcome both members rank last, held up only by each vote being individually irrelevant. Not on the wall yet.
Driving conventionThe players are indifferent between the two conventions, so there is nothing to argue about. Not on the wall yet.
Matchmaker gameThe coordination problem is embedded in a subgame that someone else chooses whether to start. Not on the wall yet.