Mechanism Design for Two#
Working backwards from the outcome you want to the rules that would produce it
Three ideas, before anything else#
- mechanism design
- incentive compatibility
- individual rationality
Get these three straight now — Assignment 2 is built entirely out of them.
Mechanism design#
Every week so far handed you the rules and asked what happens. This week flips it: you already know what you want — chores split fairly, plans made without a fight — and the question is what rule would actually produce that, on purpose, instead of by luck.
That reverse direction — outcome first, rules second — is mechanism design.
Incentive compatibility#
A rule that only works if everyone follows it honestly isn’t really a rule, it’s a hope. “We’ll each be truthful about how tired we are” sounds fair right up until being truthful stops being anyone’s best move.
A rule that a self-interested person would still want to follow, purely out of self-interest, is incentive-compatible — it doesn’t need anyone to be good, only rational.
Individual rationality#
There’s a second bar a rule has to clear, separate from incentive compatibility: it has to be better than just opting out. A perfectly game-proof rule that one side would rather ignore entirely isn’t a mechanism, it’s a rule nobody’s actually playing.
That second bar — the rule has to beat the outside option of not playing at all — is individual rationality.
Now, back to the point#
A couple keeps fighting about who initiates date-night planning. Someone proposes a rule.
Rule one: “whoever’s less busy plans it”#
| Property | Does it hold? |
|---|---|
| Incentive-compatible? | No — claiming to be busy is free and unverifiable, so both sides have a reason to claim it |
| Individually rational? | Yes, if either side actually believes it’ll be followed |
| What happens in practice | Both sides start reporting “so busy this week,” and nobody plans anything |
The rule sounds fair. It’s gamed the moment it’s said out loud, because “busy” is cheap talk — exactly the problem week 3 named, showing up again in a rule instead of a profile.
Rule two: “we alternate, strictly, no exceptions”#
| Property | Does it hold? |
|---|---|
| Incentive-compatible? | Yes — there’s nothing to lie about; whose turn it is doesn’t depend on anyone’s claim |
| Individually rational? | Only if the burden of planning is roughly similar in a genuinely busy week and a quiet one |
| What happens in practice | Works most weeks; strains exactly when one person is actually overwhelmed and the rule can’t tell that apart from someone gaming rule one |
Rule three: alternate, with a once-a-month swap either side can call#
| Property | Does it hold? |
|---|---|
| Incentive-compatible? | Yes — calling a swap costs a scarce token, so it isn’t worth spending unless the week is genuinely bad |
| Individually rational? | Yes — strictly better than either rule one or straight alternation for both sides |
| What happens in practice | Genuine bad weeks get covered; the token’s scarcity is what stops it from becoming rule one again |
The fix wasn’t asking people to be more honest. It was making honesty the cheapest option, by attaching a real cost to claiming an exception.
A mechanism doesn’t ask anyone to be good. It arranges things so that being good and being self-interested point the same direction.
Tutorial 11#
Swap your Assignment 2 draft rule with a partner and try, deliberately, to find a way a rational, self-interested participant could follow it to the letter while defeating its intent. Revise in response to what they find.
What today doesn’t settle#
Every rule above assumed someone gets to propose it and the other side just responds. But in a real relationship, there’s no neutral outside designer choosing the best rule for both of you — whoever proposes the “ground rules” is also a player who has to live under them, and has every reason to propose a rule that’s incentive-compatible for the other person and quietly favorable to themselves.
That’s the same missing ingredient this course keeps finding under a new name: week 7 couldn’t say who breaks a standoff, week 8 couldn’t say who gets labeled the proposer, week 9 couldn’t say whose outside-option claim gets believed — and this week, mechanism design can’t say who gets to design the mechanism in the first place.
Week 12 is where this, and every prior week’s gap, come back at once.
See you next week#
Week 12: Exit Markets & the Redesign