Week 11: Mechanism Design for Two

Working backwards from the outcome you want to the rules that would produce it

8 May 2028

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Every prior week analyzed a market as given: these are the rules, what happens? Mechanism design runs the direction: this is the outcome we want, what rules would produce it, and are those rules incentive-compatible — do they still work once everyone plays them strategically rather than honestly?

Applied to a relationship, this reframes “we should set some ground rules” as a genuine design problem with a genuine failure mode: a rule that isn’t incentive-compatible doesn’t get followed, it gets gamed. Assignment 2 asks you to design one that would actually hold.

Incentive compatibility isn’t the only bar a rule has to clear, either. A rule can be perfectly game-proof and still fail if it’s worse than just walking away from it — nobody’s obligated to play a mechanism, however cleverly designed, that leaves them worse off than opting out entirely. That second requirement, individual rationality, is easy to forget precisely because the incentive-compatibility puzzle is the more interesting one to solve, and a redesign that nails the first while ignoring the second produces a rule that’s technically ungameable and practically ignored.

The households in this week’s examples show why a rule fails in stages, not all at once. “Whoever’s less busy plans date night” fails immediately, because being busy is cheap to claim and expensive to check — the same cheap-talk problem week 3 diagnosed in a profile now diagnosing a household rule instead. A stricter fix, strict alternation with no exceptions, becomes incentive-compatible by removing the thing anyone could lie about — but it can fail individual rationality the moment one side is genuinely, not strategically, overwhelmed, and the rule has no way to tell the difference between a real bad week and a gamed one. The redesign that actually holds usually attaches a real, scarce cost to claiming an exception, so that only a genuinely bad week is worth spending it on.

That’s the shape Assignment 2 wants back: not a rule that sounds fair, but one you can show surviving an attempt, by a rational and self-interested person, to break it on purpose.

Outline#

• mechanism design as inverse game theory: outcome first, rules second
• incentive compatibility, and why a rule everyone agrees to isn’t the same as a rule everyone will keep following
• individual rationality, and why a game-proof rule can still fail by being worse than opting out
• watching a household rule fail, get patched, and fail again — cheap talk, then a blind spot around genuine bad weeks, then a real cost attached to claiming an exception
• what makes a household “rule” a mechanism rather than a wish

One thing this framework won’t explain#

Every mechanism this week designs assumes a neutral party choosing the best rule for both sides — the framework itself is silent about who actually gets to propose the rule in a relationship that has no outside designer. Whoever puts a ground rule on the table is also a player who will live under it, with every reason to make it incentive-compatible for the other person while quietly favoring themselves, and mechanism design has no term for that conflict of interest.

That’s the same missing ingredient this course keeps finding under a different name each time it shows up: 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, week 10 couldn’t say which of many equilibria two people settle into — and this week, nothing says 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.

Further reading#

• Hurwicz, L. (1973). “The Design of Mechanisms for Resource Allocation.” The American Economic Review, 63(2), 1–30. The paper that named the field this week draws on — Hurwicz shared the 2007 Nobel Memorial Prize in Economic Sciences for founding mechanism design as its own subject, separate from the game theory it reverses.
• Myerson, R. B., & Satterthwaite, M. A. (1983). “Efficient Mechanisms for Bilateral Trading.” Journal of Economic Theory, 29(2), 265–281. A mechanism design problem for exactly two people — one buyer, one seller — proving that no rule can simultaneously be efficient, incentive-compatible, individually rational, and require no outside subsidy. Worth sitting with before Assignment 2: even the two-person case has a hard limit on how good a rule can be.