A government wants to allocate a radio spectrum license to the company that values it most. Companies are strategic and will shade their bids. Which auction format makes truthful bidding a dominant strategy for each bidder?
AA first-price sealed-bid auction, where the highest bidder wins and pays their own bid
BAn open-outcry ascending auction with no reserve price
CSimply asking companies to submit their true valuations on an honor system
DA second-price sealed-bid auction, where the winner pays the second-highest bid
In a first-price auction, each bidder shades their bid below their true valuation to capture surplus — if you value the license at $10M and bid $10M, you break even even if you win. This means bids are not truthful. In a second-price (Vickrey) auction, the winner pays the second-highest bid regardless of what they bid. Bidding your true valuation is a dominant strategy: if you overbid and win, you may end up paying more than your valuation; if you underbid and lose, you miss a profitable opportunity. The second-price format 'implements' the efficient allocation by making truth-telling individually rational.
Question 2 Multiple Choice
What is the fundamental challenge that mechanism design addresses that standard game theory does not?
AComputing Nash equilibria for games with many players
BDesigning the rules of a game so that self-interested agents with private information produce a socially desired outcome in equilibrium
CFinding cooperative strategies that improve on Nash equilibrium outcomes
DPredicting irrational behavior by agents who do not maximize expected utility
Game theory takes a game as given and asks what rational players will do. Mechanism design reverses the question: given a desired outcome, what game should be designed so that rational players produce that outcome? The designer cannot control what agents know or want — those are fixed. The challenge is designing message spaces and outcome functions so that honest reporting (or at least the desired behavior) is an equilibrium strategy. The private information problem is central: agents who know their own valuations have incentives to misrepresent them, and the mechanism must neutralize this.
Question 3 True / False
In a well-designed mechanism, agents are assumed to act cooperatively or altruistically to achieve the designer's goals.
TTrue
FFalse
Answer: False
This is the central premise that makes mechanism design both hard and powerful. Mechanism design assumes agents are rational and self-interested — they will behave however best serves their own interests, not the designer's goals. A well-designed mechanism must make self-interested behavior *compatible* with the desired outcome; it cannot rely on agents being told to behave cooperatively and simply obeying. The insight is that the designer's power lies entirely in choosing the rules, not in controlling agents' motivations.
Question 4 True / False
Incentive compatibility constraints limit what outcomes a mechanism can achieve, because not every socially optimal outcome can be implemented when agents behave strategically.
TTrue
FFalse
Answer: True
This is one of the central results of mechanism design theory. The set of outcomes that can be achieved in dominant strategy equilibrium or Bayesian Nash equilibrium is a constrained subset of all outcomes that would be socially desirable. Classic impossibility results (like the Gibbard-Satterthwaite theorem) show that no mechanism can be simultaneously efficient, individually rational, and budget-balanced for all environments. The tension between what is socially optimal and what is incentive-compatible is the discipline's central problem.
Question 5 Short Answer
A school district wants to match students to schools in a way that maximizes overall satisfaction. Explain why simply asking students to rank their preferences and assigning them accordingly is insufficient, and what mechanism design must do instead.
Think about your answer, then reveal below.
Model answer: If students believe that ranking their true preferences could hurt them — for example, if naming a popular school first makes it less likely they receive their second choice — they will strategically misreport their preferences. The mechanism must be designed so that truthful reporting is in each student's best interest (incentive compatible) and so that no student would prefer to have strategically manipulated their submission (strategy-proof). The Deferred Acceptance algorithm achieves this: under student-proposing DA, it is a dominant strategy for each student to submit their true preference ranking, because misreporting can only leave them worse off. The mechanism designer's task is to find or construct rules with this property.
This matching problem illustrates how mechanism design applies beyond auctions. The key insight is always the same: the designer cannot trust agents to reveal information voluntarily if doing so could disadvantage them. A correctly designed mechanism must align individual incentives with socially desired information revelation. In matching markets (schools, hospitals, organ donors), getting this right has enormous real-world consequences.