Questions & explanations
1. Give an example of an allocation rule that is not implementable using Myerson's Lemma.
Suppose in a single-item auction, we want to give the item to the bidder with the second-highest value, not the highest. This allocation rule is not monotone because if a bidder increases their value from low to high, they might lose the item. For instance, with two bidders, if bidder A has value 5 and B has value 3, A wins. But if A raises value to 10, B might still win? Actually here A would still win, but consider a rule that awards to runner-up: if A=5, B=3, B wins; if A raises to 10, B still wins? Wait, that is monotone? Actually if A increases value, they still lose, which is not monotone because increasing value does not change outcome from lose to win. It's monotone in the sense that if they win at low value they also win at high? But they never win, so it's vacuously monotone? The issue: the allocation must be monotone in the sense that if a bidder wins at a value, they must win at all higher values. Here, no one ever wins at any value? Actually the runner-up rule: the highest bidder never wins, so if a bidder is never winning, it's monotone. But the rule must be based on al
2. Give an example of TTC with three people and three houses.
People A, B, C each own a house: A owns house1, B owns house2, C owns house3. Preferences: A: house2 > house1 > house3; B: house1 > house2 > house3; C: house1 > house2 > house3. Round 1: A points to house2, B points to house1, C points to house1. house1 points to owner B, house2 points to A, house3 points to C. Cycles: A->house2->A (cycle: A trades with himself, gets house2), B->house1->B (B keeps house1? Wait, B points to house1 which points to B, so cycle B gets house1). But house1 is pointed to by two people, so we need to check proper cycles. Actually, house1 points to B, so the cycle is B->house1->B, so B gets house1. Then house2 points to A, and A points to house2, so A gets house2. C points to house1, but house1 is taken, so C is left with house3. After round 1, A gets house2, B gets house1, C gets house3. Efficient? Yes, A and B are happier, C gets own house.
3. Compare exclusive-use licenses with shared access approaches in spectrum management.
Exclusive-use licenses give one owner the sole right to use a specific frequency band in a certain area, preventing interference from others. This provides reliability and long-term investment certainty, but can lead to underused spectrum if the owner doesn't need it all the time. Shared access allows multiple users to use the same band, often with rules to avoid interference, like sensing for free channels or using low power. Sharing is more efficient for quickly changing uses, but it can cause interference if not managed well. For example, Wi-Fi uses shared unlicensed spectrum, leading to many devices coexisting but also congestion. A mix of both is often best: exclusive licenses for critical services and shared bands for flexible, low-cost use.
4. Why is interference a problem in radio spectrum markets, and how can market design help?
Interference happens when two devices use the same frequency band and disrupt each other's signals. This can cause poor call quality or slow internet. Market design can help by assigning different frequencies to different users, like auctioning licenses for exclusive use. Some markets allow secondary trading, where a license holder can sell or lease their unused spectrum to others, so frequencies are used more efficiently. Another method is to set rules that limit signal power or require devices to cooperate. For example, TV white spaces (unused channels) can be shared with wireless internet if devices avoid interference. Good market design balances the need for exclusive rights with flexible sharing to maximize the value of spectrum.
5. Discuss a challenge of using satellite data in field experiments, such as measurement error or missing data, and how to mitigate it.
Satellite data can have clouds that block the view, leading to missing images for some days. Also, the resolution might be too coarse to see small plots. For example, if a satellite measures a 30-meter pixel but farm plots are only 10 meters, the data is a mixture. This introduces measurement error that can bias results. To handle clouds, researchers can take the average of multiple days or use images from a satellite that sees through clouds (radar). For resolution, they can use very high-resolution satellites (like 1-meter) if budget allows, or use ground-level data to correct the satellite data. Another way is to show that measurement error is not related to treatment, so it only makes the effect harder to detect but not biased.
6. What are ethical pitfalls in field experiments?
Ethical pitfalls are problems that can harm participants or communities in a study. Three common pitfalls are lack of informed consent, unfair treatment, and community lobbying. Informed consent means telling people what the study involves and getting their approval without pressure. Unfairness happens when one group gets a benefit that the other does not, like a new teaching method while the other group gets nothing. Community lobbying occurs when local leaders try to influence who gets the treatment, which can bias results and harm trust. Researchers must design studies carefully to avoid these issues and ensure that participants are respected and treated equally. This protects both the people and the quality of the research.
7. Give an example of a social choice rule that violates monotonicity and thus cannot be implemented in Nash equilibrium.
Consider a rule that chooses the alternative that is ranked last by a majority of voters. Suppose initial preferences: voters 1 and 2 rank A last, voter 3 ranks B last. Rule picks A? Actually need careful: Suppose rule chooses the alternative with the most last-place votes. If two voters have A last and one has B last, rule picks A. Now change preferences: voters 1 and 2 move A up to second place, but still A is last for no one? Then B might have more last-place votes. The outcome changes from A to B even though A improved in everyone's ranking (it went from last to not last). This violates monotonicity because improving A's rank made it lose. Such a rule cannot be implemented in Nash equilibrium according to Maskin's theorem.
8. How can market design address the hold-up problem where a spectrum owner refuses to allow sharing?
The hold-up problem occurs when a spectrum owner demands a very high price for sharing, blocking efficient use by others. Market design can solve this by setting default sharing rules or a mandatory price mechanism. For example, regulators can require that if an owner does not use a band, they must allow sharing at a regulated, reasonable fee. Another approach is to create a database that coordinates sharing rights, where owners can offer short-term leases at posted prices. Also, auctions of spectrum access rights (like three-dimensional rights for space, time, and location) can reduce hold-up by making it clear what is being sold. These measures ensure that unused spectrum can be accessed, increasing overall efficiency.
9. What does Milgrom and Weber's linkage principle say about information in auctions?
The linkage principle says that an auctioneer can increase expected revenue by linking the price a winner pays to additional information about the item's value, not just to other bids. For example, revealing a pre-auction appraisal of a painting and tying the final price to that appraisal can boost revenue. This works because bidders become more confident and bid more aggressively when they know the price will reflect more information. The principle suggests that English auctions (where bids are open) tend to raise more revenue than sealed-bid first-price auctions, because they release more information during bidding. In practice, auction designers often use reserve prices or royalty payments to implement linkage.
10. Give an example where a researcher uses a prior distribution in a field experiment on job training programs. Why is choosing the prior important?
Suppose a researcher runs a field experiment on a new job training program. They look at past studies and think the program might increase earnings by $500 on average, with some uncertainty. They use that as a prior: a bell-shaped curve centered at $500. After the experiment, they get new data showing an increase of $800. The Bayesian posterior will combine the prior and data, giving an estimate between $500 and $800. Choosing the prior is important because if the prior is too strong or wrong, it can pull the results away from the truth. For instance, if the prior is very tight around $0, it will ignore strong new evidence. So researchers must pick priors based on solid past evidence or use neutral priors.
11. Give an example of a governance decision in a cryptocurrency network and how it can be made.
For example, in Bitcoin, the community might decide to increase the block size to allow more transactions. This is a governance decision about changing the protocol. It can be made through rough consensus among developers, miners, and users, often signaled by software updates. Some cryptocurrencies like Ethereum have formal on-chain governance where holders of a governance token vote directly on proposals. The outcome of the vote is automatically executed by the blockchain. Off-chain governance relies on discussion forums and signaling, then miners or validators adopt the change. The process differs: off-chain is informal but flexible; on-chain is transparent but can be manipulated by large token holders.
12. What is the Bulow-Klemperer Theorem?
The Bulow-Klemperer Theorem compares two ways for a seller to increase revenue in an auction: setting an entry fee or using a reserve price. It says that if the seller can attract more bidders, the benefit of having a larger pool of bidders outweighs the gain from setting an optimal reserve price. Specifically, the theorem states that the expected revenue from an efficient auction (like a second-price auction without reserve) with n+1 bidders is at least the expected revenue from an optimal auction (with an optimal reserve price) with n bidders. This highlights the power of competition over sophisticated pricing. It guides sellers to focus on attracting bidders rather than fine-tuning reserve prices.