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57.7%. That's the value of remittances received by Tajikistan in 2025, expressed as a share of its GDP, according to the World Bank.

Tajikistan is a small, landlocked country in Central Asia. Large numbers of its citizens work abroad, particularly in Russia, and send money home to their families.

Why does this matter?

Remittances can be an economic lifeline. They help families buy food, pay for education, build homes and start businesses. Unlike foreign aid, the money goes directly to households, which decide how to spend it.

But there is a catch.

A country can become increasingly dependent on income generated outside its own economy.

If migrant workers lose their jobs, the host country enters recession or migration restrictions tighten, the flow of money can suddenly weaken. And when remittances finance spending on imported goods rather than domestic investment, they may do relatively little to expand local productive capacity.

There is also a subtler economic effect. Large foreign-currency inflows can put upward pressure on the exchange rate, making domestic exporters less competitive — a version of the Dutch disease problem.

Yet without those remittances, millions of households could be considerably poorer.

So here's the question: are remittances helping Tajikistan develop its economy, or making it increasingly dependent on economic growth elsewhere?

And perhaps more provocatively: if your country relies on citizens working abroad to sustain living standards at home, is emigration a solution to underdevelopment — or a symptom of it?

Last time, five oil companies bid for the right to drill in an offshore field whose value nobody knew for certain, and we asked: why might winning an auction be bad news?

Bidding £100m, exactly your estimate, is risky. Think about what can happen if you win:

So bidding your estimate leaves no profit if you’re exactly right, exposes you to losses if you’ve overestimated, and gives you a profit only if the field turns out to be worth more than you thought. And because winning means your estimate was higher than everyone else’s, that last possibility may be less likely than you hoped.

Before deciding how much to bid, you’d want to know:

E wins, with the highest bid of £130m. The field is worth £100m, so E loses £30m.

What should E have inferred? Think about what winning means: all four other companies estimated the field at less than £130m. Each did its own independent research, and every one came up with a lower number.

E should be suspicious of its estimate. Four independently researched estimates are lower than its own. That doesn’t prove E is wrong, but it is evidence that E may have been too optimistic.

As a rough check, the average of all five estimates is (80 + 92 + 105 + 118 + 130) ÷ 5 = £105m, much closer to the true value than E’s £130m. The average isn’t guaranteed to be right either, but it uses everyone’s information, not just E’s.

The lesson: winning is information. The fact that you outbid everyone tells you that everyone else was less optimistic than you. And that should make you less confident in your own estimate.

No: it’s built into how the auction works.

Start with a simple example. Imagine five people independently guess the number of sweets in a jar, and each is equally likely to guess too high or too low. For the highest guess to be too low, all five guesses would have to be too low. That’s like five coin tosses all landing tails: possible, but unlikely. So the highest guess is usually too high.

An auction does exactly this. Each company’s estimate may be unbiased on its own, but the auction picks out the highest one. Choosing the highest of several imperfect estimates creates an upward selection bias: even when every individual estimate is right on average, the highest one is, on average, too high. If everyone bids their estimate, the winner is the company with the most optimistic estimate.

(A note for the careful reader: “unbiased” means right on average, not equally likely to be too high or too low. If estimates are usually a little too low but occasionally far too high, the highest estimate can be too low more often than not. But on average, it’s still too high.)

With 50 companies, it gets worse. The more estimates there are, the more likely it is that someone guesses much too high, and that company wins. So the highest estimate tends to be further above the true value.

Does more competition make the auction work better? Not necessarily. If bidders ignore the problem, more competition makes the overpayment worse. Bidders who understand it should take more account of what winning would tell them as the number of rivals grows.

This is the winner’s curse. It’s what Capen, Clapp and Campbell were describing in 1971: in auctions for something with one uncertain value, the winner tends to be the bidder with the most optimistic estimate. Their advice to their own company was to bid below their estimates, especially when there were many rivals.

Under the second-price rule, E still wins, because it still has the highest bid. But now E pays the second-highest bid: D’s £118m.

E’s loss is now £118m − £100m = £18m, smaller than the £30m loss before, but still a loss.

Why doesn’t the new rule solve the problem? Because the second-highest estimate is also one of the more optimistic ones. D’s £118m is above the true value too. The rule changes what the winner pays, but the price is still set by an optimistic estimate.

In this example, the second-price rule reduces the winner’s loss, but doesn’t eliminate it. (In practice, bidders would also change how they bid under different rules, so we shouldn’t read too much into comparing the two auctions with the same bids.)

First, fill in the grid. Remember: if you win, you pay the highest rival bid, not your own.

Now compare the columns, row by row:

So bidding £100 is never worse than either alternative, and sometimes better. Economists call this a weakly dominant strategy.

Why does this hold for any rival bid, not just these three? The key is that your bid never changes what you pay: if you win, you pay the rival’s bid. Your bid only decides whether you win.

Bidding exactly £100 does both, automatically.

What if the rival bids exactly £100? Then winning means paying £100 for something worth £100 (profit £0), and losing also gives £0. You’re indifferent, so bidding £100 is still never worse.

This result is due to the economist William Vickrey (1961), who shared the Nobel Prize in Economics in 1996. Second-price auctions are often called Vickrey auctions. eBay’s automatic bidding works on a similar, though not identical, principle: you enter the most you’d pay, and you pay just above the next-highest bid.

Each of the five independent estimates is like a coin toss: above V (heads) or below V (tails), with equal probability. Each coin has 2 outcomes, so five coins give 2 × 2 × 2 × 2 × 2 = 32 equally likely combinations.

When is the highest bid below V? Only if every estimate is below V: all five tails. That’s just 1 of the 32 combinations.

So the probability that the highest bid exceeds V is 1 − 1/32 = 31/32, about 97%.

With n bidders, there are 2ⁿ combinations, and only one has all tails, so the probability is 1 − (½)ⁿ:

Now the second-highest bid. It’s below V only if at most one estimate is above V. Count those combinations:

That’s 6 of the 32. So the probability that the second-highest bid exceeds V is 1 − 6/32 = 26/32, about 81%.

With n bidders, there’s 1 combination with no heads and n with exactly one, so the probability is 1 − (n + 1)/2ⁿ:

So even in a second-price auction, if everyone bids their estimate, the winner pays more than the field is worth about 81% of the time with five bidders, and almost always with ten.

Why is the painting different?

Economists distinguish private-value auctions (like the painting) from common-value auctions (like the oilfield). In a common-value auction, the right question isn’t “what do I think it’s worth?” but “what is it worth, given that I’ve won?” In this simple setting, that typically means adjusting your bid below your initial estimate. Paul Milgrom and Robert Wilson won the 2020 Nobel Prize in Economics for their work on auction theory, including common-value auctions and the design of auctions for radio spectrum.

Because, when everyone is estimating the same uncertain value, winning tells you that you were the most optimistic. And the most optimistic estimate is, on average, too high.

The winner’s curse isn’t simply bad luck. It’s selection: the auction systematically favours the most optimistic estimate, which can be dangerously high. The cure isn’t to stop bidding, but to think ahead: ask what the field would be worth if you won, and bid accordingly.

And it goes well beyond oilfields: company takeovers, football transfers, house purchases and spectrum auctions all involve bidding for something whose true value is uncertain.

Marginal gains… Answer for today’s question is out in two days… Come back then or subscribe to get it direct to your inbox!

P.P.S.

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