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The Missing Chapter

The Art of Rent-Seeking

Why rational people spend $100 fighting over a $100 prize — and everyone loses

An extension of Jordan Ellenberg's "How Not to Be Wrong"

Chapter 97

The $100 Bill on the Sidewalk

There's a $100 bill sitting on a table. Two people can compete for it by spending money on "lobbying" — whoever spends more is more likely to win, but neither gets their spending back. How much should you spend?

Here's a game that economists love and everyone else should find deeply unsettling. I'm going to put a hundred-dollar bill on the table. You and one other person can each spend money trying to win it. The more you spend relative to your opponent, the more likely you are to grab the prize. Specifically: if you spend $60 and your opponent spends $40, you win with probability 60/100 = 60%.

So what's your expected payoff? You win $100 with probability 60%, so your expected winnings are $60. But you spent $60 to get there. Your expected profit is $60 − $60 = exactly zero.1

Your opponent isn't doing any better. They win $100 with probability 40%, for expected winnings of $40, minus their $40 spent: also zero. Between the two of you, you've spent $100 — the entire value of the prize — and produced absolutely nothing. The money just... evaporated.

This is the Tullock contest, named after the economist Gordon Tullock, who described it in 1967.2 And it's not just a thought experiment. It's a disturbingly accurate model of how enormous amounts of real wealth get destroyed every single day.

· · ·

The word "rent" in economics doesn't mean what your landlord charges you — or rather, it does, but in a very specific way. Economic rent is income you earn not because you produced something, but because you control something scarce. Your landlord doesn't earn rent because they built the land. They earn it because they own the land, and land is scarce. The rent would exist whether or not the landlord did anything useful at all.

Rent-seeking, then, is the activity of spending resources to capture those rents — to get your hands on income that already exists, rather than creating new wealth. It's fighting over the pie instead of baking it.

Creating Value $100 $200 Pie grows — everyone gains Rent-Seeking $100 (same size) -$50 -$50 Pie stays fixed — resources wasted
Value creation grows the pie. Rent-seeking just rearranges who holds the knife.
Chapter 97

The Tullock Contest Function

Let's be precise about the math, because the math is where the horror lives.

Two players compete for a prize of value V. Player A spends a and Player B spends b. The probability that A wins is:

The Tullock Contest Function
P(A wins) = a / (a + b)
When both spend zero, each wins with probability ½
V
Value of the prize
a
Player A's spending
b
Player B's spending

Player A's expected payoff is therefore:

E(A) = V · a/(a+b) a

Now here's the key question: what's the Nash equilibrium? What level of spending makes neither player want to change their strategy?

Player A maximizes their payoff by choosing a such that the derivative equals zero. Taking the derivative and setting it to zero (with some calculus I'll spare you), the best response for A given B's spending b is:

a* = √(V · b) b

By symmetry, B's best response is the same with a and b swapped. In the symmetric Nash equilibrium, both players spend the same amount, so a* = b*. Solving, we get:

a* = b* = V/4
Each player spends one-quarter of the prize value

So with two players and a $100 prize, each spends $25 in equilibrium. Total spending: $50. That's half the prize wasted on pure contest, producing nothing.3

But wait — it gets worse. With n players, the equilibrium total spending is V · (n−1)/n. Three players? Total spending is $66.67. Ten players? $90. A hundred players? $99. As the number of competitors grows, total spending approaches the entire value of the prize. Complete dissipation. All the value, destroyed in the fight over it.

🏆 The Tullock Contest

Set the prize value and each player's spending to see how the contest plays out. Or find the Nash equilibrium.

$100
$25
$25
Player A
$25
Win: 50.0%
E[profit]: $25.00
vs
Player B
$25
Win: 50.0%
E[profit]: $25.00
$50 wasted
Total spending: $50 of $100 prize (50% dissipation)
2
Nash Equilibrium (n players)
$25.00 each
Total wasted: $50.00 (50.0% of prize)
Chapter 97

Three Trillion Dollars of Nothing

Okay, you might say, this is a cute model. But who actually plays Tullock contests in real life?

Everyone. All the time.

In 2023, the United States lobbying industry spent $4.1 billion — just the part that's officially reported.4 That's $4.1 billion spent not on building factories, developing products, or training workers. It's spent on convincing legislators to tilt the rules in the spender's favor. It's spending money to get money — the textbook definition of rent-seeking.

The U.S. sugar program restricts sugar imports and guarantees domestic sugar producers high prices. The result: Americans pay roughly twice the world price for sugar. The total cost to consumers is about $3.5 billion per year. The benefit to sugar producers is about $1.5 billion per year. The remaining $2 billion? Gone. Deadweight loss. Pure waste.

But here's why it persists. The cost is spread across 330 million consumers — about $10.60 per person per year. Nobody's going to march on Washington over $10.60. The benefit, however, is concentrated among a few thousand sugar producers who each gain hundreds of thousands of dollars. They have every incentive to lobby, and they do.5

This is Mancur Olson's collective action problem, described in his 1965 book The Logic of Collective Action.6 When benefits are concentrated and costs are diffuse, the beneficiaries will organize to defend their rents, and the people paying for it won't bother to organize against them. Not because they're stupid — because it's individually rational not to bother.

The math is simple. If fighting the sugar tariff would save you $10.60 per year, but joining an anti-tariff lobbying group costs $50 in dues and ten hours of your time — why would you bother? You wouldn't. And neither does anyone else. And so the tariff persists.

Concentrated Benefits, Diffuse Costs Producers (few) +$300K each/year Will lobby? YES ✓ policy Consumers (millions) −$10.60 each Will lobby? No way. Total: ~$1.5B gain Total: ~$3.5B cost
The asymmetry that makes rent-seeking so durable: a few people gain a lot, everyone else loses a little.

The Rent-Seeking Zoo

Lobbying is the obvious example, but rent-seeking wears many costumes:

Patent trolls — companies that acquire patents not to build products but to sue people who do. They produce nothing; they just extract money from people who produce things, using the legal system as their Tullock contest arena. Patent troll lawsuits cost the U.S. economy an estimated $29 billion per year in direct costs alone.7

Taxi medallions — In New York City, a taxi medallion (the license to operate a cab) sold for over $1 million in 2013. The medallion doesn't make the driver better. It doesn't make the car safer. It's a government-created artificial scarcity that generates rents for medallion holders at the expense of riders and would-be drivers. When Uber arrived, medallion values crashed to under $200,000 — revealing that over $800,000 of that value was pure rent.

Occupational licensing — Louisiana requires 500 hours of training to become a licensed florist. Five hundred hours. To arrange flowers. Who do you think pushed for that requirement? Not consumers worried about dangerous bouquets. It was existing florists, using the state to limit competition — the definition of rent-seeking.

Regulatory capture — When the industry being regulated effectively controls its regulators. The revolving door between Wall Street and the SEC, between pharmaceutical companies and the FDA, between telecom giants and the FCC. The regulations that were meant to protect the public end up protecting the incumbents from competition.

"The problem with rent-seeking is not that people are greedy. It's that the incentive structure makes grabbing more profitable than creating."
Chapter 97

Counting the Waste

In 1974, Anne Krueger published a landmark paper attempting to quantify rent-seeking losses.8 She looked at two countries — India and Turkey — where government-issued import licenses created huge rents for license holders. Her estimates were staggering: rent-seeking consumed approximately 7.3% of India's GDP and 15% of Turkey's GDP.

Think about what that means. In Turkey, roughly one out of every seven dollars of economic activity wasn't creating value — it was fighting over who gets to capture value that already exists. Imagine if those resources had been invested productively instead. That's not an accounting abstraction. That's hospitals not built, research not funded, businesses not started.

Estimated GDP Lost to Rent-Seeking (Krueger 1974) India 7.3% Productive economy Turkey 15% Productive economy Rent-seeking waste Productive output
Krueger's 1974 estimates — the red slices represent resources spent capturing transfers rather than creating value.

And the deadweight loss from rent-seeking is actually worse than the direct spending. When an industry spends $100 million lobbying for a $2 billion subsidy, the social cost isn't just the $100 million spent lobbying. It's also the $2 billion in misallocated subsidies — money that could have gone to more productive uses. The lobbying spending is the visible tip; the iceberg below is the distorted policy itself.

💰 Lobbying ROI Calculator

An industry spends money lobbying for subsidies or protection. See the private ROI — and the social cost that dwarfs it.

$50M
$2,000M
25%
8%
Private Lobbying ROI
3,900%
Spend $50M → get $2,000M. Great deal... for the lobbyist.
Total Social Cost
$550M
Deadweight Loss
$500M
If Invested Productively
$54M/yr
Lobbying $ Wasted
$50M
The Tragedy

The $50M spent lobbying produces nothing. The policy it buys costs society $500M in deadweight loss. If that $50M had been invested productively at 8%, it would generate $4M per year in real value.

Chapter 97

Why Can't We Stop?

If rent-seeking is so wasteful, why does it persist? Because of a cruel structural asymmetry.

Consider the situation from the perspective of any individual firm. Suppose your competitors are all lobbying for favorable regulations. If you don't lobby, you're at a competitive disadvantage — you'll be subject to rules designed to benefit your rivals. So you lobby too. It's a prisoner's dilemma: everyone would be better off if nobody lobbied, but given that others are lobbying, each firm's best individual response is to lobby as well.

This is exactly the logic of the Tullock contest. Each player knows that the total spending is wasteful. But no individual player can improve their position by unilaterally reducing their spending. The waste is the equilibrium.

The Rent-Seeking Trap

Rent-seeking persists not because people are irrational, but because they are individually rational in a system with perverse incentives. The problem isn't bad people — it's bad game theory. Every participant is responding optimally to the incentives they face. The waste emerges from the structure of the game, not from individual moral failures.

Tullock himself had a dark sense of humor about this. He pointed out that the true social cost of rent-seeking includes not just the resources spent on lobbying, but also the resources spent defending against lobbying. When one industry lobbies for tariffs, competing industries have to lobby against them. The lawyers, PR firms, and political consultants on both sides are all consuming resources that produce no value. It's an arms race where the weapons are briefcases.

The Prescription

The Tullock model suggests a clear (if politically difficult) solution: reduce the number of prizes. If the government can't hand out special favors — can't create artificial monopolies, can't give out selective subsidies, can't impose tariffs that benefit specific industries — then there's nothing to rent-seek over. The contest disappears because the prize disappears.

This is the logic behind deregulation, behind trade liberalization, behind constitutional constraints on government spending. Not because government is inherently bad, but because every discretionary government action creates a rent that someone will spend resources trying to capture.

Of course, some government action is necessary and valuable. The art is in distinguishing between policies that create genuine public goods and policies that mainly create rents for well-organized interest groups. The Tullock contest gives us the conceptual framework: whenever you see a policy, ask yourself — how much of this policy's cost is being spent in the fight over the policy itself?

The next time someone tells you that a particular regulation is essential for public safety, or that a particular subsidy is vital for national security, you might ask: who, specifically, is paying for the lobbyists? Because someone is always paying for the lobbyists. And the answer to that question often tells you more about the policy's true purpose than any official justification ever could.

"The most important thing the government can do to fight rent-seeking is to have less to seek."

Notes & References

  1. This assumes the standard linear Tullock contest success function. In the general case, Tullock introduced an exponent r that governs the sensitivity of win probability to spending. When r = 1 (our case), the function is proportional; when r > 1, small spending differences produce larger probability differences.
  2. Tullock, G. (1967). "The Welfare Costs of Tariffs, Monopolies, and Theft." Western Economic Journal, 5(3), 224–232. The paper that launched the rent-seeking literature, though Tullock didn't use the term "rent-seeking" — that was coined later by Anne Krueger.
  3. With n symmetric players, the Nash equilibrium has each player spending V(n−1)/n², so total spending is V(n−1)/n. As n → ∞, total spending → V: complete rent dissipation.
  4. OpenSecrets.org. "Lobbying Data Summary." The $4.1 billion figure includes only federally reported lobbying expenditures; actual influence spending (including PR campaigns, think tank funding, and indirect lobbying) is estimated to be several times larger.
  5. Beghin, J. C. & Elobeid, A. (2015). "The Impact of the U.S. Sugar Program Redux." Applied Economic Perspectives and Policy, 37(1), 1–33.
  6. Olson, M. (1965). The Logic of Collective Action: Public Goods and the Theory of Groups. Harvard University Press. Olson's key insight: large diffuse groups face higher per-capita organizing costs and stronger free-rider problems than small concentrated groups.
  7. Bessen, J. & Meurer, M. J. (2014). "The Direct Costs from NPE Disputes." Cornell Law Review, 99, 387–424. NPE = non-practicing entity, the polite term for patent troll.
  8. Krueger, A. O. (1974). "The Political Economy of the Rent-Seeking Society." American Economic Review, 64(3), 291–303. This paper coined the term "rent-seeking" and provided the first empirical estimates of its costs.