Measured Games · Paper 20 of 07 · Experimental economics

Rent seeking

After G. Tullock (1980); laboratory record surveyed by E. Dechenaux, D. Kovenock and R. M. Sheremeta (2015)

Abstract

Competitors spend to raise their probability of winning a prize rather than to win it outright, which makes effort an investment in odds. Equilibrium spending rises with the number of competitors and approaches the whole value of the prize, so the resources devoted to capturing it approach the resources at stake. In the laboratory people reliably spend more than that, dissipating more than the prize is worth, and the overspending is one of the most replicated findings in experimental economics.

Keywordscontest success function · rent dissipation · over-expenditure · probabilistic contest

1Setup

Setup

A prize is going to be awarded and several parties can spend to improve their chances of getting it. Lobbying for a licence, competing for a promotion, litigating over a patent. Spending does not buy the prize. It buys a share of the probability of the prize, and it is spent whether or not the spender wins.

The question the model asks is not who wins. It is how much of the prize's value gets consumed by the competition to obtain it, because that spending produces nothing. Every hour and pound devoted to capturing an existing prize is an hour and pound not devoted to making anything.

2The model

The model

# N players spend xᵢ on a prize worth V # the contest success function turns spending into odds P(i wins) = xi / Σ xj payoffi = V · xi / Σ xj - xi # symmetric Nash equilibrium x* = V (N-1) / N2 # total spent, the rent dissipated total = V (N-1) / N N = 2 → half the prize N = 10 → 90 per cent N → ∞ → all of it

Unlike an all-pay auction decided by the highest bid, spending here buys probability, so a competitor who is outspent still has a chance and still has an incentive to be in the contest at all. That is what keeps everyone in and drives the total towards the whole value of the prize as the field grows.

Figure 1A Tullock contest against equilibrium opponents

This figure needs JavaScript. The panels below are live simulations rather than images, so with scripting turned off they stay empty and the controls do nothing. Everything the figure demonstrates is also stated in the surrounding text: the model is given in full in section 2 and the result in section 3.

Your payoff against your spending, with the others at equilibrium

Rent dissipated against the number of competitors · hover to read any field size

Spending in the current contest

Your payoff Equilibrium With observed overbidding Whole prize

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Competitors N

Prize value V

Your spending

Overbidding by others

Equilibrium spend—

Predicted dissipation—

Actual dissipation—

Your expected payoff—

Your win rate—

Contests0

Figure 1. The payoff curve is computed against opponents spending the equilibrium amount, scaled by the overbidding slider, so your best response is genuinely a best response to what they are doing. Two things to try: raise the number of competitors and watch dissipation climb towards the whole prize, and push overbidding past about 1.3, which is the range laboratory subjects reliably occupy. Past that point the field collectively spends more than the prize is worth and the average competitor loses money.

3Results

Results

Tullock (1980) introduced the contest success function that makes spending buy odds rather than certainty, and the symmetric equilibrium follows directly. The comparative static is the point: dissipation rises with the number of competitors and tends to the entire value of the prize. A contest with many entrants consumes what it is fought over.

That result reframes what a prize is. If a licence, a monopoly or a subsidy is worth a certain amount, and obtaining it is open to competition, then the amount is not a transfer from one party to another. It is approximately burned. The policy implication is that creating something worth competing for is not neutral even when the award itself is.

The equilibrium also explains why competitors stay in when they are outspent. Because spending buys probability rather than the prize, being behind does not mean being out, which is exactly what sustains the total.

4Evidence

Evidence

The laboratory record is where this model earns its place, and the finding is not the one the theory predicts. Across a large experimental literature, subjects spend substantially more than the Nash equilibrium. The over-expenditure is robust: it appears across designs, prize values, group sizes and subject pools, and it frequently pushes total spending above the value of the prize, so participants lose money in aggregate.

Dechenaux, Kovenock and Sheremeta (2015) survey the experimental work on contests, tournaments and contest games and report over-expenditure as one of the field's most consistent regularities, alongside high variance in individual behaviour and a tendency for spending to fall somewhat with experience without reaching equilibrium.

Explanations offered include a utility of winning that is separate from the prize, misperception of the probability that spending buys, relative-payoff concerns, and simple noise in a setting where the payoff function is flat near the optimum. None commands agreement, which is itself worth stating.

5Limitations

Limitations

The dissipation result depends on the form of the contest success function. Tullock's proportional rule is one choice among many, and changing the returns-to-spending parameter changes the equilibrium sharply, up to the point where the contest becomes an all-pay auction with no pure equilibrium at all. Applied work that reports a dissipation figure is reporting a consequence of that modelling choice as much as a fact about the world.

Full dissipation also assumes free entry, symmetric competitors and risk neutrality. Real contests have incumbency advantages, differing costs of effort, and participants who are not indifferent to variance, all of which reduce the total.

The evidence base is laboratory rather than field. Estimating rent dissipation in an actual lobbying or litigation setting requires observing spending that is often deliberately unobservable, which is why the empirical claim in this paper is about experimental subjects and not about legislatures.

References

Dechenaux, E., Kovenock, D., & Sheremeta, R. M. (2015). A survey of experimental research on contests, all-pay auctions and tournaments. Experimental Economics, 18(4), 609–669. https://doi.org/10.1007/s10683-014-9421-0
Krueger, A. O. (1974). The political economy of the rent-seeking society. The American Economic Review, 64(3), 291–303.
Millner, E. L., & Pratt, M. D. (1989). An experimental investigation of efficient rent-seeking. Public Choice, 62(2), 139–151. https://doi.org/10.1007/BF00124330
Sheremeta, R. M. (2013). Overbidding and heterogeneous behavior in contest experiments. Journal of Economic Surveys, 27(3), 491–514. https://doi.org/10.1111/joes.12022
Tullock, G. (1967). The welfare costs of tariffs, monopolies, and theft. Western Economic Journal, 5(3), 224–232. https://doi.org/10.1111/j.1465-7295.1967.tb01923.x
Tullock, G. (1980). Efficient rent seeking. In J. M. Buchanan, R. D. Tollison, & G. Tullock (Eds.), Toward a theory of the rent-seeking society (pp. 97–112). Texas A&M University Press.

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