The incidence of overdissipation in rent-seeking contests
Tullock’s analysis of rent seeking and overdissipation is reconsidered. We show that, while equilibrium strategies do not permit overdissipation in expectation, for particular realizations of players’ mixed strategies the total amount spent competing for rents can exceed the value of the prize. We also show that the cross-sectional incidence of overdissipation in the perfectly discriminating contest ranges from 0.50 to 0.44 as the number of players increases from two to infinity. Thus, even though the original analysis of overdissipation is flawed, there are instances in which rent-seekers spend more than the prize is worth.
KeywordsNash Equilibrium Public Choice Mixed Strategy Symmetric Equilibrium Rent Seek
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- 1.See, for instance Posner (1975) and Fudenberg and Tirole (1987) in industrial organization, Krueger (1974) and Bhagwati (1982) in international trade, and Linster (1993) in the analysis of international alliances.Google Scholar
- 2.See surveys by Brooks and Heijdra (1989), Nitzan (1994), or Rowley (1991).Google Scholar
- 3.Tullock (1989) noted regarding the overdissipation result… “when I demonstrated that perfect calculation leads to decidedly odd results even in a competitive market with free entry, I astonished myself”. He went on to note that the original (1980) paper “was rejected by the Journal of Political Economy on the argument that it could not possibly be true that a competitive market would reach these results”. In explaining why experiments run with MBA students for n = 2 and R = 3 did not yield overdissipation on average he reasoned “it is clear that the people concerned are not making correct calculations”, and “it seems to me that… these people do not understand the game”.Google Scholar
- 4.In addition, numerous studies focus on the special case where R = 1 (see, for instance, Nitzan (1991); Paul and Wilhite (1991)). In this case, the solution to the first-order conditions do indeed yield a Nash equilibrium, but there is not overdissipation in the corresponding equilibrium.Google Scholar
- 5.Baye, Kovenock and de Vries (1994) analyze the case of n = 2 and R > 2. The method of proof is similar for n > 2 and R > n/(n-1).Google Scholar
- 6.In the case of a tie among m players for the highest bid, each has a probability (1/m) of winning the prize.Google Scholar
- 9.The working paper version of this paper (Baye, Kovenock, and de Vries, 1997) contains a more detailed response to Tullock’s (1995) comments.Google Scholar
- 10.Recent work by Che and Gale (1996) shows that the symmetric equilibrium mixed-strategies that we identify are identical to the pure strategy bidding functions that arise when rent-seekers face budget constraints and incomplete information about the size of rivals’ budgets.Google Scholar