Public Choice 46:259-263 (1985). © 1985 Martinus Ni jho f f Publishers, Dordrecht. Printed in the Netherlands.

Efficient rents 3

Back to the bog

GORDON TULLOCK Center for Study of Public Choice, George Mason University, Fairfax, VA 22030

My role in connection with the efficient rent-seeking model (Tullock 1980) is, I think, a rather ill-omened one. I began the discussion by inventing a model with an apparent paradox. The market doesn't clear even with free entry and competition. There have been a number of efforts to deal with this problem (Corcoran, 1984; I commented on it in the same issue, pp. 95-98). (1985) Corcoran and Karels and Higgins, Shughart, and Tollison (1985) are further efforts to solve the problem.

It is my unfortunate role, having discovered this particular intellectual swamp, to frustrate efforts to get out by pushing people back in. I first in- vent a difficult problem and then when people try to solve it, I say that their solutions are either wrong or at least incomplete. I should therefore say, that I do think that the work of Corcoran, Karels, Tollison, Shughart, and Hig- gins, has indeed made progress toward a solution even if they have not final- ly solved the problem.

Corcoran and Karels come close to solving the original problem provided we keep the framework of efficient rent-seeking rigid and unchanging. The problem is that there is one assumption in that initial framework which I now realize was unduly restrictive.

It is a usual practice among economists, when we observe a number of people engaging in the same kind of competitive activity to assume that they all behave the same. The reason for this is partly that they face the same pro- blem and we would assume they reach the same conclusion, but I think even more importantly, that an assumption that they do not behave in the same manner means that you have to explain why some of them carry out one policy and some another. 1 In the particular case of efficient rent-seeking, it is in general, more profitable to violate this rule. You will make more money if you do not make the same bid as your collegues.

Before going further, I should frankly confess that I have no solution to this problem. It appears once again to be a case of the paradox of the liar. If one deviates from the pattern, he makes a profit, if all follow his example, they lose. The sensible behavior for an individual is not sensible unless the other people are doing something else. If this gives the reader a headache, I can only recommend Tylenol.

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Let me take an obvious example from Corcoran and Karels (1985:234 f.) Table 3. Suppose that we are in the area of increasing marginal efficiency, specifically the exponent or r value is 1.5. If seven people are playing, he puts the minimum preclusive bid at $14.29. 2 Suppose that one of the players instead of putting in $14.29 puts in $14.39, while the other six stick to the $14.29. As a result, he acquires an expectancy equivalent to $14.41. The $.10 additional investment has paid off with $. 12. Each other player loses $.02.

The reason that this would occur is I suppose fairly obvious whenever r is greater than 1. This is the area of increasing marginal returns and hence the return on additional marginal units will always be greater. Many equilibria in which all of the people are assumed to make the same invest- ment will be subject to this problem. Indeed, in many cases, a complete out- sider entering and making a large bid can gain. For example, consider eight people playing with r 1.3 and each putting in $12.50. This is of course spend- ing $12.50 to buy an expectancy of $12.50. Suppose that a ninth party ar- rives and puts in $25.00. His expectancy is $26.14. The expectancy of the original eight has of course gone down sharply.

I realize the problems that this will generate. Once again, we seem to be in a situation in which there is no rational way of playing the game. If nine players each put in $25.00, the result is disasterous.

One way of dealing with this problem of course, is for individuals to at- tempt to put in individually preclusive bets before anyone else enters. The outcome of such preclusive bets is shown in the left column of Table 5, of Corcoran and Karels (p. 239). The problems here are first, the one that I mentioned in my original article (1980) which is that it leads to a previous game to be first. There is however, a second problem here which is that if we look at real-life rent-seeking activity, it is a little hard to see what the equivalent of making that single large initial investment is. A lobbyist can hardly simultaneously provide a Congressman with twenty two dinners and five blondes. In corrupt societies where cash is used, this problem of course, is less severe.

When we have an exponent less than 1, i.e., when they're declining returns to scale, Corcoran and Karels essentially depend on the fact that there will, in practice, be a least feasible bid. I have no quarrel with this, but I should point out that there is here a problem analogous to the problem we have discussed above which makes calculation at least difficult. Look at their Table 1 (p. 230), and consider the first line. Suppose that one of the two people who are placing a bet instead of placing a bet of $12.50, places one of $12.00. He of course does not have an even chance of winning, so his expected return is not $50.00, but $49.49. His expected profit is $37.49, instead of $37.50. But his percent return on capital is better. If he had put in $12.50, he would have received a profit three times his initial capital. If he puts in $12.00, he receives a profit 3.12 times his original capital. Of

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course the other player, the one who still put in his $12.50, does better than he would had the first player also put in $12.50. Specifically, he makes an additional expected $.51. This is however, only a return of 3.04 times his capital. The explanation, of course, is that here we are in an area of declin- ing marginal returns.

Naturally I am not claiming that I have solved the problem. What I have done is make it more difficult. Let us now turn to Higgins, Shughart, and Tollison. The first thing to be said, is that all of the problems mentioned above apply here also. When playing one of their stochastic strategies, it will normally not be rational to play the same amount as the others are doing. 3 It is also subject to the problem that a single large preclusive bet normally dominates their stochastic procedure. But once again, the high profitability of such a preclusive bet means that there would be a previous game to obtain such preclusion.

The basic point of the Higgins, Shughart, and Tollison paper is to arrange through stochastic methods that all o f the players receive a normal return on their capital (as most economic work, this is shown as zero profit) by stochastic means. There are occasional situations in which the number of players for the zero profit condition is an integer. More commonly however, it is not and their stochastic model is designed to deal with this much more numerous category. Unfortunately, there is here a defect. The mathematical expression that they use has the ingenious characteristic that the same (zero as usual) profit is made by playing everytime, by playing their stochastic procedure, or by transferring ones capital to some other normally profitable activity. If however, one of their players, instead of playing stochastically, chooses to play every time, he will achieve a normal return on his strategy, the other players will suffer losses.

The reason is clear, although a little involved. When I put my bid in, whether I do it because Higgins, Shughart and Tollison's stochastic process tells me I should at this time, or for some other reason, that stochastic pro- cess followed by the other players gives me an expectancy of exactly normal profits. If I play continuously, I will get normal profits. But since I am not playing the stochastic model, I am entering more often than I should and am inflicting a negative cost on others. Everytime that I play when by the stochastic model I shouldn't , I lower the profits of the other players.

In general, in this kind of efficient rent-seeking model, an individual player imposes external costs on others. The Higgins, Shughart and Tollison model guarantees that these external costs are evenly distributed and bal- anced by profits. A single player who deviates by playing more often injures the other players.

Now it should be pointed out that there's no strong motive for a player to do this. It is true he will be able to invest more capital in an activity which gives a normal return, and he might drive some of the other players out in

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which event he would begin making positive profits. The latter possibility of course brings us into the extremely complex area of preditary competition and I don' t want to go through that very lengthy argument. I do presume my readers are already familiar with it. Suffice it to say that it does not seem as if this would be a long-run way of obtaining profits.

The other problem here is not that once the Higgins, Shughart and Tollison equalibrium stochastic process has reached equilibrium someone may deviate, but that is is very hard to see how you would get there to begin with. Clearly they are not talking about a carefully calculated conspiracy among all the players, because if there is such a conspiracy, there are far more profitable strategies to play. Their equilibrium would have to be ob- tained by players who simply find out over time that this is the appropriate strategy. Unfortunately, there seems no path by which they can do so.

As an example illustrating the problem, suppose that we have a situation in which seven players, if they all made the same and optimal bid regularly, would make a positive profit, whereas eight players, if they all made the same and equal bid would lose. We start with eight players. All of them are losing, but one of them who has read Higgins, Shughart, and Tollison calculates the efficient stochastic strategy and begins following it.

There will now be two different kinds of games. Firstly, those games in which this player, after consulting his table of random numbers, plays. In those games there will be eight players and all of them will lose. The second set are the ones in which he does not play, there are seven players, and all of them gain or at least lose less. By his behavior, he has benefitted the others for at least some of the games while in all the games in which he plays, he loses as much as before. If a second player began following the same policy once again, the players who were not playing stochastically, would do better than those who were.

Note, there's nothing in this which indicates that anybody will actually make a positive profit. It is just that the non-stochastic players will more often have a profit in a particular play than the stochastic players and these profits will on the average, be larger. Thus there is no way for the players by simple experimenting with different stochastic procedures to reach the Higgins, Shughart, and Tollison equilibrium.

As I said before, my role in this controversy is to watch people trying to get out of the swamp and then push them back in. Clearly, my role is not a constructive one, but nevertheless, I feel it is necessary. On the other hand, it seems to me that if the work of Corcoran, Carroll, Higgins, Shughart, and Tollison has not gotten us out of the swamp, it has at least moved us to a place where the mud is less deep. I don ' t know much more about the geography of the swamp but the prospect that we can find a bit of dry land somewhere has improved.

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NOTES

1. The so called Hawk-Dove literature, helps to provide an explanation for this kind of behavior under some circumstances. Unfortunately, it is not applicable to the subject of this comment.

2. This involves rounding. There are seven players and 7x 14.29 is of course slightly more than $100 but the matter is unimportant for the example.

3. I recently saw a propaganda movie about the Chinese communes. It was made severai years ago, and would not be permitted in present day China, but I saw it in Philadelphia. In one sequence each of the Commune children was encouraged to work faster than the oth-rs.

REFERENCES

Corcoran, W.J. (1984). Long-run equilibrium and total expenditures in rent-seeking. Public Choice 43 (1): 1984, 89-94.

Corcoran, W.J., and Karels, G.V. (1985). Rent-seeking behavior in the long-run. Public Choice 227-246.

Higgins, R.S., Shughart II, W.F., and Tollison, R.D. (1985). Fore entry and efficient rent- seeking. Public Choice 247-258.

Tullock, G. (1980). Efficient rent-seeking. In J.M. Buchanan, P.D. Tollison and G. TuUock (Eds.), Toward a theory o f the rent-seeking society, 97-112. College Station, Tx: Texas A&M University Press.