Recent discussion of rent-seeking games (see Tullock, 1980 and 1985; Corcoran and Karels, 1985; Higgins, Hughart and Tollison, 1985; Appelbaum and Katz, 1986) has largely involved identical players and been mainly concerned with the extent of under or over dissipation of rents, although Tullock has commented at some length on the ‘intellectual mire’ arising from possible non-existence of a Cournot-Nash equilibrium when there are increasing returns to rent-seeking expenditures. There has been very little comment on the more prevalent problem of multiple equilibria, though the credibility of any equilibrium depends on all the players recognising it as unique. Furthermore, given the rarity with which players are in practise observed to be identical, it is surprising that there has been no follow up to Tullock’s (1980) discussion of the effect of differential advantages (which he referred to as bias), even though the very notion of an n player game implies an ordering if there are more than n potential competitors, which in turn implies some differences amongst players.
KeywordsUnique Equilibrium Lottery Ticket Person Game Negative Profit Current Competition
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- 1.A note setting out the mathematical derivations of equations 2.4 to 2.7 is available from the author.Google Scholar
- 2.The model proposed by Higgins, Shughart and Tollison (1985) will generally lead to the same range of possible curves ( Al, A2 and B), so that in qualitative terms their analysis is relevant to the model used here.Google Scholar
- 3.The negative profits in Tullock ( 1980: Table 6.1) correspond to cases where players find themselves without the option of setting x = 0, although as Tullock himself points out (1984) some of the entries also correspond to joint minima rather than joint maxima and should therefore be omitted. The negative profits which underlie some of the ‘underestimates of rent-seeking’ in Table 1 of Appelbaum and Katz (1986) arise partly from the fact that all groups in society are explicitly forced to contribute to the value of the rent, and partly from the (implicit) assumption that they must all subsequently participate in the competition.Google Scholar
- 4.This point is elucidated above in Section 3, and is also evident from Table 3 of Corcoran and Karels (1985).Google Scholar
- 5.Corcoran and Karels (1985) also raise the possibility of several players combining to pre-empt further entry — thus n-players collude and jointly decide the output of lottery tickets required to deter entry by the (n + 1)th player (C-K operate in terms of expenditures rather than lottery tickets — see their Table 3). When there are increasing returns (r > 1), the most efficient way of achieving this pre-emption is that the incumbents should assign (presumably on the basis of a preliminary lottery) the whole output to a single one of their members, rather than assigning output equally amongst themselves.Google Scholar