1. For a more complete description see Tullock’s original article (1980) (the following description of the Tullock model will draw on it) or the articles in Rowley, Tollison and Tullock (1988, p. 91–126).
2. Tullock (1980, p. 105, 107), (1988a, p. 94). Baye, Kovenock and De Vries (1994) showed that the original Tullock game (which rests on simultaneous moves), does not contain a Nash equilibrium in pure strategies for r>2n/(n−1). The problem was that ‘the symmetric solution to the players’ first-order conditions for expected payoff maximization does not yield a global maximum; at this solution players have a negative expected payoff, which is dominated by bidding zero’ (Baye, Kovenock and De Vries (1999, p. 440f)). However, they provided a solution in mixed strategies, which indicates underdissipation (Baye, Kovenock and De Vries (1994)).
3. Already in 1980, Baysinger and Tollison (1980) presented a similar approach to analyse the impact of opposition under uncertainty. Under the assumption that the monopoly and the competitive outcome is equally likely, they defined the value of the expected rent as the value that corresponds to the price Pexp.= (Pm+Pc)/2, rather than using 50% of the rent at P=Pm (see also Brooks and Heijdra (1989, p. 36f)). If expected producer and consumer rents are then added together, their specification leads to an area larger than the original Tullock and Harberger triangle at P=Pm, an outcome, which for instance Ellingsen (1991, p. 655) criticises as being impossible.
4. Of course, to be powerful threat has to be credible. For a discussion on this aspect, see McChesney (1997, p. 38f).
5. For a collection of articles which address free entry or large number of rent-seekers in the Tullock-type model, see Rowley, Tollison and Tullock (1988), Chapters 8–11.