The specification of the probability functions in Tullockʹs rent-seeking contest

In his model of a rent-seeking contest, [Tullock, G., 1980, Efficient rent seeking. In: Buchanan, J.M., Tollison, R.D., Tullock, G. (Eds.). Toward a theory of the rent-seeking society. Texas A and M University Press, College Station, pp. 97–112] uses a simple concrete specification for the probability functions which determine the probability that a player wins the contest, given the bids made by the players. We discuss in general terms a set of conditions that can be imposed on probability functions in this game. Next, we show that the specification chosen by Tullock is the unique one that satisfies these conditions.