Effort and Performance in Public-Policy Contests

to one player as the Low-Benefit (LB) player and to the other player as the High-
Benefit (HB) player³. The interest groups engage in a contest that determines the
probabilities of approval and rejection of the proposed policy.⁴

Player i’s preferred policy is approved in probability Pr_i . The present
discounted value of this policy to this player is equal to ui and its value to his
opponent player j is equal to vj. By assumption then, for each player, approval of his
preferred policy is associated with a positive payoff, that is, ui > vi . Note that, in
general, the four values uL, vL, uH and vH, viz., the players’ payoffs corresponding to
the approval and rejection of the policy I proposed by the government (a ruling
politician or a bureaucrat) depend on I.

Let xi denote the effort of the risk-neutral player i. The expected net payoff of
i is given by:

(1)                     E(w_i)=Pr_iu_i(I)+ Pr_jv_j(I)- x_i , i≠ j

Given the contestants’ efforts, the probabilities of approval and rejection of the

proposed policy, PrL and PrH , are obtained by the contest success function. As in

< 0 ⁵ (the latter inequality ensures that the second order conditions are
satisfied). Since Pr_i(x_i, x_j )+Pr_j (x_j , x_i ) = 1 , i≠ j , it holds that

∂²Pr_i(x_i, x_j)        ∂²Pr_j(x_j, x_i)

∂ x_i ∂ x_j              ∂ x_i ∂ x_j

³ See Epstein and Nitzan (2001a).

⁴ Modeling the contestants as single agents presumes that they have already solved the collective action
problem. The model thus applies to already formed interest groups.

⁵ The function Pri( x_i , x ) is usually referred to as a contest success function (CSF). The functional
ij

forms of the CSF’s commonly assumed in the literature, see Nitzan (1994) and Skaperdas (1996),
satisfy these assumptions.

<<   3   4   5   6   7   8   9   >>

More intriguing information