Limit theorems for recursive delegation equilibria

Delegation games are studied in the context of a symmetric linear Cournotic duopoly where redelegation is permissible. In the absence of extraneous delegation costs, the following results are demonstrated: (1) Each principal has an incentive to redelegate, increasing the length of his delegation chain. (2) As the length of the delegation chain grows beyond bound, (i) total output at the (Cournot) equilibrium on the industry floor converges in monotonically increasing fashion to the socially efficient one, and (ii) the maximand delegated by each primal delegator converges in monotonically decreasing fashion to the (true) profit function. As a consequence it is suggested that in a linear duopoly context socially efficient and truthful outcomes can be arbitrarily closely approximated by the use of Pretend-but-Perform Mechanisms of order sufficiently large.