Strategic delegation in a sequential model with multiple stages

TL;DR

This paper examines strategic delegation in a multi-stage Stackelberg model, revealing how firms' delegation decisions and incentives vary with their order of move and comparing outcomes with Cournot competition.

Contribution

It introduces a model with multiple stages showing that later movers delegate to managers and that incentive rates increase with move order, extending prior two-stage analyses.

Findings

Later movers delegate production decisions to managers.

Equilibrium incentive rates increase with move order.

Late movers set higher incentive rates than Cournot firms.

Abstract

We analyze strategic delegation in a Stackelberg model with an arbitrary number, n, of firms. We show that the n-1 last movers delegate their production decisions to managers whereas the first mover does not. Equilibrium incentive rates are increasing in the order with which managers select quantities. Letting u_i^* denote the equilibrium payoff of the firm whose manager moves in the i-th place, we show that u_n^*>u_{n-1}^*>...>u_2^*>u_1^*. We also compare the delegation outcome of our game with that of a Cournot oligopoly and show that the late (early) moving firms choose higher (lower) incentive rates than the Cournot firms.