Sunk Costs and Strategic Commitment: A Proposed Three-Stage Equilibrium

Abstract

Dixit's I980 paper in this JOURNAL, 'The Role of Investment in Entry Deterrence', has attracted considerable interest from economists concerned with constructing a modern theory of strategic behaviour towards entry. In fact the paper has spawned quite an industry of 'commitment models', in which the equilibrium payoffs in some final period game can be influenced by strategic commitments made by the players in an earlier period. (For similar models, with important insights into strategic entry deterrence, see Eaton and Lipsey (I980; I98I), Schmalensee (I98I).) The purpose of this note is to argue that when the instrument of stragetic commitment takes the form of sunk costs, which both entrant and incumbent have to bear, as it does in Dixit's paper and in many other examples, a three-stage model rather than the two-stage model presented by Dixit is required. Although the proposed equilibrium differs from Dixit's, its qualitative features are the same. It may or may not be profitable to deter entry; and if it is, the first mover may still prefer to play an accommodation strategy and allow entry to take place. Following Dixit, we restrict our attention to the asymmetric case, in which one firm, the incumbent, makes the first move.' The two-stage game involves the first mover sinking part of its costs in advance, so that in the second-stage equilibrium it will have a current cost advantage over the entrant, which must incur the full cost of producing any desired output level. The second-period cost asymmetry ensures the incumbent a lar-ger share of the post-entry market, which may be sufficient to deter entry altogether. The problem with the two-stage game lies in the nature of sunk costs. Sunk costs, by definition, are committed before the production period takes place. If they were expended as a flow simultaneously with production, they would not be sunk. The installation of capacity is the natural example employed by Dixit and well illustrates the point. If installed capacity is a sunk cost, which it must be for the incumbent to acquire any strategic advantage at all, then the entrant's installed capacity is equally sunk, and must also be committed before the production period takes place. Given this observation, the (post-entry) final-period equilibrium should not be modelled as if the entrant were simultaneously incurring both variable and sunk costs, but the incumbent only incurs variable costs. This implies too great an asymmetry in favour of the incumbent. The final-period equilibrium should involve both firms incurring only variable