The Timing of Acquisitions

We analyse the timing of competitive bids. There are two buyers in our model, each of whom decide when and how much to bid for an object. These agents’ valuations are commonly known, but are driven by a stochastic state variable that varies randomly over time. We assume that agent 1 (2) has the higher valuation when the state is high (low). We show first that there is delay in equilibrium: agent 1 bids only when the state is sufficiently high; and agent 2 bids only when the state is sufficiently low. This delay is not necessarily present when there is a single agent; it is present with two agents because competition makes payoffs convex. Secondly, the extent of delay increases with the degree of uncertainty (i.e., both agents wait for more extreme values of the state before bidding). Thirdly, we show that there is too much delay in equilibrium, relative to the efficient solution. Finally, we show that, in our model, the seller wishes to sell immediately, and to choose the lowest degree of uncertainty about the value of the object.