This paper considers dynamic games in which multiple principals contract sequentially and non-cooperatively with the same agent. We first show that when contracting is private, i.e. when downstream principals do not observe the mechanisms offered upstream and the decisions taken in these mechanisms, all PBE outcomes can be characterized through pure-strategy profiles in which the principals offer menus of contracts and delegate to the agent the choice of the contractual terms. We then show that, in most cases of interest for applications, the characterization of the equilibrium outcomes is further facilitated by the fact that the principals can be restricted to offer incentive-compatible extended direct mechanisms in which the agent reports the endogenous payoff-relevant decisions contracted upstream in addition to his exogenous private information. Finally we show how the aforementioned results must be adjusted to accommodate alternative assumptions about the observability of upstream histories and/or the timing of contracting examined in the literature.
