This paper presents a model of dynamic competition between two firms that repeatedly engage in an innovative activity. The state of competition—measured by the difference between the number of innovations introduced by the firms—evolves stochastically according to their effort level. The structure of Markov perfect equilibria is identified. It is generally not true that competition is fiercest when firms are closest. Rather, firms invest under two distinct circumstances: while sufficiently ahead, to outstrip their rival and secure a durable leadership; while behind, to regain leadership and prevent the situation from worsening to the point where their rival outstrips them.

This paper presents a model of dynamic competition between two firms that repeatedly engage in an innovative activity. The state of competition—measured by the difference between the number of innovations introduced by the firms—evolves stochastically according to their effort level. The structure of Markov perfect equilibria is identified. It is generally not true that competition is fiercest when firms are closest. Rather, firms invest under two distinct circumstances: while sufficiently ahead, to outstrip their rival and secure a durable leadership; while behind, to regain leadership and prevent the situation from worsening to the point where their rival outstrips them.

This paper analyses a dynamic auction in which a fraction of each bid is sunk. Jump bidding is used by bidders to signal their private information. Bluffing (respectively sandbagging) occurs when a weak (respectively strong) player seeks to deceive his opponent into thinking that he is strong (respectively weak). A player with a moderate valuation bluffs by making a high bid and drops out if his bluff is called. A player with a high valuation should vary his bids and should sometimes sandbag by bidding low, to induce lower bids by his rival.

We consider a dynamic buyer–seller interaction. Instead of the buyer's valuation, it is the frequency with which he needs to trade that is the buyer's private information. The difference matters. With commitment, full surplus extraction is possible, for instance via limited‐time offers. Without commitment, ratcheting is mitigated, as not buying is not necessarily a sign of strength. Because time is informative, the seller learns and may adjust her behavior over time. When finding a suitable alternative seller is easy, she starts with a pooling offer before permanently switching to a screening offer. When finding a suitable alternative seller takes time, she starts with a pooling offer before occasionally experimenting with separating offers.

We study the role of observability in bargaining with correlated values. Short-run buyers sequentially submit offers to one seller. When previous offers are observable, bargaining is likely to end up in an impasse. In contrast, when offers are hidden, agreement is always reached, although with delay.

Performance evaluation (“rating”) systems not only provide information to users but also motivate the rated worker. This article solves for the optimal (effort-maximizing) rating within the standard career concerns framework. We prove that this rating is a linear function of past observations. The rating, however, is not a Markov process, but rather the sum of two Markov processes. We show how it combines information of different types and vintages. An increase in effort may adversely affect some (but not all) future ratings.

This paper examines moral hazard in teams over time. Agents are collectively engaged in a project whose duration and outcome are uncertain, and their individual efforts are unobserved. Free-riding leads not only to a reduction in effort, but also to procrastination. Collaboration among agents dwindles over time, but does not cease as long as the project has not succeeded. In addition, the delay until the project succeeds, if it ever does, increases with the number of agents. We show why deadlines, but not necessarily better monitoring, help to mitigate moral hazard.

A firm considers hiring an agent who may be competent for a potential project or not. The agent can prove her competence but faces a holdup problem. We propose a model of persuasion and show how gradualism helps mitigate the holdup problem. We show when it is optimal to give away part of the information at the beginning of the bargaining and sell the remainder in dribs and drabs. The agent can appropriate only part of the value of information. Introducing a third party allows her to extract the maximum surplus.

This article considers a class of experimentation games with Lévy bandits encompassing those of Bolton and Harris (1999, Econometrica, 67, 349–374) and Keller, Rady, and Cripps (2005, Econometrica, 73, 39–68). Its main result is that efficient (perfect Bayesian) equilibria exist whenever players’ payoffs have a diffusion component. Hence, the trade-offs emphasized in the literature do not rely on the intrinsic nature of bandit models but on the commonly adopted solution concept (Markov perfect equilibrium). This is not an artefact of continuous time: we prove that efficient equilibria arise as limits of equilibria in the discrete-time game. Furthermore, it suffices to relax the solution concept to strongly symmetric equilibrium.