This paper examines a declining duopoly, where the firms must choose when to exit from the market. The uncertainty is modeled by letting the revenue stream follow a geometric Brownian motion. We consider the Markovperfect equilibrium in firms' exit strategies. With a low degree of uncertainty there is a unique equilibrium, where one of the firms always exits before the other. However, when uncertainty is increased, another equilibrium with the reversed order of exit may appear ruining the uniqueness. Whether this happens or not depends on the degree of asymmetry in the firm specific parameters.

We analyze information aggregation in a stopping game with uncertain payo¤s that are correlated across players. Players learn from their own private experiences as well as by observing the actions of other players. We give a full characterization of the symmetric mixed strategy equilibrium, and show that information aggregates in randomly occurring exit waves. Observational learning induces the players to stay in the game longer. The equilibria display aggregate randomness even for large numbers of players.

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We analyze the optimal investment strategy of a firm that can complete a project either in one stage at a single freely chosen time point or in incremental steps at distinct time points. The presence of economies of scale gives rise to the following trade-off: lumpy investment has a lower total cost, but stepwise investment gives more flexibility by letting the firm choose the timing individually for each stage.Our main question is how uncertainty in market development affects this tradeoff. The answer is unambiguous and in contrast with a conventional real-options intuition: higher uncertainty makes the single-stage investment more attractive relative to the more flexible stepwise investment strategy.

This paper analyzes all-pay auctions where the bidders have affiliated values for the object for sale and where the signals take binary values. Since signals are correlated, high signals indicate a high degree of competition in the auction and since even losing bidders must pay their bid, non-monotonic equilibria arise.We show that the game has a unique symmetric equilibrium, and that whenever the equilibrium is non-monotonic the contestants earn no rents. All-pay auctions result in low expected rents to the bidders, but also induce inefficient allocations in models with affiliated private values. With two bidders, the effect on rent extraction dominates, and all-pay auction outperforms standard auctions in terms of expected revenue. With many bidders, this revenue ranking is reversed for some parameter values and the inefficient allocations persist even in large auctions.JEL CLASSIFICATION: D44, D82