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Economics

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Yale University

2019

Stopping Problem

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Progressive Participation, Dirk Bergemann, Philipp Strack Aug 2019

Progressive Participation, Dirk Bergemann, Philipp Strack

Cowles Foundation Discussion Papers

A single seller faces a sequence of buyers with unit demand. The buyers are forwardlooking and long-lived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We derive the optimal stationary mechanism in closed form and characterize its qualitative structure. As the arrival time is private information, the buyer can choose the time at which he reports his arrival. The truth-telling constraint regarding the arrival …


Progressive Participation, Dirk Bergemann, Philipp Strack Aug 2019

Progressive Participation, Dirk Bergemann, Philipp Strack

Cowles Foundation Discussion Papers

A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We derive the optimal stationary mechanism, characterize its qualitative structure, and derive a closed-form solution. As the arrival time is private information, the buyer can choose the time at which he reports his arrival. The truth-telling constraint regarding the …


Progressive Participation, Dirk Bergemann, Philipp Strack Aug 2019

Progressive Participation, Dirk Bergemann, Philipp Strack

Cowles Foundation Discussion Papers

A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive-compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We derive the optimal stationary mechanism, characterize its qualitative structure and derive a closed-form solution. As the arrival time is private information, the agent can choose the time at which he reports his arrival. The truth-telling constraint regarding the arrival …


Progressive Participation, Dirk Bergemann, Philipp Strack Aug 2019

Progressive Participation, Dirk Bergemann, Philipp Strack

Cowles Foundation Discussion Papers

A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived. The arrival time and the valuation is private information of each buyer. Any incentive compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We derive the optimal stationary mechanism in closed form and characterize its qualitative structure. As the arrival time is private information, the buyer can choose the time at which he reports his arrival. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem. The stopping time determines the …


Progressive Participation, Dirk Bergemann, Philipp Strack Aug 2019

Progressive Participation, Dirk Bergemann, Philipp Strack

Cowles Foundation Discussion Papers

A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived. Each buyer has private information about his arrival time and valuation where the latter evolves according to a geometric Brownian motion. Any incentive-compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We establish that the optimal stationary allocation policy can be implemented by a simple posted price. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem which determines the first time at which the buyer participates in the mechanism. The …