Searching for Collaboration: The Dynamics of Relationship Building

Abstract

We develop a model to examine the dynamics of collaborations in the presence of self-enforcing incentives, shedding light on the gradual expansion commonly observed in such collaborations. Two players are presented with an infinite set of potential projects, each representing a collaboration opportunity with varying benefits to the players. Assessing the benefits requires exploration of the projects at least once, after which the players can choose to exploit them by investing effort in subsequent periods. Furthermore, the players decide on exploring or exploiting up to two projects per period, and they have the option to make voluntary transfers to each other. When the players are sufficiently patient, the problem boils down to the standard exploration-exploitation trade-off. With lower patience, lengthy exploration tends to occur, particularly for the first project chosen for exploitation. In some cases, the players adopt a gradual approach, initiating exploration of a second project only after identifying a suitable first project for exploitation. In an extension, we incorporate risky projects and show that the players may postpone the exploration of such projects.