Implementing efficient allocations in bilateral networks

Agents are endowed with time that is invested in different bilateral projects. Projects generate profit depending on their time allocation. A mechanism divides the profit generated by the projects among agents. We study mechanisms that incentivize agents to contribute their time to the level that generates the maximal profit for society at the Nash equilibrium (we call this efficiency). We focus on the case of bilateral projects, that is when every project requires time allocation from only two agents. Our main result is the characterization of all the mechanisms that satisfy efficiency for any set of production functions. Furthermore, we characterize efficient mechanisms that satisfy other desirable properties such as monotonicity in the payoffs, strong Nash equilibrium of the efficient outcome, or additivity in the number of participating agents.

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