We consider contracts with common agencies stemming from the VCG-mechanism. These contracts have strategic common agents that take actions on behalf of multiple principals, while aiming to maximizes their personal profits. In these contracts the agent takes the role of the Mechanism Designer (MD) in the VCG-mechanism, but also acts strategically to maximize his private utility.
Most contracts in practice and the literature are based on classic contracts, where the principals announce prices for possible outcomes, and pay their announced price for the realized outcome. However, classic contracts may lead to extremely inefficient outcomes.
Our first paper Principal Agent VCG Contracts (Lavi and Shamash 2022) introduces a novel contract with complete information termed a VCG-contract. The structure of the VCG-contract induces M principals to announce their true values for agent actions, and N agents to choose actions similar to those acquired in a VCG-auction, where in the case of a single agent maximize social welfare.
We characterize the set of instances inducing pure sub-game perfect equilibria (SPE) and show that the worst case efficiency result in VCG-contracts is not worse than that of classic contracts, when agents have over two actions.
Our second paper Incomplete Information VCG Contracts for Common Agency (Alon et al 2021) generalizes a single agent case of Lavi and Shamash 2022 by analyzing the incomplete information setting – where each of the agent’s actions leads to a distribution over outcomes, and principals only perceive the resulting stochastic outcome of the chosen action.
We characterize the unique class of incomplete information VCG-contracts (IIVCG) that induce principals to announce their true outcome values, and the agent to choose the actions that maximizes expected social welfare.
In addition, we show that no IIVCG contract exists, that guarantees both individual rationality (IR) and limited liability (LL).
Furthermore, we develop a computationally efficient algorithm determining whether, given a specific setting, a contract belonging to IIVCG satisfying both LL and IR exists, and if so generates such a contract.