We study a market of investments on networks, where each agent (vertex) can invest in any enterprise linked to her, and at the same time, raise capital for her firm’s enterprise from other agents she is linked to. Failing to raise sufficient capital results with the firm defaulting, being unable to invest in others. Our main objective is to examine the role of collateral contracts in handling the strategic risk that can propagate to a systemic risk throughout the network in a cascade of defaults. We take a mechanism-design approach and solve for the optimal scheme of collateral contracts that capital raisers offer their investors. These contracts aim at sustaining the efficient level of investment as a unique Nash equilibrium, while minimizing the total collateral.

We study the complexity required for the implementation of multi-agent contracts under a variety of solution concepts. A contract is a mapping from strategy profiles to outcomes. Practical implementation of a contract requires it to be ''simple'', an illusive concept that needs to be formalized. A major source of complexity is the burden involving verifying the contract fulfillment (for example in a court of law). Contracts which specify a small number of outcomes are easier to verify and are less prone to disputes. We therefore measure the complexity of a contract by the number of outcomes it specifies. Our approach is general in the sense that all strategic interaction represented by a normal form game are allowed. The class of solution concepts we consider is rather exhaustive and includes Nash equilibrium with both pure and mixed strategies, dominant strategy implementation, iterative elimination of dominated strategies and strong equilibria.