BROCADE: Broker-based Contract Design for the Multi-Agency Model
Yangguang Shi, Ron Lavi, Jie Zhang
We study welfare maximization in a contract model with $m$ principals who privately value a public project's success and $n$ agents whose costly effort is unobservable. Contracts induce truthful dominant strategies for principals and equilibrium effort by agents, maximizing the expected total value of eligible principals. We develop three tools: a broker that separates payments from principals and payments to agents, an extension of Myerson's Lemma characterizing dominant-strategy incentive compatibility (DSIC), and a black-box reduction to budget-constrained single-principal contract design. When the success probability is a strictly monotone XOS function of agents' actions, these tools yield three results. First, a deterministic DSIC contract achieves a constant approximation against a benchmark that qualifies every principal and maximizes success probability using budget $\sum_j v^j$, but may violate budget balance (BB). Second, against benchmarks with budgets at least the largest principal value, deterministic DSIC and BB contracts admit no finite approximation guarantee, even with two agents. Universally DSIC and universally BB randomized contracts have an $Ω(n)$ approximation lower bound, even for a fixed number of principals. Third, using one quarter of the optimal fixed-price revenue supported by at least two principals as the benchmark budget, we obtain a universally DSIC and universally BB randomized contract with an $O(\log m)$ approximation ratio independent of $n$.
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