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on Contract Theory and Applications |
| By: | Tal Alon; Paul D\"utting; Yingkai Li; Inbal Talgam-Cohen |
| Abstract: | We study a generalization of both the classic single-dimensional mechanism design problem, and the hidden-action principal-agent problem of contract theory. In this setting, the principal seeks to incentivize an agent with a private Bayesian type to take a costly action. The goal is to design an incentive compatible menu of contracts which maximizes the expected revenue. Our main result concerns linear contracts, the most commonly-used contract form in practice. We establish that in Bayesian settings, under natural small-tail conditions, linear contracts provide an $O(1)$-approximation to the optimal, possibly randomized menu of contracts. This constant approximation result can also be established via a smoothed-analysis style argument. We thus obtain a strong worst-case approximation justification of linear contracts. These positive findings stand out against two sets of results, which highlight the challenges of obtaining (near-)optimal contracts with private types. First, we show that the combination of private type and hidden action makes the incentive compatibility constraints less tractable: the agent's utility has to be convex (as without hidden action), but it also has to satisfy additional curvature constraints. Second, we show that the optimal menu of contracts can be complex and/or exhibit undesirable properties - such as non-monotonicity of the revenue in the type distribution. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.06850&r=cta |
| By: | Banghua Zhu; Stephen Bates; Zhuoran Yang; Yixin Wang; Jiantao Jiao; Michael I. Jordan |
| Abstract: | We study the hidden-action principal-agent problem in an online setting. In each round, the principal posts a contract that specifies the payment to the agent based on each outcome. The agent then makes a strategic choice of action that maximizes her own utility, but the action is not directly observable by the principal. The principal observes the outcome and receives utility from the agent's choice of action. Based on past observations, the principal dynamically adjusts the contracts with the goal of maximizing her utility. We introduce an online learning algorithm and provide an upper bound on its Stackelberg regret. We show that when the contract space is $[0,1]^m$, the Stackelberg regret is upper bounded by $\widetilde O(\sqrt{m} \cdot T^{1-C/m})$, and lower bounded by $\Omega(T^{1-1/(m+2)})$. This result shows that exponential-in-$m$ samples are both sufficient and necessary to learn a near-optimal contract, resolving an open problem on the hardness of online contract design. When contracts are restricted to some subset $\mathcal{F} \subset [0,1]^m$, we define an intrinsic dimension of $\mathcal{F}$ that depends on the covering number of the spherical code in the space and bound the regret in terms of this intrinsic dimension. When $\mathcal{F}$ is the family of linear contracts, the Stackelberg regret grows exactly as $\Theta(T^{2/3})$. The contract design problem is challenging because the utility function is discontinuous. Bounding the discretization error in this setting has been an open problem. In this paper, we identify a limited set of directions in which the utility function is continuous, allowing us to design a new discretization method and bound its error. This approach enables the first upper bound with no restrictions on the contract and action space. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.05732&r=cta |
| By: | M. Vannini; BC. McCannon; R. Marselli; C. Detotto |
| Abstract: | We explore the use of experts in arbitration proceedings by analyzing public procurement contract disputes in Italy. Balancing cost with accuracy, participants to a contract select arbitration when speedy dispute resolution is valued highly. Alternative dispute resolution mechanisms tend to give appointed arbitrators discretion in how to proceed. Consequently, principal-agent problems can arise. Using an IV approach, we show that the use of an expert causes a slowing down of the case resolution, without having an effect on the outcome of the dispute nor resolving uncertainty as measured by unanimous decisions by the panel of arbitrators. Conflict resolution mechanism designers should consider the alignment of incentives between the disputants and the service providers. |
| Keywords: | Arbitration; Expert; Italy; Principal-agent problem; Procurement contract |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:cns:cnscwp:202204&r=cta |
| By: | Kohei Daido (Kwansei Gakuin University); Takeshi Murooka (Osaka University) |
| Abstract: | We study multitasking problems where an agent engages in both a contractible task and a non-contractible task, which are substitutes. The agent has private information on the value of the non-contractible task, and there are followers who can also contribute to this task. We highlight a new mechanism by incorporating leading-by-example (Hermalin, 1998) in a multi-tasking model. To prevent excessive effort by the agent with low value on the non-contractible task, the principal provides high-powered incentives for the contractible task. We discuss its organizational implications to pay for performance, incentives to help colleagues, and prevention of overwork. |
| Keywords: | Multitasking, Signaling, Leadership, Pay for Performance, Help, Overwork |
| JEL: | D82 D86 J33 M52 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:kgu:wpaper:242&r=cta |
| By: | Xuejun Zhao; Ruihao Zhu; William B. Haskell |
| Abstract: | The rise of big data analytics has automated the decision-making of companies and increased supply chain agility. In this paper, we study the supply chain contract design problem faced by a data-driven supplier who needs to respond to the inventory decisions of the downstream retailer. Both the supplier and the retailer are uncertain about the market demand and need to learn about it sequentially. The goal for the supplier is to develop data-driven pricing policies with sublinear regret bounds under a wide range of possible retailer inventory policies for a fixed time horizon. To capture the dynamics induced by the retailer's learning policy, we first make a connection to non-stationary online learning by following the notion of variation budget. The variation budget quantifies the impact of the retailer's learning strategy on the supplier's decision-making. We then propose dynamic pricing policies for the supplier for both discrete and continuous demand. We also note that our proposed pricing policy only requires access to the support of the demand distribution, but critically, does not require the supplier to have any prior knowledge about the retailer's learning policy or the demand realizations. We examine several well-known data-driven policies for the retailer, including sample average approximation, distributionally robust optimization, and parametric approaches, and show that our pricing policies lead to sublinear regret bounds in all these cases. At the managerial level, we answer affirmatively that there is a pricing policy with a sublinear regret bound under a wide range of retailer's learning policies, even though she faces a learning retailer and an unknown demand distribution. Our work also provides a novel perspective in data-driven operations management where the principal has to learn to react to the learning policies employed by other agents in the system. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.04586&r=cta |