We initiate the study of online contracts, which integrate the game-theoretic considerations of economic contract theory, with the algorithmic and informational challenges of online algorithm design. Our starting point is the classic online setting with preemption of Buchbinder et al. [SODA'15], in which a hiring principal faces a sequence of adversarial agent arrivals. Upon arrival, the principal must decide whether to tentatively accept the agent to their team, and whether to dismiss previous tentative choices. Dismissal is irrevocable, giving the setting its online decision-making flavor. In our setting, the agents are rational players: once the team is finalized, a game is played where the principal offers contracts (performance-based payment schemes), and each agent decides whether or not to work. Working agents reward the principal, and the goal is to choose a team that maximizes the principal's utility. Our main positive result is a 1/2-competitive algorithm when agent rewards are additive, which matches the best-possible competitive ratio. Our algorithm is randomized and this is necessary, as we show that no deterministic algorithm can attain a bounded competitive ratio. Moreover, if agent rewards are allowed to exhibit combinatorial structure known as XOS, even randomized algorithms might fail. En route to our competitive algorithm, we develop the technique of balance points, which can be useful for further exploration of online contracts in the adversarial model.

翻译：本文开创性地研究了在线合约设计，该领域融合了经济合约理论的博弈论考量与在线算法设计的算法与信息挑战。我们的研究起点是Buchbinder等人[SODA'15]提出的具有抢占机制的经典在线设定：一位雇佣方面临一系列对抗性智能体到达序列。每当智能体到达时，雇佣方必须决定是否暂时接受该智能体加入团队，以及是否解雇先前暂定的选择。解雇决定不可撤销，这赋予该设定在线决策的特性。在我们的设定中，智能体是理性参与者：当团队最终确定后，将进行一场博弈，雇佣方提供合约（基于绩效的支付方案），每个智能体决定是否工作。工作的智能体会为雇佣方带来收益，目标在于选择能最大化雇佣方效用的团队。当智能体收益具有可加性时，我们的主要正向结果是一个1/2竞争比的算法，这匹配了最优可能的竞争比。我们的算法是随机化的，且这是必要的，因为我们证明确定性算法无法获得有界竞争比。此外，若允许智能体收益呈现称为XOS的组合结构，即使随机化算法也可能失效。在构建竞争算法的过程中，我们发展了平衡点技术，该技术可为进一步探索对抗模型中的在线合约提供有益工具。