Mechanism Design for Scheduling with Uncertain Execution Time

We study the problem where a task (or multiple unrelated tasks) must be executed, there are multiple machines/agents that can potentially perform the task, and our objective is to minimize the expected sum of the agents' processing times. Each agent does not know exactly how long it will take him to finish the task; he only knows the distribution from which this time is drawn. These times are independent across agents and the distributions fulfill the monotone hazard rate condition. Agents are selfish and will lie about their distributions if this increases their expected utility. We study different variations of the Vickrey mechanism that take as input the agents' reported distributions and the players' realized running times and that output a schedule that minimizes the expected sum of processing times, as well as payments that make it an ex-post equilibrium for the agents to both truthfully report their distributions and exert full effort to complete the task. We devise the ChPE mechanism, which is uniquely tailored to our problem, and has many desirable properties including: not rewarding agents that fail to finish the task and having non-negative payments.

[1]  Moshe Babaioff.  Truthful Mechanisms for One-Parameter Agents , 2016, Encyclopedia of Algorithms.

[2]  Terence R. Johnson,et al.  Procurement with Adverse Selection and Dynamic Moral Hazard , 2012 .

[3]  Dimitris Fotakis,et al.  Truthfulness Flooded Domains and the Power of Verification for Mechanism Design , 2013, WINE.

[4]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[5]  Ron Lavi,et al.  Algorithmic Mechanism Design , 2008, Encyclopedia of Algorithms.

[6]  Edith Elkind,et al.  Mechanism design: from partial to probabilistic verification , 2012, EC '12.

[7]  Jerry R. Green,et al.  Partially Verifiable Information and Mechanism Design , 1986 .

[8]  Nicholas R. Jennings,et al.  Algorithms and mechanisms for procuring services with uncertain durations using redundancy , 2011, Artif. Intell..

[9]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[10]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[11]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[12]  Carmine Ventre,et al.  Combinatorial auctions with verification are tractable , 2010, Theor. Comput. Sci..

[13]  Sarvapali D. Ramchurn,et al.  Trust-Based Mechanisms for Robust and Efficient Task Allocation in the Presence of Execution Uncertainty , 2009, J. Artif. Intell. Res..

[14]  Carmine Ventre,et al.  New Constructions of Mechanisms with Verification , 2006, ICALP.

[15]  Moshe Tennenholtz,et al.  Mechanism design with uncertain inputs: (to err is human, to forgive divine) , 2011, STOC '11.

[16]  Moshe Tennenholtz,et al.  Fault tolerant mechanism design , 2008, Artif. Intell..