Task Scheduling. There are three tasks a,b,c to be assigned to two agents. An agent may be assigned all tasks, some tasks, or no tasks; however, alls tasks must be assigned. The minimum times required for each task by each agent are provided in the following table. agent 1 a 2 2 task b 1 C 2 3 3 (a) Determine the task allocation and payments under a VCG mechanism. (b) Determine the task allocation and payments under a compensation and penalty mechanism. See definition 10.6.1 in the Multiagent Systems book. For the payment to (or from) an agent i, let the first term (i.e. hi(-i)) be the value of the mechanism's objective function when i does not participate (in the form of a payment to agent i). 3 For both parts assume that agents know something about mechanism design. In particular, agents will be truthful and they also know how long it will take to complete each task.

Task Scheduling. There are three tasks a,b,c to be assigned to two agents. An agent may be assigned all tasks, some tasks, or no tasks; however, alls tasks must be assigned. The minimum times required for each task by each agent are provided in the following table. agent 1 a 2 2 task b 1 C 2 3 3 (a) Determine the task allocation and payments under a VCG mechanism. (b) Determine the task allocation and payments under a compensation and penalty mechanism. See definition 10.6.1 in the Multiagent Systems book. For the payment to (or from) an agent i, let the first term (i.e. hi(-i)) be the value of the mechanism's objective function when i does not participate (in the form of a payment to agent i). 3 For both parts assume that agents know something about mechanism design. In particular, agents will be truthful and they also know how long it will take to complete each task.