Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Game-Theoretic Approach to a Task Delegation Problem

Donya G. Dobakhshari, Lav R. Varshney, Vijay Gupta

TL;DR

This work designs a mechanism for selecting the agent and incentivizing the selected agent to realize a priority sequence for executing the tasks that achieves socially optimal performance and shows that the proposed mechanism is individually rational and incentive compatible.

Abstract

We study a setting in which a principal selects an agent to execute a collection of tasks according to a specified priority sequence. Agents, however, have their own individual priority sequences according to which they wish to execute the tasks. There is information asymmetry since each priority sequence is private knowledge for the individual agent. We design a mechanism for selecting the agent and incentivizing the selected agent to realize a priority sequence for executing the tasks that achieves socially optimal performance. Our proposed mechanism consists of two parts. First, the principal runs an auction to select an agent to allocate tasks to with minimum declared priority sequence misalignment. Then, the principal rewards the agent according to the realized priority sequence with which the tasks were performed. We show that the proposed mechanism is individually rational and incentive compatible. Further, it is also socially optimal for the case of linear cost of priority sequence modification for the agents.

A Game-Theoretic Approach to a Task Delegation Problem

TL;DR

This work designs a mechanism for selecting the agent and incentivizing the selected agent to realize a priority sequence for executing the tasks that achieves socially optimal performance and shows that the proposed mechanism is individually rational and incentive compatible.

Abstract

We study a setting in which a principal selects an agent to execute a collection of tasks according to a specified priority sequence. Agents, however, have their own individual priority sequences according to which they wish to execute the tasks. There is information asymmetry since each priority sequence is private knowledge for the individual agent. We design a mechanism for selecting the agent and incentivizing the selected agent to realize a priority sequence for executing the tasks that achieves socially optimal performance. Our proposed mechanism consists of two parts. First, the principal runs an auction to select an agent to allocate tasks to with minimum declared priority sequence misalignment. Then, the principal rewards the agent according to the realized priority sequence with which the tasks were performed. We show that the proposed mechanism is individually rational and incentive compatible. Further, it is also socially optimal for the case of linear cost of priority sequence modification for the agents.

Paper Structure

This paper contains 10 sections, 2 theorems, 13 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Model
  4. Problem Formulation
  5. Main Results
  6. Proposed Mechanism
  7. Discussion
  8. Conclusion
  9. Proof of Theorem \ref{['th1']}
  10. Proof of Theorem \ref{['pro1']}

Key Result

Theorem 1

Consider the problem $\mathcal{P}_{1}.$ The proposed mechanism $\mathcal{M}$ is incentive compatible, i.e., every agent $i$ reports $\theta_i'=\theta_i.$ Further, it satisfies the individual rationality constraint.

Figures (1)

  • Figure 1: Timeline of the interaction between the principal and the agent.

Theorems & Definitions (9)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Theorem 1
  • proof
  • Remark 5
  • Theorem 2
  • proof