Game-Theoretic Modeling of Multi-Agent Systems: Applications in Systems Engineering and Acquisition Processes

Salar Safarkhani, Purdue University

Abstract

The process of acquiring the large-scale complex systems is usually characterized with cost and schedule overruns. To investigate the causes of this problem, we may view the acquisition of a complex system in several different time scales. At finer time scales, one may study different stages of the acquisition process from the intricate details of the entire systems engineering process to communication between design teams to how individual designers solve problems. At the largest time scale one may consider the acquisition process as series of actions which are, request for bids, bidding and auctioning, contracting, and finally building and deploying the system, without resolving the fine details that occur within each step. In this work, we study the acquisition processes in multiple scales. First, we develop a game-theoretic model for engineering of the systems in the building and deploying stage. We model the interactions among the systems and subsystem engineers as a principal-agent problem. We develop a one-shot shallow systems engineering process and obtain the optimum transfer functions that best incentivize the subsystem engineers to maximize the expected system-level utility. The core of the principal-agent model is the quality function which maps the effort of the agent to the performance (quality) of the system. Therefore, we build the stochastic quality function by modeling the design process as a sequential decision-making problem. Second, we develop and evaluate a model of the acquisition process that accounts for the strategic behavior of different parties. We cast our model in terms of government-funded projects and assume the following steps. First, the government publishes a request for bids. Then, private firms offer their proposals in a bidding process and the winner bidder enters in a contract with the government. The contract describes the system requirements and the corresponding monetary transfers for meeting them. The winner firm devotes effort to deliver a system that fulfills the requirements. This can be assumed as a game that the government plays with the bidder firms. We study how different parameters in the acquisition procedure affect the bidders’ behaviors and therefore, the utility of the government. Using reinforcement learning, we seek to learn the optimal policies of involved actors in this game. In particular, we study how the requirements, contract types such as cost-plus and incentive-based contracts, number of bidders, problem complexity, etc., affect the acquisition procedure. Furthermore, we study the bidding strategy of the private firms and how the contract types affect their strategic behavior.

Degree

Ph.D.

Advisors

Bilionis, Purdue University.

Subject Area

Design|Theoretical Mathematics

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