Mechanism Design for Single Leader Stackelberg Problems and Application to Procurement Auction Design

Abstract

In this paper, we focus on mechanism design for single leader Stackelberg problems, which are a special case of hierarchical decision making problems in which a distinguished agent, known as the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">leader</i> , makes the first move and this action is followed by the actions of the remaining agents, which are known as the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">followers</i> . These problems are also known as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">single</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">leader</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rest</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">follower</i> (SLRF) problems. There are many examples of such problems in the areas of electronic commerce, supply chain management, manufacturing systems, distributed computing, transportation networks, and multiagent systems. The game induced among the agents for these problems is a Bayesian Stackelberg game, which is more general than a Bayesian game. For this reason, classical mechanism design, which is based on Bayesian games, cannot be applied as is for solving SLRF mechanism design problems. In this paper, we extend classical mechanism design theory to the specific setting of SLRF problems. As a significant application of the theory developed, we explore two examples from the domain of electronic commerce- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first-price</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">second-price</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">electronic</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">procurement</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">auctions</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">with</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reserve</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">prices</i> . Using an SLRF model for these auctions, we derive certain key results using the SLRF mechanism design framework developed in this paper. The theory developed has many promising applications in modeling and solving emerging game theoretic problems in engineering.