Mechanism design for single leader Stackelberg problems and application to procurement auction design

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 leader, makes the first move and this action is followed by the actions of the remaining agents, which are known as the followers. These problems are also known as single leader rest follower (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-first-price and second-price electronic procurement auctions with reserve prices. 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

Sequential All-Pay Auctions with Head Starts and Noisy Outputs

We study a sequential (Stackelberg) all-pay auction with two contestants who are privately informed about a parameter (ability) that affects their cost of effort. Contestant 1 (the fi?rst mover) exerts an effort in the fi?rst period, while contestant 2 (the second mover) observes the effort of contestant 1 and then exerts an effort in the second period. Contestant 2 wins the contest if his effort is larger than or equal to the effort of contestant 1; otherwise, contestant 1 wins. We characterize the unique subgame perfect equilibrium of this sequential all-pay auction and analyze the use of head starts to improve the contestants' performances. We also study this model when contestant 1 exerts an effort in the fi?rst period which translates into an observable output but with some noise. We study two variations of this model where contestant 1 either knows or does not know the realization of the noise before she chooses her effort. Contestant 2 does not know the realization of the noise in both variations. For both variations, we characterize the subgame perfect equilibrium and investigate the effect of a random noise on the contestants' performance.Sequential all-pay auctions, head starts, noisy outputs.

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

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 leader, makes the first move and this action is followed by the actions of the remaining agents, which are known as the followers. These problems are also known as single leader rest follower (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—first-price and second-price electronic procurement auctions with reserve prices. 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