Algorithmic Mechanism Design

This report emerged from the seminar Mechanism Design held in the summer term 2007 at the ITI Sanders, Universität Karlsruhe (TH). It is based on the paper Algorithmic Mechanism Design of Noan Nisan and Amir Ronen [5]. Within this report we try to present their results in an illustrative manner using several additional examples. Mechanism Design is a subfield of game theory. It deals with problems in which multiple selfish agents are to be organized in a way that the global outcome meets specified goals. The organizing entity, called mechanism, tries to motivate the agents to reveal their true characters. This is achieved by payments given to the agents. Thus, the mechanism is able to guide the agents towards a social choice. In the first chapter the term Mechanism Design is motivated and introduced formally. The second chapter deals with a famous concept, the Vickrey-Groves-Clarke Mechanism which exhibits desirable properties. Furthermore, two examples illustrate useful applications. In the third chapter the Task Scheduling Problem is discussed as a Mechanism Design Problem. A lower and an upper bound for approximation mechanisms are given. The fourth chapter transfers the paradigm of randomization to the field of Mechanism Design. A randomized mechanism for the Task Scheduling Problem is proposed that beats the lower bound for deterministic mechanisms. Finally, the fifth chapter presents an enhanced model, Mechanisms with Verification, in which the mechanism has further information about the behavior of the agents. Two optimal, but computationally intractable , mechanisms as well as a approximation mechanism are investigated.