### Abstract

We consider an optimal mechanism design problem for single machine scheduling that has been proposed by Heydenreich et al. in 2008. There, an example was presented to show that the 2-dimensional mechanism design problem does not satisfy a condition called IIA - independence of irrelevant alternatives. That example was flawed. In the flavour of recent work on automated mechanism design, we formulate the optimal mechanism design problem for this scheduling application as Mixed Integer Linear Programming problem (MIP). By generating problem instances systematically at random, we found minimal examples for the facts that (i) the optimal mechanism does in general not satisfy the IIA condition, and (ii) Bayes-Nash incentive compatibility and Dominant Strategy incentive compatibility are not equivalent.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | Centre for Telematics and Information Technology (CTIT) |

Number of pages | 3 |

Publication status | Published - Jul 2011 |

### Publication series

Name | CTIT Technical Report Series |
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Publisher | University of Twente, Centre for Telematics and Information Technology (CTIT) |

No. | TR-CTIT-11-15 |

ISSN (Print) | 1381-3625 |

### Keywords

- EWI-20311
- DMMP-DeCOM: Design and Complexity of Optimal Mechanisms
- Mechanism Design
- Mathematical Programming
- Machine Scheduling
- IR-77644
- METIS-277707

## Cite this

Duives, J., & Uetz, M. J. (2011).

*Mathematical Programming Approach to Multidimensional Mechanism Design for Single Machine Scheduling*. (CTIT Technical Report Series; No. TR-CTIT-11-15). Enschede: Centre for Telematics and Information Technology (CTIT).