### Abstract

We consider the problem of designing auctions in social networks for goods that exhibit single-parameter submodular network externalities in which a bidder's value for an outcome is a fixed private type times a known submodular function of the allocation of his friends. Externalities pose many issues that are hard to address with traditional techniques; our work shows how to resolve these issues in a specific setting of particular interest. We operate in a Bayesian environment and so assume private values are drawn according to known distributions. We prove that the optimal auction is APX-hard. Thus we instead design auctions whose revenue approximates that of the optimal auction. Our main result considers step-function externalities in which a bidder's value for an outcome is either zero, or equal to his private type if at least one friend has the good. For these settings, we provide a e/e+1-approximation. We also give a $0.25$-approximation auction for general single-parameter submodular network externalities, and discuss optimizing over a class of simple pricing strategies.

Original language | English (US) |
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Title of host publication | EC'11 - Proceedings of the 12th ACM Conference on Electronic Commerce |

Pages | 11-20 |

Number of pages | 10 |

DOIs | |

State | Published - Jun 30 2011 |

Event | 12th ACM Conference on Electronic Commerce, EC'11 - San Jose, CA, United States Duration: Jun 5 2011 → Jun 9 2011 |

### Publication series

Name | Proceedings of the ACM Conference on Electronic Commerce |
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### Other

Other | 12th ACM Conference on Electronic Commerce, EC'11 |
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Country | United States |

City | San Jose, CA |

Period | 6/5/11 → 6/9/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Computer Science Applications
- Computer Networks and Communications

### Cite this

*EC'11 - Proceedings of the 12th ACM Conference on Electronic Commerce*(pp. 11-20). (Proceedings of the ACM Conference on Electronic Commerce). https://doi.org/10.1145/1993574.1993577

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*EC'11 - Proceedings of the 12th ACM Conference on Electronic Commerce.*Proceedings of the ACM Conference on Electronic Commerce, pp. 11-20, 12th ACM Conference on Electronic Commerce, EC'11, San Jose, CA, United States, 6/5/11. https://doi.org/10.1145/1993574.1993577

**Optimal auctions with positive network externalities.** / Haghpanah, Nima; Immorlica, Nicole; Mirrokni, Vahab; Munagala, Kamesh.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Optimal auctions with positive network externalities

AU - Haghpanah, Nima

AU - Immorlica, Nicole

AU - Mirrokni, Vahab

AU - Munagala, Kamesh

PY - 2011/6/30

Y1 - 2011/6/30

N2 - We consider the problem of designing auctions in social networks for goods that exhibit single-parameter submodular network externalities in which a bidder's value for an outcome is a fixed private type times a known submodular function of the allocation of his friends. Externalities pose many issues that are hard to address with traditional techniques; our work shows how to resolve these issues in a specific setting of particular interest. We operate in a Bayesian environment and so assume private values are drawn according to known distributions. We prove that the optimal auction is APX-hard. Thus we instead design auctions whose revenue approximates that of the optimal auction. Our main result considers step-function externalities in which a bidder's value for an outcome is either zero, or equal to his private type if at least one friend has the good. For these settings, we provide a e/e+1-approximation. We also give a $0.25$-approximation auction for general single-parameter submodular network externalities, and discuss optimizing over a class of simple pricing strategies.

AB - We consider the problem of designing auctions in social networks for goods that exhibit single-parameter submodular network externalities in which a bidder's value for an outcome is a fixed private type times a known submodular function of the allocation of his friends. Externalities pose many issues that are hard to address with traditional techniques; our work shows how to resolve these issues in a specific setting of particular interest. We operate in a Bayesian environment and so assume private values are drawn according to known distributions. We prove that the optimal auction is APX-hard. Thus we instead design auctions whose revenue approximates that of the optimal auction. Our main result considers step-function externalities in which a bidder's value for an outcome is either zero, or equal to his private type if at least one friend has the good. For these settings, we provide a e/e+1-approximation. We also give a $0.25$-approximation auction for general single-parameter submodular network externalities, and discuss optimizing over a class of simple pricing strategies.

UR - http://www.scopus.com/inward/record.url?scp=79959600624&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959600624&partnerID=8YFLogxK

U2 - 10.1145/1993574.1993577

DO - 10.1145/1993574.1993577

M3 - Conference contribution

AN - SCOPUS:79959600624

SN - 9781450302616

T3 - Proceedings of the ACM Conference on Electronic Commerce

SP - 11

EP - 20

BT - EC'11 - Proceedings of the 12th ACM Conference on Electronic Commerce

ER -