## Abstract

We continue the study of welfare maximization in unit-demand (matching) markets, in a distributed information model where agent's valuations are unknown to the central planner, and therefore communication is required to determine an efficient allocation. Dobzinski, Nisan and Oren (STOC'14) showed that if the market size is n, then r rounds of interaction (with logarithmic bandwidth) suffice to obtain an n(1/(r+1))-approximation to the optimal social welfare. In particular, this implies that such markets converge to a stable state (constant approximation) in time logarithmic in the market size. We obtain the first multi-round lower bound for this setup. We show that even if the allowable per-round bandwidth of each agent is nε(r), the approximation ratio of any r-round (randomized) protocol is no better than Omega(n(exp(-r)), implying an Omega(log log n) lower bound on the rate of convergence of the market to equilibrium. Our construction and technique may be of interest to round-communication tradeoffs in the more general setting of combinatorial auctions, for which the only known lower bound is for simultaneous (r = 1) protocols [DNO14].

Original language | English |
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Title of host publication | Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015 |

Publisher | IEEE Computer Society |

Pages | 1499-1512 |

Number of pages | 14 |

ISBN (Electronic) | 9781467381918 |

DOIs | |

State | Published - 11 Dec 2015 |

Event | 56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015 - Berkeley, United States Duration: 17 Oct 2015 → 20 Oct 2015 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 2015-December |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015 |
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Country/Territory | United States |

City | Berkeley |

Period | 17/10/15 → 20/10/15 |

### Bibliographical note

Publisher Copyright:© 2015 IEEE.

## Keywords

- Distributed matchings
- Information theory
- Multiparty Communication complexity
- Welfare maximization