### Abstract

As is well known, many classes of markets have efficient equilibria, but this depends on agents being non-strategic, i.e. that they declare their true demands when offered goods at particular prices, or in other words, that they are price-takers. An important question is how much the equilibria degrade in the face of strategic behavior, i.e. what is the Price of Anarchy (PoA) of the market viewed as a mechanism? Often, PoA bounds are modest constants such as -4/3 or 2. Nonetheless, in practice a guarantee that no more than 25% or 50% of the economic value is lost may be unappealing. This paper asks whether significantly better bounds are possible under plausible assumptions. In particular, we look at how these worst case guarantees improve in the following large settings. - Large Walrasian auctions: These are auctions with many copies of each item and many agents. We show that the PoA tends to 1 as the market size increases, under suitable conditions, mainly that there is some uncertainty about the numbers of copies of each good and demands obey the gross substitutes condition. We also note that some such assumption is unavoidable. - Large Fisher markets: Fisher markets are a class of economies that has received considerable attention in the computer science literature. A large market is one in which at equilibrium, each buyer makes only a small fraction of the total purchases; the smaller the fraction, the larger the market. Here the main condition is that demands are based on homogeneous monotone utility functions that satisfy the gross substitutes condition. Again, the PoA tends to 1 as the market size increases. Furthermore, in each setting, we quantify the tradeoff between market size and the PoA.

Original language | English (US) |
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Title of host publication | EC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation |

Publisher | Association for Computing Machinery, Inc |

Pages | 791-808 |

Number of pages | 18 |

ISBN (Electronic) | 9781450339360 |

DOIs | |

State | Published - Jul 21 2016 |

Event | 17th ACM Conference on Economics and Computation, EC 2016 - Maastricht, Netherlands Duration: Jul 24 2016 → Jul 28 2016 |

### Other

Other | 17th ACM Conference on Economics and Computation, EC 2016 |
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Country | Netherlands |

City | Maastricht |

Period | 7/24/16 → 7/28/16 |

### Fingerprint

### Keywords

- Fisher markets
- Large market games
- Price of anarchy
- Walrasian auctions

### ASJC Scopus subject areas

- Statistics and Probability
- Computer Science (miscellaneous)
- Economics and Econometrics
- Computational Mathematics

### Cite this

*EC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation*(pp. 791-808). Association for Computing Machinery, Inc. https://doi.org/10.1145/2940716.2940720

**Large market games with near optimal efficiency.** / Cole, Richard; Tao, Yixin.

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

*EC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation.*Association for Computing Machinery, Inc, pp. 791-808, 17th ACM Conference on Economics and Computation, EC 2016, Maastricht, Netherlands, 7/24/16. https://doi.org/10.1145/2940716.2940720

}

TY - GEN

T1 - Large market games with near optimal efficiency

AU - Cole, Richard

AU - Tao, Yixin

PY - 2016/7/21

Y1 - 2016/7/21

N2 - As is well known, many classes of markets have efficient equilibria, but this depends on agents being non-strategic, i.e. that they declare their true demands when offered goods at particular prices, or in other words, that they are price-takers. An important question is how much the equilibria degrade in the face of strategic behavior, i.e. what is the Price of Anarchy (PoA) of the market viewed as a mechanism? Often, PoA bounds are modest constants such as -4/3 or 2. Nonetheless, in practice a guarantee that no more than 25% or 50% of the economic value is lost may be unappealing. This paper asks whether significantly better bounds are possible under plausible assumptions. In particular, we look at how these worst case guarantees improve in the following large settings. - Large Walrasian auctions: These are auctions with many copies of each item and many agents. We show that the PoA tends to 1 as the market size increases, under suitable conditions, mainly that there is some uncertainty about the numbers of copies of each good and demands obey the gross substitutes condition. We also note that some such assumption is unavoidable. - Large Fisher markets: Fisher markets are a class of economies that has received considerable attention in the computer science literature. A large market is one in which at equilibrium, each buyer makes only a small fraction of the total purchases; the smaller the fraction, the larger the market. Here the main condition is that demands are based on homogeneous monotone utility functions that satisfy the gross substitutes condition. Again, the PoA tends to 1 as the market size increases. Furthermore, in each setting, we quantify the tradeoff between market size and the PoA.

AB - As is well known, many classes of markets have efficient equilibria, but this depends on agents being non-strategic, i.e. that they declare their true demands when offered goods at particular prices, or in other words, that they are price-takers. An important question is how much the equilibria degrade in the face of strategic behavior, i.e. what is the Price of Anarchy (PoA) of the market viewed as a mechanism? Often, PoA bounds are modest constants such as -4/3 or 2. Nonetheless, in practice a guarantee that no more than 25% or 50% of the economic value is lost may be unappealing. This paper asks whether significantly better bounds are possible under plausible assumptions. In particular, we look at how these worst case guarantees improve in the following large settings. - Large Walrasian auctions: These are auctions with many copies of each item and many agents. We show that the PoA tends to 1 as the market size increases, under suitable conditions, mainly that there is some uncertainty about the numbers of copies of each good and demands obey the gross substitutes condition. We also note that some such assumption is unavoidable. - Large Fisher markets: Fisher markets are a class of economies that has received considerable attention in the computer science literature. A large market is one in which at equilibrium, each buyer makes only a small fraction of the total purchases; the smaller the fraction, the larger the market. Here the main condition is that demands are based on homogeneous monotone utility functions that satisfy the gross substitutes condition. Again, the PoA tends to 1 as the market size increases. Furthermore, in each setting, we quantify the tradeoff between market size and the PoA.

KW - Fisher markets

KW - Large market games

KW - Price of anarchy

KW - Walrasian auctions

UR - http://www.scopus.com/inward/record.url?scp=84983486379&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983486379&partnerID=8YFLogxK

U2 - 10.1145/2940716.2940720

DO - 10.1145/2940716.2940720

M3 - Conference contribution

SP - 791

EP - 808

BT - EC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation

PB - Association for Computing Machinery, Inc

ER -