## Bernard Lebrun

Associate Professor

**Office:** Vari Hall, 1074

**Phone:** (416) 736-2100 Ext: 33653

**Email:** blebrun@yorku.ca

**Primary website:** http://blebrun.info.yorku.ca/

I am interested in microeconomics, industrial organization, and game theory applied to economic theory. My current research is in auction theory. I received my PhD from the Université Catholique de Louvain.

** Revenue-Superior Variants of the Second-Price Auction**

* Economic Theory * , 59, 2, 245-275, 2015

**Abstract:** With two bidders, one strong and one weak, the introduction of at least some degree of anonymous "pay-your-bid" in the payment rule of the second-price auction behooves any risk-neutral seller who, while possibly efficiency minded, cares about revenues. This can be achieved by adding to the winner's payment a uniform proportion of his own bid, as in Guth and van Damme's auction, or by having bidders receive a uniform proportion of the losing bid, as in Goeree and Offerman's Amsterdam auction, or even by selling uniform toeholds to the bidders prior to the auction. We demonstrate one-to-one relations between the equilibria of these auctions and of first-price auctions. By assuming a power relation between the bidders' value cumulative or decumulative functions, we obtain explicit expressions for the first-order effects of the pay-your-bid rule.

[go to paper]

** Optimality and the English and Second-Price Auctions with Resale**

* Games and Economic Behavior * , 75, 2, 731-751, 2012

**Abstract:** In the presence of resale and under more general assumptions than Zheng's (2002), implementation of Myerson's (1981) optimal allocation with two bidders is achieved through the second-price auction. In a special class of asymmetric n-bidder models, it is achieved through the English auction.

[go to paper]

** Revenue Ranking of First-Price Auctions with Resale **

* Journal of Economic Theory * , 145, 5, 2037-2043, 2010

**Abstract:** When the price setter in post-auction resale is chosen according to exogenous probabilities, Hafalir and Krishna (2008) showed that the first-price auction brings more expected revenues than the second-price auction with truth-bidding bidders. We complete their revenue ranking by proving that the first-price auction produces higher expected revenues the higher the probability the auction winner sets the resale price.

[go to paper]

** First-Price Auctions with Resale and with Outcomes Robust to Bid Disclosure**

* Rand Journal of Economics * , 41, 1, 165-178, 2010

**Abstract:** Although there exists a pure separating equilibrium of the two-bidder first-price auction with resale when the bids are kept secret, the ratchet effect prevents the existence of such an equilibrium if the bidders are heterogeneous and the bids are fully disclosed. Nevertheless, we construct a behavioral equilibrium under full disclosure that is equivalent to the pure separating equilibrium under no disclosure. Thus, if the bidders follow this equilibrium, the choice of the disclosure regime does not affect the final allocation of the item nor the expected payoffs.

[go to paper]

** Auctions with Almost Homogeneous Bidders**

* Journal of Economic Theory * 144, 3, 1341-1351, 2009

**Abstract:** We prove that, around the symmetric case, where the values are identically distributed, the equilibrium of the first price auction is jointly differentiable with respect to general bidder-specific parameters of the value distributions. We show that the revenue equivalence between the first-price and the second-price auctions to the first-order in the size of the parameters is an immediate consequence of this differentiability and the Revenue Equivalence Theorem; thereby formally establishing the first-order equivalence Fibich et al. [G. Fibich, A. Gavious, A. Sela, Revenue equivalence in asymmetric auctions, J. Econ. Theory 115 (2004) 309-321] noticed for their particular perturbation.

[go to paper]

### Upcoming Courses

Term | Course Number | Section | Title | Type |
---|---|---|---|---|

Fall 2024 | AP/ECON1540 3.0 | A | Introductory Mathematical Economics II | LECT |

Fall 2024 | AP/ECON1540 3.0 | B | Introductory Mathematical Economics II | LECT |

Winter 2025 | AP/ECON2350 3.0 | P | Intermediate Microeconomic Theory II | LECT |

Winter 2025 | AP/ECON2350 3.0 | Q | Intermediate Microeconomic Theory II | LECT |

Winter 2025 | AP/ECON1540 3.0 | T | Introductory Mathematical Economics II | LECT |

I am interested in microeconomics, industrial organization, and game theory applied to economic theory. My current research is in auction theory. I received my PhD from the Université Catholique de Louvain.

### All Publications

** Revenue-Superior Variants of the Second-Price Auction**

* Economic Theory * , 59, 2, 245-275, 2015

**Abstract:** With two bidders, one strong and one weak, the introduction of at least some degree of anonymous "pay-your-bid" in the payment rule of the second-price auction behooves any risk-neutral seller who, while possibly efficiency minded, cares about revenues. This can be achieved by adding to the winner's payment a uniform proportion of his own bid, as in Guth and van Damme's auction, or by having bidders receive a uniform proportion of the losing bid, as in Goeree and Offerman's Amsterdam auction, or even by selling uniform toeholds to the bidders prior to the auction. We demonstrate one-to-one relations between the equilibria of these auctions and of first-price auctions. By assuming a power relation between the bidders' value cumulative or decumulative functions, we obtain explicit expressions for the first-order effects of the pay-your-bid rule.

[go to paper]

** Optimality and the English and Second-Price Auctions with Resale**

* Games and Economic Behavior * , 75, 2, 731-751, 2012

**Abstract:** In the presence of resale and under more general assumptions than Zheng's (2002), implementation of Myerson's (1981) optimal allocation with two bidders is achieved through the second-price auction. In a special class of asymmetric n-bidder models, it is achieved through the English auction.

[go to paper]

** Revenue Ranking of First-Price Auctions with Resale **

* Journal of Economic Theory * , 145, 5, 2037-2043, 2010

**Abstract:** When the price setter in post-auction resale is chosen according to exogenous probabilities, Hafalir and Krishna (2008) showed that the first-price auction brings more expected revenues than the second-price auction with truth-bidding bidders. We complete their revenue ranking by proving that the first-price auction produces higher expected revenues the higher the probability the auction winner sets the resale price.

[go to paper]

** First-Price Auctions with Resale and with Outcomes Robust to Bid Disclosure**

* Rand Journal of Economics * , 41, 1, 165-178, 2010

**Abstract:** Although there exists a pure separating equilibrium of the two-bidder first-price auction with resale when the bids are kept secret, the ratchet effect prevents the existence of such an equilibrium if the bidders are heterogeneous and the bids are fully disclosed. Nevertheless, we construct a behavioral equilibrium under full disclosure that is equivalent to the pure separating equilibrium under no disclosure. Thus, if the bidders follow this equilibrium, the choice of the disclosure regime does not affect the final allocation of the item nor the expected payoffs.

[go to paper]

** Auctions with Almost Homogeneous Bidders**

* Journal of Economic Theory * 144, 3, 1341-1351, 2009

**Abstract:** We prove that, around the symmetric case, where the values are identically distributed, the equilibrium of the first price auction is jointly differentiable with respect to general bidder-specific parameters of the value distributions. We show that the revenue equivalence between the first-price and the second-price auctions to the first-order in the size of the parameters is an immediate consequence of this differentiability and the Revenue Equivalence Theorem; thereby formally establishing the first-order equivalence Fibich et al. [G. Fibich, A. Gavious, A. Sela, Revenue equivalence in asymmetric auctions, J. Econ. Theory 115 (2004) 309-321] noticed for their particular perturbation.

[go to paper]

### Upcoming Courses

Term | Course Number | Section | Title | Type |
---|---|---|---|---|

Fall 2024 | AP/ECON1540 3.0 | A | Introductory Mathematical Economics II | LECT |

Fall 2024 | AP/ECON1540 3.0 | B | Introductory Mathematical Economics II | LECT |

Winter 2025 | AP/ECON2350 3.0 | P | Intermediate Microeconomic Theory II | LECT |

Winter 2025 | AP/ECON2350 3.0 | Q | Intermediate Microeconomic Theory II | LECT |

Winter 2025 | AP/ECON1540 3.0 | T | Introductory Mathematical Economics II | LECT |