Discovering Equilibrium Strategies for a Combinatorial First Price Auction

The 9th IEEE International Conference on E-Commerce Technology and The 4th IEEE International Conference on Enterprise Computing, E-Commerce and E-Services (CEC-EEE 2007) ◽

10.1109/cec-eee.2007.41 ◽

2007 ◽

Cited By ~ 2

Author(s):

Jim Wilenius ◽

Arne Andersson

Keyword(s):

Equilibrium Strategies ◽

Price Auction

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A First Price Auction with an Arbitrary Number of Asymmetric Bidders

The B E Journal of Theoretical Economics ◽

10.1515/bejte-2018-0105 ◽

2018 ◽

Vol 19 (2) ◽

Author(s):

Nicola Doni ◽

Domenico Menicucci

Keyword(s):

Closed Form ◽

Arbitrary Number ◽

Equilibrium Strategies ◽

Private Values ◽

Price Auction ◽

Second Price Auction

Abstract We examine an auction setting with private values and $n\geq 2$ bidders, which differ in the probability to have a low (high) value. We prove that for the first price auction, the equilibrium strategies can be written in closed form and there are gaps in the equilibrium bid distribution of each bidder except the strongest two. Our equilibrium characterization allows to prove that in this setting the seller prefers the second price auction to the first price auction for each $n\geq 2$.

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On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2019057 ◽

2020 ◽

Vol 26 ◽

pp. 41

Author(s):

Tianxiao Wang

Keyword(s):

Optimal Control ◽

Closed Loop ◽

Optimal Control Problems ◽

Mean Field ◽

Open Loop ◽

Time Inconsistency ◽

Control Problems ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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