arXiv subjects

Aurélien Bechler

Publications and source records attributed to Aurélien Bechler.

3 recordsLinked to original sources

arXiv2025

Dynamics of multidimensional Simple Clock Auctions

Simple Clock Auctions (SCA) are a mechanism commonly used in spectrum auctions to sell lots of frequency bandwidths. We study such an auction with one player having access to perfect information against straightforward bidders. When the opponents' valuations satisfy the ordinary substitutes condition, we show that it is optimal to bid on a fixed lot overtime. In this setting, we consider a continuous-time version of the SCA auction in which the prices follow a differential inclusion with a piecewise-constant dynamics. We show that there exists a unique solution in the sense of Filippov. This guarantees that the continuous-time model coincides with the limit of the discrete-time auction when price increments tend to zero. Moreover, we show that the value function of this limit auction is piecewise linear (though possibly discontinuous). Finally, we illustrate these results by analyzing a simplified version of the multiband Australian spectrum auction of 2017.

cs.GT↗

arXiv2025

Optimal strategy against straightforward bidding in clock auctions

We study a model of auction representative of the 5G auction in France. We determine the optimal strategy of a bidder, assuming that the valuations of competitors are unknown to this bidder and that competitors adopt the straightforward bidding strategy. Our model is based on a Partially Observable Markov Decision Process (POMDP). This POMDP admits a concise statistics, avoiding the solution of a dynamic programming equation in the space of beliefs. In addition, under this optimal strategy, the expected gain of the bidder does not decrease if competitors deviate from straightforward bidding. We illustrate our results by numerical experiments, comparing the value of the bidder with the value of a perfectly informed one.

math.OC↗

arXiv2024

Bidding efficiently in Simultaneous Ascending Auctions with incomplete information using Monte Carlo Tree Search and determinization

For decades, Simultaneous Ascending Auction (SAA) has been the most widely used mechanism for spectrum auctions, and it has recently gained popularity for allocating 5G licenses in many countries. Despite its relatively simple rules, SAA introduces a complex strategic game with an unknown optimal bidding strategy. Given the high stakes involved, with billions of euros sometimes on the line, developing an efficient bidding strategy is of utmost importance. In this work, we extend our previous method, a Simultaneous Move Monte-Carlo Tree Search (SM-MCTS) based algorithm named $SMS^α$ to incomplete information framework. For this purpose, we compare three determinization approaches which allow us to rely on complete information SM-MCTS. This algorithm addresses, in incomplete framework, the four key strategic issues of SAA: the exposure problem, the own price effect, budget constraints, and the eligibility management problem. Through extensive numerical experiments on instances of realistic size with an uncertain framework, we show that $SMS^α$ largely outperforms state-of-the-art algorithms by achieving higher expected utility while taking less risks, no matter which determinization method is chosen.

cs.GT↗