Bidding efficiently in Simultaneous Ascending Auctions with budget and eligibility constraints using Simultaneous Move Monte Carlo Tree Search

TL;DR

This work tackles efficient bidding in Simultaneous Ascending Auctions under complete information (SAA-c), where four intertwined strategic challenges—exposure, own price effect, budget constraints, and eligibility management—govern outcomes. It introduces SMS^α, a Simultaneous Move Monte Carlo Tree Search algorithm with a novel closing-price prediction method and a risk-averse reward that lets bidders trade off expected profit and risk. The method jointly handles all four strategic issues, employing a convergent closing-price predictor, a capped action-space search, and transposition tables to scale to realistic instances, and it substantially outperforms state-of-the-art bidders in extensive experiments. The results suggest that SMS^α achieves higher expected utility with lower exposure and more efficient allocation, offering a strong benchmark for complete-information spectrum auctions and a foundation for future work on incomplete-information extensions and mechanism design analysis.

Abstract

For decades, Simultaneous Ascending Auction (SAA) has been the most popular mechanism used for spectrum auctions. It has recently been employed by many countries for the allocation of 5G licences. Although SAA presents relatively simple rules, it induces a complex strategic game for which the optimal bidding strategy is unknown. Considering the fact that sometimes billions of euros are at stake in an SAA, establishing an efficient bidding strategy is crucial. In this work, we model the auction as a $n$-player simultaneous move game with complete information and propose the first efficient bidding algorithm that tackles simultaneously its four main strategic issues: the $\textit{exposure problem}$, the $\textit{own price effect}$, $\textit{budget constraints}$ and the $\textit{eligibility management problem}$. Our solution, called $SMS^α$, is based on Simultaneous Move Monte Carlo Tree Search (SM-MCTS) and relies on a new method for the prediction of closing prices. By introducing a new reward function in $SMS^α$, we give the possibility to bidders to define their own level of risk-aversion. Through extensive numerical experiments on instances of realistic size, we show that $SMS^α$ largely outperforms state-of-the-art algorithms, notably by achieving higher expected utility while taking less risks.

Figures (10)

• Figure 1: Extensive form of a three player SAA-c game with information sets and chance nodes
• Figure 2: MCTS scheme
• Figure 3: SM-MCTS tree structure with explicit chance nodes for SAA-c game with 3 players
• Figure 4: Convergence of sequence $p_t^1$ with its respective upper bound $g(t)$ and lower bound $h(t)$ in Example 1.
• Figure 5: Evolution of player 1's expected utility $\mathop{\mathrm{\mathbb{E}}}\nolimits(\sigma_1)$ depending on strategy versus player 2's budget $b_2$ given that player 2 plays optimally ($\varepsilon=0.1$).

Theorems & Definitions (8)

• Theorem 2.1
• proof
• Theorem 2.2
• proof
• Example
• Definition 3.1
• Conjecture 3.1
• Example