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

TL;DR

This work addresses bidding in Simultaneous Ascending Auctions under incomplete information (SAA-inc), where exposure, own-price effects, budgets, and eligibility constraints complicate strategy. It extends Simultaneous Move Monte Carlo Tree Search with EXP3-based selection to incomplete information via three determinization approaches, coupled with a type-generation framework and a budget-exposure inference method. Empirical results show that the proposed determinization-based strategies substantially outperform state-of-the-art PPB methods across uncertainty levels, with DSMS^{\alpha}_{EXP3} delivering the best performance when coordination is favorable. The findings offer a practical framework for robust, efficient spectrum bidding under uncertainty, with implications for regulators and bidders in large-scale SAA deployments.

Abstract

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.

Figures (9)

• Figure 1: Extensive form of a two player SAA-inc game with information sets and chance nodes. The first chance node corresponds to the draw by Nature of each player's type. For example, the couple $(t_1,t'_2)$ means the first player is type $t_1$ and the second player is type $t'_2$.
• Figure 2: Representation of the three different determinization approaches applied to a SAA-inc game with two players from the point of view of player $1$, with $T=|supp(\mathcal{T}_2)|$. In (b), dashed edges represent moves non consistent with $l$ and are ignored.
• Figure 3: Comparing our determinization approaches with PPB approaches through normal-form SAA-inc games in expected utility with a level of certainty of $(\eta_v,\eta_b)=(0.5,0.5)$.
• Figure 4: Comparing our three determinization approaches through normal-form SAA-inc games in expected utility with a level of certainty of $(\eta_v,\eta_b)=(0.5,0.5)$.
• Figure 5: Comparing our three determinization approaches to $CSMS_{EXP3}^\alpha$ through normal-form SAA-inc games in expected utility with a level of certainty of $(\eta_v,\eta_b)=(0.5,0.5)$.

Theorems & Definitions (3)

• Definition 3.1
• Definition 4.1
• Example