Reconfigurable intelligent surfaces (RISs) hold great potential to enhance coverage, spectral efficiency, and communication security by intelligently configuring their reflecting elements. When owned by a neutral RIS operator, these elements can be offered as resources for which legitimate receivers and eavesdroppers compete. This paper investigates such competition and evaluates its impact on the physical-layer security performance of legitimate receivers. To model the competition, we develop a sequential RIS auction (SRA) framework, in which a bundle of RIS elements is auctioned in each round through a first-price sealed-bid mechanism, with each bidder submitting its bid based on the achievable rate gain and remaining budget. We then formulate the sequential bidding process as a Markov game by specifying its states, actions, rewards, and state transitions. To solve the game, we propose a multi-bidder deep deterministic policy gradient (MADDPG)-based multi-bidder reinforcement learning (MARL) approach under centralized training and decentralized execution (CTDE), enabling legitimate receivers and eavesdroppers to learn bidding strategies that maximize their long-term economic surplus. Numerical results show that, under the considered eavesdropper bidding strategies, the RL-based strategy enables legitimate receivers to achieve the highest secrecy rate per unit cost, outperforming random and fixed strategies and approaching the ideal physical-layer upper bound.

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