<p>The rapid growth of new energy vehicles (NEV) has led to a significant increase in the retirement of power batteries (PBs), making PBs recycling an increasingly prominent issue. In order to encourage the recycling of retired PBs, the government has implemented a deposit policy, and NEV manufacturers have actively invested in advertising to fulfil the Extended Producer Responsibility. This study aims to investigate the effects of deposit policy and advertising investment on recycling decisions and model selection within the closed-loop supply chain (CLSC). Three recycling game models were constructed, both with and without the influence of the deposit policy. MATLAB software is used for numerical simulations, and the selection of the best recovery model is discussed from different perspectives. Results show that: (1) Under different recycling models, the wholesale prices of PBs and the sales prices of NEVs are equal, but the recycling prices and transfer prices differ. (2) The deposit policy and advertising investment both promote the forward decision-making of the CLSC but have the opposite impact on the reverse decision-making. (3) Considering economic benefits, environmental benefits, government surplus, and consumer surplus, it is evident that PB manufacturer and NEV manufacturer alliance recycling model yields relatively better results. (4) When incremental recycling falls below a certain threshold, NEV manufacturers need to carefully consider economic and environmental benefits when determining the levels of advertising investment. These findings can offer valuable suggestions for formulating government deposit policies, selecting power battery recycling models, and determining advertising investments for NEV manufacturers.</p>