SIAM Journal on Financial Mathematics, Volume 12, Issue 1, Page 446-486, January 2021.
Following the recent literature on make-take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent approach, where the agents (the market makers) optimize their quotes in a Nash equilibrium fashion, providing best response to the contract proposed by the principal (the exchange). This contract aims at attracting liquidity on the platform. This is because the wealth of the exchange depends on the arrival of market orders, which is driven by the spread of market makers. We compute the optimal contract in quasi-explicit form and also derive the optimal spread policies for the market makers. Several new phenomena appears in this multi market-maker setting. In particular we show that it is not necessarily optimal to have a large number of market makers in the presence of a contracting scheme.

中文翻译：

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多做市商环境中的最佳做市商费用

SIAM 金融数学杂志，第 12 卷，第 1 期，第 446-486 页，2021 年 1 月。
根据最近关于成套费用政策的文献，我们考虑希望与多家做市商签订合适合约以提高其平台上的交易质量的交易所。为此，我们使用委托代理方法，其中代理（做市商）以纳什均衡方式优化他们的报价，对委托人（交易所）提出的合同提供最佳响应。该合约旨在吸引平台上的流动性。这是因为交易所的财富取决于市场订单的到来，这是由做市商的价差驱动的。我们以准显式形式计算最优合约，并为做市商推导出最优价差策略。在这种多做市商环境中出现了几个新现象。