Stochastic Games

The Invisible Handshake: Tacit Collusion between Adaptive Market Agents ArXiv ID: 2510.15995 “View on arXiv” Authors: Luigi Foscari, Emanuele Guidotti, Nicolò Cesa-Bianchi, Tatjana Chavdarova, Alfio Ferrara Abstract We study the emergence of tacit collusion between adaptive trading agents in a stochastic market with endogenous price formation. Using a two-player repeated game between a market maker and a market taker, we characterize feasible and collusive strategy profiles that raise prices beyond competitive levels. We show that, when agents follow simple learning algorithms (e.g., gradient ascent) to maximize their own wealth, the resulting dynamics converge to collusive strategy profiles, even in highly liquid markets with small trade sizes. By highlighting how simple learning strategies naturally lead to tacit collusion, our results offer new insights into the dynamics of AI-driven markets. ...

Optimal Execution and Macroscopic Market Making ArXiv ID: 2504.06717 “View on arXiv” Authors: Unknown Abstract We propose a stochastic game modelling the strategic interaction between market makers and traders of optimal execution type. For traders, the permanent price impact commonly attributed to them is replaced by quoting strategies implemented by market makers. For market makers, order flows become endogenous, driven by tactical traders rather than assumed exogenously. Using the forward-backward stochastic differential equation (FBSDE) characterization of Nash equilibria, we establish a local well-posedness result for the general game. In the specific Almgren-Chriss-Avellaneda-Stoikov model, a decoupling approach guarantees the global well-posedness of the FBSDE system via the well-posedness of an associated backward stochastic Riccati equation. Finally, by introducing small diffusion terms into the inventory processes, global well-posedness is achieved for the approximation game. ...

Macroscopic Market Making Games via Multidimensional Decoupling Field ArXiv ID: 2406.05662 “View on arXiv” Authors: Unknown Abstract Building on the macroscopic market making framework as a control problem, this paper investigates its extension to stochastic games. In the context of price competition, each agent is benchmarked against the best quote offered by the others. We begin with the linear case. While constructing the solution directly, the \textit{“ordering property”} and the dimension reduction in the equilibrium are revealed. For the non-linear case, we extend the decoupling approach by introducing a multidimensional \textit{“characteristic equation”} to analyse the well-posedness of the forward-backward stochastic differential equations. Properties of the coefficients in this characteristic equation are derived using tools from non-smooth analysis. Several new well-posedness results are presented. ...