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Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…

Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to…

We study equilibrium feedback strategies for a family of dynamic mean-variance problems with competition among a large group of agents. We assume that the time horizon is random and each agent's risk aversion depends dynamically on the…

We study a dynamic market setting where an intermediary interacts with an unknown large sequence of agents that can be either sellers or buyers: their identities, as well as the sequence length $n$, are decided in an adversarial, online…

In this paper, we consider a Nash equilibrium seeking problem for a class of high-order multi-agent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of…

We consider a single buyer with a combinatorial preference that would like to purchase related products and services from different vendors, where each vendor supplies exactly one product. We study the general case where subsets of products…

We consider a one-sided assignment market or exchange network with transferable utility and propose a model for the dynamics of bargaining in such a market. Our dynamical model is local, involving iterative updates of 'offers' based on…

We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of…

Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…

We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand,…

We model a system of n asymmetric firms selling a homogeneous good in a common market through a pay-as-bid auction. Every producer chooses as its strategy a supply function returning the quantity S(p) that it is willing to sell at a minimum…

We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company…

We investigate the effects of competition in a problem of resource extraction from a common source with diffusive dynamics. In the symmetric version with identical extraction rates we prove the existence of a Nash equilibrium where the…

In this paper we deal with linear production situations in which there is a limited common-pool resource, managed by an external agent. The profit that a producer, or a group of producers, can attain depends on the amount of common-pool…

When randomness in demand affects the sales of a product, retailers use dynamic pricing strategies to maximize their profits. In this article, we formulate the pricing problem as a continuous-time stochastic optimal control problem and find…

We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. First, we propose a tractable…

We model real-world data markets, where sellers post fixed prices and buyers are free to purchase from any set of sellers, as a simultaneous game. A key component here is the negative externality buyers induce on one another due to data…

Motivated by recent progress on pricing in the AI literature, we study marketplaces that contain multiple vendors offering identical or similar products and unit-demand buyers with different valuations on these vendors. The objective of…

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…

Motivated by recent empirical findings on the periodic phenomenon of aggregated market volumes in equity markets, we aim to understand the causes and consequences of periodic trading activities through a game-theoretic perspective,…