Related papers: Optimal Execution and Macroscopic Market Making
We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE.…
Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
This paper presents a multi-agent reinforcement learning algorithm to represent strategic bidding behavior in freight transport markets. Using this algorithm, we investigate whether feasible market equilibriums arise without any central…
We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…
In a many-to-one matching market, we analyze the matching game induced by a stable rule when firms' choice function satisfy substitutability. We show that any stable rule implements the individually rational correspondence in Nash…
We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal…
We consider the process of bidding by electricity suppliers in a day-ahead market context where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other…
Systems of competing agents can often be modeled as games. Assuming rationality, the most likely outcomes are given by an equilibrium (e.g. a Nash equilibrium). In many practical settings, games are influenced by context, i.e. additional…
We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…
We analyze a continuous-time optimal trade execution problem in multiple assets where the price impact and the resilience can be matrix-valued stochastic processes that incorporate cross-impact effects. In addition, we allow for stochastic…
Spot electricity markets are considered under a Game-Theoretic framework, where risk averse players submit orders to the market clearing mechanism to maximise their own utility. Consistent with the current practice in Europe, the market…
Examining the behavior of multi-agent systems is vitally important to many emerging distributed applications - game theory has emerged as a powerful tool set in which to do so. The main approach of game-theoretic techniques is to model…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
One attractive approach to market dynamics is the level $k$ model in which a level $0$ player adopts a very simple response to current conditions, a level $1$ player best-responds to a model in which others take level $0$ actions, and so…
Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…
In the present paper, we study the optimal execution problem under stochastic price recovery based on limit order book dynamics. We model price recovery after execution of a large order by accelerating the arrival of the refilling order,…
We propose a market designed using game theory to optimally utilize the flexibility of distributed energy resources (DERs) like solar, batteries, electric vehicles, and flexible loads. Market agents perform multiperiod optimization to…
We study a two-player discounted zero-sum stochastic game model for dynamic operational planning in military campaigns. At each stage, the players manage multiple commanders who order military actions on objectives that have an open line of…