Related papers: Dynamic Bertrand Oligopoly
We find an approximate Nash equilibrium in a game between decentralized exchanges (DEXs) that compete for order flow by setting dynamic trading fees. We characterize the equilibrium via a coupled system of partial differential equations and…
I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must…
We study nonzero-sum stochastic games for continuous time Markov decision processes on a denumerable state space with risk-sensitive ergodic cost criterion. Transition rates and cost rates are allowed to be unbounded. Under a Lyapunov type…
Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we…
We investigate a time-inconsistent, non-Markovian finite-player game in continuous time, where each player's objective functional depends non-linearly on the expected value of the state process. As a result, the classical Bellman optimality…
We study equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes.…
This paper explores the gain maximization problem of two nations engaging in non-cooperative bilateral trade. Probabilistic model of an exchange of commodities under different price systems is considered. Volume of commodities exchanged…
Data is the central commodity of the digital economy. Unlike physical goods, it is non-rival, replicable at near-zero cost, and traded under heterogeneous licensing rules. These properties defy standard supply--demand theory and call for…
We consider a deterministic continuous time model of monopolistic firm, which chooses production and pricing strategies of a single good. Firm's goal is to maximize the discounted profit over infinite time horizon. The no-backlogging…
This paper studies a nonzero-sum Dynkin game in discrete time under non-exponential discounting. For both players, there are two levels of game-theoretic reasoning intertwined. First, each player looks for an intra-personal equilibrium…
Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural…
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…
The framework of multi-agent learning explores the dynamics of how individual agent strategies evolve in response to the evolving strategies of other agents. Of particular interest is whether or not agent strategies converge to well known…
We study a class of nonzero-sum stochastic differential games between two teams with agents in each team interacting through graphon aggregates. On the one hand, in each large population group, agents act together to optimize a common…
Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to…
A noncooperative differential (dynamic) game model of opinion dynamics is proposed. In this game, the agents' motives are shaped by their expectations of the nature of others' opinions as well as how susceptible they are to get influenced…
We analyse a coalition formation game between strategic service providers of a congestible service. The key novelty of our formulation is that it is a constant sum game, i.e., the total payoff across all service providers (or coalitions of…
We consider the problem in which n items arrive to a market sequentially over time, where two agents compete to choose the best possible item. When an agent selects an item, he leaves the market and obtains a payoff given by the value of…
We study risk-sharing economies where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled…
Statistical mechanics is based on interplay between energy minimization and entropy maximization. Here we formalize this interplay via axioms of cooperative game theory (Nash bargaining) and apply it out of equilibrium. These axioms capture…