arXiv research

Study optimal stopping times for multi-dimensional processes with non-exponential discounting.

This paper analyzes complex equilibria in a networked bivirus epidemic model.

We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of vector fields on differentiable stacks. Here we argue in favor of the usefulness of …

Given a multifunction from $X$ to the $k-$fold symmetric product $Sym_k(X)$, we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixe…

A new game-theoretic approach balances downside risk with expected reward.

Study finds unique self-expanders for mean curvature flow.

Study explores optimal strategies in games with multiple players and mean-field interactions.

The paper analyzes game theory in convertible contracts during liquidity events.

We present a framework for studying the dynamics of equivariant vector fields near relative equilibria. To overcome the lack of linearization at a relative equilibrium or the possible non-smoothness of the orbit space, we categorify the space of equivariant vector fields. A category where the objects are equivariant ve…

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that me…

Game theory helps analyze ESOs/EBIs in production and service sectors.

Modeling European spot power markets with game theory for Nash equilibria.

Study shows randomized strategies can't be Nash equilibria in markets with transient price impact.

Extends algorithms for computing $Φ$-equilibria to higher polynomial dimensions.

The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.

We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…

For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.

Paper develops efficient algorithms for learning rationalizable equilibria in multiplayer games.

A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak …

Game theory finds nowadays a broad range of applications in engineering and machine learning. However, in a derivative-free, expensive black-box context, very few algorithmic solutions are available to find game equilibria. Here, we propose a novel Gaussian-process based approach for solving games in this context. We f…

Study global geometry of dynamical systems with entire vector fields.

We study constrained nonconvex optimization problems in machine learning, signal processing, and stochastic control. It is well-known that these problems can be rewritten to a minimax problem in a Lagrangian form. However, due to the lack of convexity, their landscape is not well understood and how to find the stable e…

The dual crises of the sub-prime mortgage crisis and the global financial crisis has prompted a call for explanations of non-equilibrium market dynamics. Recently a promising approach has been the use of agent based models (ABMs) to simulate aggregate market dynamics. A key aspect of these models is the endogenous emer…

Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of recent advances in equilibrium computation for probabilistic inference. We present formulations of inference problems in Markov random f…

New results on financial equilibria in markets with general semimartingales.

We prove a criterion for stability of relative equilibria in symmetric Hamiltonian systems at singular points of the momentum map. This generalizes a theorem of G.W. Patrick. The method of the proof is also useful in studying the bifurcation of relative equilibria.

New findings show pure strategy equilibria are more robust in a war of attrition game.

We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.

Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the equilibrium allocation are m…

In this paper the possibility of computing equilibrium in pure exchange and production economies by a homotopy method is investigated. The performance of the algorithm is tested on examples with known equilibria taken from the literature on general equilibrium models and numerical results are presented. In computing eq…

End-to-end model predicts multiagent trajectories using game theory and neural nets.

The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.

Study of MHD equilibria with orientation-reversing symmetry, showing all orbits are periodic.

Study on symmetries and equilibria in Poisson manifolds, with applications to rigid body dynamics.

New method finds all Nash equilibria via vector optimization.

We obtain a formula for the number of horizontal equilibria of a planar convex body $K$ with respect to a center of mass $O$ in terms of the winding number of the evolute of $\partial K$ with respect to $O$. The formula extends to the case where $O$ lies on the evolute of $\partial K$ and a suitably modified version ho…

We undertake a fundamental study of network equilibria modeled as solutions of fixed point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk in networks of financial institutions interconnected by mutual obligations and is…

New approach tackles non-stationary multi-agent games with black-box methods.

We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist.

We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function whose output is being applied to a bilinear zero-sum game. This class of games is motivated by the indirect nature of the competition in Ge…

This work finds mixed equilibria in zero-sum games using interacting particle dynamics.

The paper explores scaling symmetries in symplectic geometry and their applications to central configurations.

The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria in games where the payoffs are probability distributions. Our appr…

The paper defines and solves time-inconsistent stopping control problems in multi-dimensional diffusion models.

Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal constraints.We deal with random endowment density streams which admit jumps and g…

In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We p…

The paper solves portfolio optimization problems with risk constraints.

Optimal fees for CFMMs prevent liquidity pools from competing to the bottom.