This paper simplifies the Nash Bargaining Solution for use in intellectual property cases.
problem Limited application of Nash Bargaining Solution in assigning intellectual property damages.
method Normalizes the Nash Bargaining Solution and provides a methodology for determining bargaining weight.
result Clarifies the application of Nash Bargaining Solution to specific case facts.
Paper refines royalty determination using Bayesian methods.
problem Determining a reasonable royalty with risk and uncertainty.
method Bayesian Cost approach to refine Nash Bargaining Solution.
result Nash Bargaining Solution emerges as more reliable.
The paper tackles fair sharing of exploration costs across groups in online learning.
problem Sharing the cost of exploration fairly across multiple groups in online learning.
method The paper introduces the 'grouped' bandit model and uses axiomatic bargaining theory, specifically the Nash bargaining solution, to formalize fairness.
result The paper derives policies that are optimally fair and regret-optimal, showing that regret-optimal policies can be unfair.
NAMEx merges experts using Nash bargaining for improved performance.
problem Sparse Mixture of Experts merging strategies lack a principled weighting mechanism.
method Reinterpreting expert merging through game theory, introducing Nash Merging and complex momentum.
result NAMEx consistently outperforms competing methods across various tasks and system sizes.
We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents' strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial…
Proposes a value-oriented forecast reconciliation method for renewables in electricity markets.
problem Forecast reconciliation overlooks the value of forecasts in decision-making, leading to unfair outcomes.
method Value-oriented forecast reconciliation using a Nash bargaining framework and a primal-dual algorithm for parameter estimation.
result Consistently increases profits for all agents involved in an aggregated wind energy trading problem.
A new approach to group fairness treats it as a bargaining problem.
problem Fairness in deploying predictors across subpopulations.
method Interpreting fairness as a bargaining problem and proposing relative improvement.
result Relative improvement provides axiomatic justification and finite-sample convergence guarantees.
We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an epsi…
Our work extends Coase's theorem to settings with uncertainty, showing how to maximize social welfare through property rights and learning.
problem Theoretical models of externality often assume perfect knowledge, limiting practical solutions.
method We extend Coase's theorem to a two-player bandit setting with uncertainty, designing a learning policy to maximize social welfare.
result We show that property rights and learning can recover Coase's theorem in settings with uncertainty.
PropFair algorithm ensures fair performance in federated learning.
problem Ensuring fair performance in federated learning for diverse clients.
method PropFair, a novel algorithm based on bargaining games, finds proportionally fair solutions.
result PropFair approximately finds proportional fairness solutions and balances average and worst 10% client performances.
We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations which do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world and the reservation prices …
The article improves the display of acceptable exchange ratios for merging companies.
problem Determining feasible exchange ratios for merging companies.
method Exploits a diagrammatic approach to display the bargaining region.
result Shares face upper and lower bounds for acceptable exchange ratios.
New method finds all Nash equilibria via vector optimization.
problem Finding all Nash equilibria in games.
method Formulate vector optimization problem to find Pareto optimal solutions.
result Characterize set of all Nash equilibria as Pareto optimal solutions.
Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash equilibrium (NE), which implies that there are no guarantees on the quality of the found…
Paper analyzes solutions to quasilinear elliptic equations on manifolds using Nash-Moser iteration.
problem Analyzing positive solutions to quasilinear elliptic equations on manifolds with bounded Ricci curvature.
method Employing Nash-Moser iteration technique to derive logarithmic gradient estimates and Liouville properties.
result Derives universal logarithmic gradient estimates for positive solutions under certain conditions.
Study Nash equilibrium between broker and informed trader in dealer and lit markets.
problem Nash equilibrium between broker and informed trader in dealer and lit markets with partial information.
method Convex analysis, FBSDEs, polynomial approximation.
result Existence and uniqueness of Nash equilibrium for short time horizons.
Ancient Ricci flows with bounded Nash entropy have uniform Sobolev inequalities.
problem Bounding Nash entropy in ancient Ricci flows.
method Uniformly bounded Nash entropy implies uniform bounds on the ν-functional, leading to uniform logarithmic and Sobolev inequalities.
result Uniform logarithmic and Sobolev inequalities on ancient Ricci flows with bounded Nash entropy.
Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and…
I derive practical formulas for optimal arrangements between sophisticated stock market investors (namely, continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lend them cash for leveraged bets on a high Sharpe asset (i.e. the market portfolio). Rather than, say, the broker posting a m…
The paper studies gradient estimates for solutions of a nonlinear elliptic equation on Riemannian manifolds.
problem Gradient estimates for solutions of a specific nonlinear elliptic equation on Riemannian manifolds.
method Nash-Moser iteration method
result Gradient estimates and Liouville type theorems for positive solutions.
Study shows how multiple traders can trade together without excessive price impact.
problem Coordination issues in trading to exploit a common signal.
method Closed-loop Nash competition model for stochastic differential games.
result Excessive trading reduced but not significantly for practical parameters.
Study Nash equilibrium between broker and trader in a lit exchange with price impact.
problem Optimizing trading strategies between informed and uninformed traders with broker's inventory penalties.
method Characterized Nash equilibrium through FBSDEs, solved explicitly.
result Explicit solution to trading strategies of broker and informed trader.
Study Nash competition among dealers quoting prices to clients with unknown trading motives.
problem Adverse selection and inventory costs in dealer-client interactions.
method Analyzes one-shot Nash competition with unknown client type and inventory constraints.
result Unique symmetric Nash equilibrium exists and can be characterized by a nonlinear ODE.
Agents trained with reinforcement learning deviate from Nash equilibrium in optimal execution game.
problem Deviation of reinforcement learning strategies from Nash equilibrium in optimal execution game.
method Two-player optimal execution game with reinforcement learning algorithms (Double Deep Q-Learning).
result Strategies learned by agents deviate significantly from Nash equilibrium, exhibiting supra-competitive solutions.
Study Nash equilibria in mean field portfolio games with consumption.
problem Finding Nash equilibria in mean field portfolio games with consumption.
method Established a correspondence between equilibria and solutions to FBSDEs, using martingale and dynamic programming principles.
result Proved the uniqueness of Nash equilibrium in closed form under certain conditions.
Improves GANs training through game theory.
problem Hard training of GANs due to antagonistic networks.
method Rewrote GAN training as a variational inequality and introduced a stochastic relaxed forward-backward algorithm.
result Algorithm converges to an exact solution or a neighborhood of it under monotonicity.
Develops a game-theoretic approach to solve SGEP efficiently.
problem Efficiently solving the symmetric generalized eigenvalue problem for large datasets.
method Formulates SGEP as a Nash equilibrium in a game-theoretic context and develops a parallelizable algorithm.
result Achieves O(dk) runtime complexity, making it feasible for large-scale problems. Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.
problem Time-inconsistent stochastic control problems with mean and higher-order moments.
method Developed closed-loop and open-loop Nash equilibrium controls using PDEs and maximum principles.
result Identical closed-loop and open-loop Nash equilibria controls, independent of state value and random path.
We analyze a market impact game between n risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in t…
Study analyzes portfolio liquidation games influenced by self-exciting order flow.
problem Analyzing portfolio liquidation strategies with market order dynamics.
method Mean-field control problem, novel FBSDE system, sufficient maximum principle.
result Existence and uniqueness of open-loop Nash equilibria proved.
Investigates time-inconsistent portfolio selection under MMV preferences.
problem Time-inconsistent optimal strategies for MMV preferences.
method Nash equilibrium controls for MMV and MV preferences, solving FBSDE and HJB equations.
result MMV optimal strategies lead to higher investment amounts than MV strategies, narrowing over time.
We provide an exact analytical solution of the Nash equilibrium for k- price auctions. We also introduce a new type of auction and demonstrate that it has fair solutions other than the second price auctions, therefore paving the way for replacing second price auctions.
New systemic risk models for banks choosing their group memberships.
problem Analyzing systemic risk for banks in disjoint and overlapping groups.
method Proposed new models with realistic game features, introducing Nash equilibrium for optimal solution.
result Explicit solution for risk allocation and existence/uniqueness of Nash equilibrium.
Transient market impact explained via Nash equilibrium in a game.
problem Understanding the transient nature of market impact.
method Analyzing a game between a trader and an arbitrageur, deriving decay kernels.
result Implied transient impact can be derived from trader behavior at Nash equilibrium.
We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain aroun…
We consider n risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions f…
The paper provides new gradient estimates for solutions to a nonlinear elliptic equation on smooth metric measure spaces.
problem Gradient estimates for solutions to a specific nonlinear elliptic equation on smooth metric measure spaces.
method Nash-Moser iteration technique to obtain local gradient estimates.
result New local gradient estimates for positive solutions to the equation.
Gradient estimates derived for solutions of a specific elliptic equation on Riemannian manifolds.
problem Gradient estimates for solutions of a specific elliptic equation on Riemannian manifolds.
method Nash-Moser iteration technique to derive gradient estimates.
result Gradient estimates for positive solutions under certain curvature conditions.
Proposes a deep learning method for solving complex financial games with delays.
problem Financial modeling with multi-agent interactions and delayed effects.
method Parameterizes controls using recurrent neural networks and trains them with modified fictitious play.
result Demonstrates effectiveness on finance problems with known solutions and new problems with derived Nash equilibria.
This paper tackles global Nash equilibrium in non-convex multi-player games.
problem Challenges in finding global Nash equilibrium due to non-convexity.
method Conjugate transformation and variational inequality formulation to prove existence and design algorithms.
result Designs an ODE-based algorithm with exponential convergence rate and proves its effectiveness in practical scenarios.
Generative Adversarial Networks (GAN) have become one of the most successful frameworks for unsupervised generative modeling. As GANs are difficult to train much research has focused on this. However, very little of this research has directly exploited game-theoretic techniques. We introduce Generative Adversarial Netw…
Let M and N be Nash manifolds, and f and g Nash maps from M to N. If M and N are compact and if f and g are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, Cinfty R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash…
This work models GHG offset credit markets to find optimal strategies for market participants.
problem Optimizing GHG offset credit markets to reduce emissions and penalize excess emissions.
method Characterized optimal behavior in single-player and two-player GHG offset credit markets using optimal stopping and control problems, and mixed-Nash equilibria.
result Market participants benefit from optimal OC trading and generation, highlighting the importance of acting optimally.
Study analyzes market equilibrium returns with price impact and transaction costs.
problem Modeling equilibrium returns in markets with strategic order placement and transaction costs.
method Analyzes frictionless and transaction-cost markets, characterizes Nash equilibrium via FBSDEs.
result Equilibrium returns are affected by transaction costs, especially with noise traders.
New formulas derived for scalar curvature in generalized Ricci flow.
problem Scalar curvature in generalized Ricci flow.
method Derivation of weighted scalar curvature monotonicity formulas and Perelman-type energy/entropy formulas.
result New convex Nash entropies and pseudolocality principles.
Optimizes asset allocation for risk measures in a Lévy market.
problem Maximizing time-consistent mean-risk reward with general risk measures.
method Uses a generalized Lévy market model and Hamilton-Jacobi-Bellman equation.
result Deterministic optimal solution under certain conditions.
Nash's theorem proved with Günther's trick
problem Proving Nash's smooth embedding theorem
method Using Günther's trick
result Nash's theorem proved
The paper uses Nash-Moser iteration to prove gradient estimates for nonlinear equations on Riemannian manifolds.
problem Proving gradient estimates for solutions of nonlinear equations on Riemannian manifolds.
method Employing Nash-Moser iteration technique to establish gradient estimates.
result Gradient estimates for solutions of nonlinear equations on Riemannian manifolds are proven.