This paper tackles learning Stackelberg equilibrium in asymmetric games efficiently from noisy samples.
problem Learning Stackelberg equilibrium in asymmetric, general-sum games efficiently from noisy samples.
method The paper initiates the theoretical study of sample-efficient learning of the Stackelberg equilibrium in bandit feedback setting.
result Sharp positive results on sample-efficient learning of Stackelberg equilibrium with value optimal up to a fundamental gap identified.
Study of insurance market equilibria with risk-averse policyholders.
problem Analyzing optimal insurance contracts in a monopoly market with risk-averse policyholders.
method Modeling Stackelberg equilibria with a profit-maximizing insurer and a risk-averse policyholder.
result Equilibrium contracts exhibit a layer-type structure, providing full insurance over pessimistic loss layers and no coverage over optimistic ones.
Endogenous reinsurance pricing in large insurance markets
problem Endogenous reinsurance pricing in large insurance markets
method Stackelberg leader and insurer equilibrium analysis
result Characterization of insurers' equilibrium retention and Stackelberg equilibria
Study on local convergence of min-max algorithms to differential equilibria on Riemannian manifolds.
problem Solving zero-sum differential games on Riemannian manifolds.
method Analysis of two simultaneous min-max algorithms, τ-GDA and τ-SGA, to differential Stackelberg and Nash equilibria, with conditions for linear convergence and asymptotic approximation. result Established sufficient conditions for linear convergence of τ-GDA and demonstrated faster convergence of τ-SGA in some cases. New RL algorithms find SNE in Markov games with myopic followers.
problem Finding SNE in Markov games with myopic followers.
method Optimistic and pessimistic variants of least-squares value iteration, incorporating function approximation.
result First provably efficient RL algorithms for SNEs in general-sum Markov games with myopic followers.
We deal with the problem of outsourcing the debt for a big investment, according two situations: either the firm outsources both the investment (and the associated debt) and the exploitation to a private consortium, or the firm supports the debt and the investment but outsources the exploitation. We prove the existence…
Paper proposes a game-theoretic approach to generate unlearnable examples.
problem Generating imperceptible perturbations to degrade deep learning models.
method Formulated as a Stackelberg game, proposing a novel attack method GUE.
result GUE effectively poisons models with minimal training data and generalizes well.
A new algorithm learns policies from batch data in hierarchical RL.
problem Learning policies from fixed batches of data without full exploration.
method Modeling RL as a two-player game with a leader-follower structure, proposing StackelbergLearner.
result StackelbergLearner achieves competitive performance in batch RL and real-world datasets.
Neural operators approximate Stackelberg game solutions.
problem Intractability of follower's best-response operator in dynamic Stackelberg games.
method Used attention-based neural operators to approximate the best-response operator.
result Approximate best-response operator yields close game value.
We introduce CSE for MLSF games and devise online learning algorithms for achieving no-external Stackelberg-regret.
problem Learning equilibrium in leader-follower games with noisy bandit feedback.
method Proposed Correlated Stackelberg Equilibrium (CSE) and online learning algorithms balancing exploration and exploitation.
result Achieves no-external Stackelberg-regret, converging to approximate CSE.
Develops a generic two-layer framework for adaptive ABMs.
problem Bi-level adaptation problem in ABMs: agents adapt to environment, and environment adapts to agents.
method Formalizes bi-level problem as a Stackelberg game with conditional policies, solving coupled non-linear equations.
result Unified framework for adaptive ABMs, addressing traditional ABM limitations.
Paper proposes a new method to optimize robot body structure and control policy.
problem Optimizing robot body structure and control policy in a coupled manner.
method Revisits co-design problem as a Stackelberg game, incorporating control adaptation dynamics.
result Stackelberg PPO outperforms standard PPO in stability and performance.
RL models improve target control in SSGs for security applications.
problem Improving RL algorithms for target control in SSGs.
method Investigates improvements to target representations in RL algorithms.
result Enhanced RL models control targets better in SSGs.
Study on reinsurance decisions using mean-variance criterion with irreversible contracts.
problem Optimizing reinsurance premiums and contracts in a Stackelberg game with irreversible contracts.
method Unified singular control framework applied to both discrete and continuous time reinsurance contracts.
result A single once-for-all reinsurance contract is preferred over multiple contracts, and the signing time is crucial.
MAXMINLCB optimizes unknown target functions with preference feedback using a Stackelberg game approach.
problem Optimizing unknown target functions with pairwise comparisons and human feedback.
method MAXMINLCB, a zero-sum Stackelberg game, balances exploration and exploitation.
result MAXMINLCB consistently outperforms existing algorithms with a rate-optimal regret guarantee.
Study optimal investment-reinsurance strategies in equity-linked insurance products using Stackelberg game theory.
problem Optimizing investment and reinsurance strategies in equity-linked insurance products with capital guarantees.
method Modelled as a Stackelberg game where reinsurer acts as leader and insurer as follower, with general utility functions and power utility functions analyzed.
result Derive Stackelberg equilibrium for general utility functions and calculate it explicitly for power utility functions, finding reinsurer optimizes premium to incentivize maximal reinsurance purchase.
Stackelberg Games are gaining importance in the last years due to the raise of Adversarial Machine Learning (AML). Within this context, a new paradigm must be faced: in classical game theory, intervening agents were humans whose decisions are generally discrete and low dimensional. In AML, decisions are made by algorit…
Investors with asymmetric information play a game to optimize their portfolios.
problem Two investors with different information levels compete in portfolio selection.
method Modelled as a Stackelberg game with entropy-regularized mean-variance objectives.
result Equilibria exist where follower's strategy depends on leader's actions.
Federated learning (FL) rests on the notion of training a global model in a decentralized manner. Under this setting, mobile devices perform computations on their local data before uploading the required updates to improve the global model. However, when the participating clients implement an uncoordinated computation …
This paper analyzes a game between insurer and reinsurer under ambiguity and risk aversion, optimizing reinsurance and investment strategies.
problem Optimizing reinsurance and investment strategies in a game between insurer and reinsurer under ambiguity and risk aversion.
method Stackelberg game, α-maxmin mean-variance criterion, Heston's stochastic volatility, Hamilton-Jacobi-Bellman equations, Riccati differential equations. result Excess-of-loss reinsurance is optimal for the insurer, and the equilibrium strategies are determined by specific equations.
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→∞. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that me…
Study shows randomized strategies can't be Nash equilibria in markets with transient price impact.
problem Existence of pure Nash equilibria in markets with transient price impact.
method Considered randomized strategies and showed that they cannot be Nash equilibria.
result Nash equilibria cannot contain randomized strategies.
The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.
problem Characterizing and comparing different types of equilibria for time-inconsistent stopping problems.
method Analyzes log sub-additive discount functions and one-dimensional diffusion processes to derive necessary and sufficient conditions for weak equilibria and other types of equilibria.
result Conditions for weak equilibria and their implications for other types of equilibria are provided.
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.
problem Learning rationalizable behavior in multiplayer games under bandit feedback.
method New algorithms for finding rationalizable Coarse Correlated Equilibria and Correlated Equilibria with polynomial sample complexity.
result Achieved polynomial sample complexity for learning rationalizable equilibria, improving over existing exponential complexity.
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 …
Study global geometry of dynamical systems with entire vector fields.
problem Understanding the global structure of equilibria and their basins.
method Step-by-step analysis of basins of centers, nodes, and foci; introduction of global elliptic sectors.
result Characterization of heteroclinic regions connecting equilibria.
New results on financial equilibria in markets with general semimartingales.
problem Existence and uniqueness of mean-variance equilibria in semimartingale markets.
method Analysis of dynamic mean-variance hedging and fixed-point problems.
result First results allowing for general semimartingales and both discrete and continuous time.
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.
This paper analyzes complex equilibria in a networked bivirus epidemic model.
problem Identify conditions for coexistence equilibria in a networked bivirus model.
method Employ Poincaré-Hopf Theorem with modifications and Morse inequalities.
result Establish properties on the local stability/instability of coexistence equilibria.
New findings show pure strategy equilibria are more robust in a war of attrition game.
problem Analyzing a game of war of attrition under complete information.
method Examined the stability of equilibria in pure and mixed strategies under varying payoffs.
result Pure strategy equilibria are more robust to perturbations of the canonical model.
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
An informed broker optimizes trading strategies in a market influenced by many traders.
problem Optimizing trading strategies for an informed broker in a market with many traders.
method Developed a mean-field game approach to derive equilibrium strategies for both the broker and traders.
result The broker's optimal strategy involves a Stackelberg equilibrium, leading and traders following.
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…
A game-theoretic approach simplifies MBRL design and improves sample efficiency.
problem Designing stable and efficient MBRL algorithms using rich function approximators.
method Develops a game-theoretic framework where MBRL is modeled as a Stackelberg game between policy and model players.
result Proposed algorithms are highly sample efficient and match asymptotic performance of model-free policy gradient.
This paper investigates a hybrid stochastic differential reinsurance and investment game between one reinsurer and two insurers, including a stochastic Stackelberg differential subgame and a non-zero-sum stochastic differential subgame. The reinsurer, as the leader of the Stackelberg game, can price reinsurance premium…
Study optimal reinsurance pricing under model uncertainty for multiple insurers.
problem Optimal reinsurance pricing in the presence of multiple sources of model uncertainty.
method Solves a continuous-time Stackelberg game for general reinsurance contracts, considering entropy penalties and ambiguity in insurers' models.
result Reinsurer prices under a distortion of the barycentre of insurers' models, maximizing expected wealth with an entropy penalty.
The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.
problem Existence and uniqueness of Nash equilibria in multiplicative performance criteria games.
method General characterization of Nash equilibria for a large class of utility functions.
result Existence and uniqueness of Nash equilibria for arbitrary initial wealth vectors.
Study of MHD equilibria with orientation-reversing symmetry, showing all orbits are periodic.
problem Understanding MHD equilibria with non-reflection symmetry.
method Topological techniques to analyze invariant 2-tori and their orbits.
result All orbits on tori are periodic under certain conditions.
Study on symmetries and equilibria in Poisson manifolds, with applications to rigid body dynamics.
problem Characterizing conformal relative equilibria on Poisson manifolds.
method Introducing conformally Poisson actions and momentum maps, establishing algebraic criteria.
result Classification of nontrivial conformal relative equilibria in Lie algebras, with applications to rigid body dynamics.
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.
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 ∂K with respect to O. The formula extends to the case where O lies on the evolute of ∂K and a suitably modified version ho…
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 …
Study optimal stopping times for multi-dimensional processes with non-exponential discounting.
problem Optimal stopping in multi-dimensional processes with non-exponential discounting.
method Probabilistic potential theory to establish existence of optimal equilibria.
result Existence of optimal equilibria for multi-dimensional stopping problems.
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.
problem Challenges in learning equilibria in non-stationary multi-agent systems.
method Versatile black-box approach applicable to various games, including general-sum, potential, and Markov games.
result Achieves optimal regret bounds for non-stationary games, with or without knowledge of total variation.