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. 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.
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.
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.
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 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.
The paper analyzes strategic interactions in a multi-agent reinsurance chain using game theory.
problem Strategic behavior and competition among insurers and reinsurers in a multi-layer reinsurance chain.
method Employed Stackelberg differential games and non-zero-sum game models to characterize strategic interactions. Used dynamic programming and game theory to derive equilibrium strategies for investment and reinsurance.
result Intensified competition leads to reduced safety loadings in reinsurance contracts.
Two-layer model studies reinsurance contracts and competition between insurer and reinsurers.
problem Modeling and analyzing reinsurance contracts and competition between insurer and reinsurers.
method Two-layer stochastic game model with insurer negotiating with reinsurers, and reinsurers competing for business.
result Existence and uniqueness of equilibrium strategies for the insurer and reinsurers, characterized in semiclosed form.
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
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.
The paper analyzes reinsurance strategies in a competitive multi-agent system.
problem Strategic interactions and competitive behavior in multi-layer reinsurance chains.
method Stochastic differential games and non-zero-sum game models to characterize strategic interactions. Dynamic programming and game theory to derive equilibrium strategies.
result Intensified competition reduces safety loadings in reinsurance contracts.
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.
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.
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.
Study on optimal trading in a finite population with market frictions and asymmetric information.
problem Optimal trading in a finite population with market frictions and asymmetric information.
method Investigates stochastic differential games with asymmetric information and market frictions, proving existence and uniqueness of Nash and Stackelberg-Nash equilibria.
result Existence and uniqueness of Nash and Stackelberg-Nash equilibria in both unconstrained and constrained trading scenarios.
Brokers and an informed trader compete for liquidity, affecting trading costs and inventory risk.
problem How brokers and an informed trader manage liquidity and trading costs.
method Sequential Stackelberg game, solving for trading strategies, numerical solutions.
result Equilibrium strategies and liquidity prices determined, not Pareto efficient.
New RL algorithms learn QSE from strategic feedbacks with sample efficiency.
problem Learning QSE in Markov games with strategic feedbacks.
method Proposes sample-efficient algorithms for online and offline settings, combining quantal response model learning and RL.
result Achieves sublinear regret bounds and quantifies model uncertainty.
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.
Optimal penalties for RECs balance environmental and revenue impacts.
problem Optimizing penalties for RECs to balance environmental and revenue impacts.
method Mean field games and extended McKean-Vlasov control problems.
result Optimal penalty function is linear in agents' state.
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.
Game theory model for optimal trading with end-of-day constraints.
problem Optimal trading strategy in a game between slow and fast traders.
method Coupled stochastic control problems, Fredholm integral equation solution.
result Explicit solution to the game with profitable strategies for both players.
Study of 2imes2 zero-sum games with noisy observations and commitments.
problem Analyzing 2imes2 zero-sum games with noisy observations and commitments. method Modeling a 2imes2 zero-sum game with a leader committing to a strategy and a follower observing a noisy version of the leader's action. result Observing the leader's action is either beneficial or immaterial for the follower, and the equilibrium payoff is bounded.
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 study the problem of alleviating the instability issue in the GAN training procedure via new architecture design. The discrepancy between the minimax and maximin objective values could serve as a proxy for the difficulties that the alternating gradient descent encounters in the optimization of GANs. In this work, we…
Paper proposes incentive mechanism to encourage participation in federated learning.
problem Users are reluctant to participate in federated learning due to privacy concerns.
method Formulated as a two-stage Stackelberg game, designed an incentive mechanism to select and compensate users.
result Demonstrated effectiveness of the proposed incentive mechanism through simulations.
Paper analyzes convergence of GDA for nonconvex-nonconcave minimax problems.
problem Understanding convergence of GDA for nonconvex-nonconcave minimax problems.
method Local convergence analysis of GDA with stepsize ratio Θ(κ).
result Stepsize ratio of Θ(κ) is necessary and sufficient for local convergence of GDA to a Stackelberg Equilibrium.
Optimal dynamic allocation of carbon allowances reduces emissions efficiently.
problem Reducing carbon emissions from firms over time with dynamic allocation and trading.
method Variational approach to solve the Stackelberg game between regulator and firms.
result Optimal policies lead to constant abatement effort and allowance price, outperforming static allocations.
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.
SLHF uses sequential game theory to optimize preferences from human feedback.
problem Optimizing preferences from human feedback in sequential settings.
method SLHF frames the problem as a sequential-move game between Leader and Follower, decomposing the optimization into refinement and adversarial optimization.
result SLHF achieves strong alignment across diverse preference datasets and scales to large models.
For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as…
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.
EI-MTD defends edge intelligence against adversarial attacks with dynamic scheduling.
problem Adversarial attacks on edge intelligence models.
method EI-MTD uses differential knowledge distillation to create robust member models and a dynamic scheduling policy based on a Bayesian Stackelberg game.
result EI-MTD effectively protects edge intelligence from black-box adversarial attacks.
We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the generation of permanent price impact, thereby aggregating an ever increasing risky position in foreign reserves. We describe this situation…
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.
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…
We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and …
Paper generalizes Hardy-Rogers maps for market equilibrium analysis in duopoly markets.
problem Existence and uniqueness of market equilibrium in duopoly markets with non-differentiable, nonlinear response functions.
method Coupled fixed points approach for generalized Hardy-Rogers maps.
result Enriched understanding of market equilibrium in duopoly markets with non-differentiable response functions.
Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
problem Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
method Established existence of solution for Markovian quadratic BSDEs with discontinuous generators using unique continuation and backward uniqueness.
result Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
Deep fictitious play converges to Nash equilibrium in stochastic differential games.
problem Finding Nash equilibrium in large stochastic differential games.
method Decouples the game into sub-optimization problems and solves each player's optimal strategy with deep BSDE method.
result Deep fictitious play converges to the true Nash equilibrium.
This paper studies the transition from disequilibrium to equilibrium in financial markets.
problem Modeling financial markets as disequilibrium models and analyzing their transition to equilibrium.
method Mathematical analysis using asymptotic limits and Tikhonov-Fenichel reduction.
result Stability of the reduced equilibrium model and economic implications are discussed.
Study shows finite agent equilibrium converges to mean-field limit in asset pricing.
problem Asset pricing equilibrium in markets with finite vs infinite agents.
method Existence of finite agent equilibrium and strong convergence to mean-field limit.
result Finite agent equilibrium converges to mean-field limit under suitable conditions.
Insider trading is reduced when penalized, affecting expected penalties in a non-monotone way.
problem Reducing insider trading behavior when insiders face legal penalties.
method Characterized via a backward stochastic differential equation (BSDE) with a non-linear operator.
result The insider's expected penalties are non-monotone in the fee structure and determined by relative entropy.
Study how transaction costs impact stock returns and holdings in equilibrium.
problem Impact of quadratic transaction costs on equilibrium stock returns and holdings.
method Developed a continuous-time risk-sharing model with FBSDEs to characterize equilibrium stock holdings and trading rates.
result Equilibrium stock holdings and trading rates are uniquely determined by FBSDEs, and equilibrium return by a system of coupled FBSDEs.
Modeling DEX liquidity with heterogeneous LPs and MEV bots.
problem Understanding and predicting the dynamics of decentralized cryptocurrency exchanges.
method Mean-field game approach to model liquidity providers' optimal strategies and interactions.
result Calibrated model produces consistent pool exchange rate dynamics and liquidity evolution.
Proposes a robust equilibrium strategy for mean-variance portfolio selection.
problem Time-inconsistency in mean-variance portfolio selection.
method Introduces a novel definition of robust equilibrium strategy and solves the corresponding PDE system.
result A classical solution to the PDE system implies a robust equilibrium strategy.
Optimal insurance contracts are designed to screen risk preferences and risk types under asymmetric information.
problem Designing optimal insurance contracts under asymmetric information and risk types.
method Constructing a menu of contracts that maximizes mean-variance utilities, subject to truth-telling constraints.
result Equilibrium contracts exhibit nonlinear pricing with decreasing risk loadings, inducing self-selection.
In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional…