Related papers: Zero-Sum Stochastic Stackelberg Games
A growing line of work reframes preference-based fine-tuning of large language models game-theoretically: Nash Learning from Human Feedback (NLHF) recasts the problem as a zero-sum game over policies. However, optimization is over expected…
We consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
Resource competition problems are often modeled using Colonel Blotto games, where players take simultaneous actions. However, many real-world scenarios involve sequential decision-making rather than simultaneous moves. To model these…
Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain…
We study the game modification problem, where a benevolent game designer or a malevolent adversary modifies the reward function of a zero-sum Markov game so that a target deterministic or stochastic policy profile becomes the unique Markov…
In this paper, we first devise two algorithms to determine whether or not a bimatrix game has a strategically equivalent zero-sum game. If so, we propose an algorithm that computes the strategically equivalent zero-sum game. If a given…
We study model-based and model-free policy optimization in a class of nonzero-sum stochastic dynamic games called linear quadratic (LQ) deep structured games. In such games, players interact with each other through a set of weighted…
The Stackelberg game model, where a leader commits to a strategy and the follower best responds, has found widespread application, particularly to security problems. In the security setting, the goal is for the leader to compute an optimal…
We consider the problem of efficiently learning to play single-leader multi-follower Stackelberg games when the leader lacks knowledge of the lower-level game. Such games arise in hierarchical decision-making problems involving…
Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…
This paper introduces the new concept of (follower) satisfaction in Stackelberg games and compares the standard Stackelberg game with its satisfaction version. Simulation results are presented which suggest that the follower adopting…
In this work, we use a Stackelberg infinite discrete-time dynamic game model to study the optimal supply schedule and the optimal demand response under a market-driven dynamic price. A two-layer optimization framework is established. At the…
We study finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals. We derive the Nash equilibrium explicitly by converting the first-order conditions into a coupled…
In this paper, we investigate a class of nonzero-sum dynamic stochastic games, where players have linear dynamics and quadratic cost functions. The players are coupled in both dynamics and cost through a linear regression (weighted average)…
The mathematical characterization of social-distancing games in classical epidemic theory remains an important question, for their applications to both infectious-disease theory and memetic theory. We consider a special case of the dynamic…
By utilizing tools from game theory, we develop a novel multi-period-multi-company demand response framework considering the interactions between companies (sellers of energy) and their consumers (buyers of energy). We model the…
This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost…
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…
We study nonzero-sum stochastic switching games. Two players compete for market dominance through controlling (via timing options) the discrete-state market regime $M$. Switching decisions are driven by a continuous stochastic factor $X$…