Related papers: On Dynamic Programming Theory for Leader-Follower …
Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…
In this paper, we consider a discrete-time Stackelberg mean field game with a finite number of leaders, a finite number of major followers and an infinite number of minor followers. The leaders and the followers each observe types privately…
In supervised learning, decision trees are valued for their interpretability and performance. While greedy decision tree algorithms like CART remain widely used due to their computational efficiency, they often produce sub-optimal solutions…
In this paper we study stochastic dynamic games with many players; these are a fundamental model for a wide range of economic applications. The standard solution concept for such games is Markov perfect equilibrium (MPE), but it is well…
Synthesizing near-optimal mixed strategies for zero-sum differential games (ZSDGs) has been a longstanding challenge. Existing research mainly focuses on characterizing the theoretical value function, while the practical design of…
This paper studies a new class of dynamic optimization problems of large-population (LP) system which consists of a large number of negligible and coupled agents. The most significant feature in our setup is the dynamics of individual…
It is well known that for any finite state Markov decision process (MDP) there is a memoryless deterministic policy that maximizes the expected reward. For partially observable Markov decision processes (POMDPs), optimal memoryless policies…
Similar to the role of Markov decision processes in reinforcement learning, Stochastic Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. In this paper, we derive…
This paper focuses on zero-sum stochastic differential games in the framework of forward-backward stochastic differential equations on a finite time horizon with both players adopting impulse controls. By means of BSDE methods, in…
We study the performance of the gradient play algorithm for stochastic games (SGs), where each agent tries to maximize its own total discounted reward by making decisions independently based on current state information which is shared…
We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that…
We present a method for active inference with partial observations in stochastic systems through incentive design, also known as the leader-follower game. Consider a leader agent who aims to infer a follower agent's type given a finite set…
Many real-world decision problems involve the interaction of multiple self-interested agents with limited sensing ability. The partially observable stochastic game (POSG) provides a mathematical framework for modeling these problems,…
Through a stochastic control theoretic approach, we analyze reputation games where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the…
As intelligent robots like autonomous vehicles become increasingly deployed in the presence of people, the extent to which these systems should leverage model-based game-theoretic planners versus data-driven policies for safe,…
This paper is concerned with the leader-following output consensus problem in the framework of distributed nonlinear observers. In stead of certain hypotheses on the leader system, a group of geometric conditions is put forward to develop a…
There has been significant recent interest in leader-follower security games, where the leader dominates the decision process with the Stackelberg equilibrium (SE) strategy. However, such a leader-follower scheme may become invalid in…
In a stochastic Stackelberg asymmetric security game, the strong Stackelberg equilibrium (SSE) strategy is a popular option for the defender to get the highest utility against an attacker with the best response (BR) strategy. However, the…
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…
Recent work [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits linear optimal cost and the associated…