Related papers: The Inaccessible Game
This work is an application of game theory to quantum information. In a state estimate, we are given observations distributed according to an unknown distribution $P_{\theta}$ (associated with award $Q$), which Nature chooses at random from…
Pursuit-evasion scenarios appear widely in robotics, security domains, and many other real-world situations. We focus on two-player pursuit-evasion games with concurrent moves, infinite horizon, and discounted rewards. We assume that the…
This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with perfect or almost perfect information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general…
We study zero-sum differential games with state constraints and one-sided information, where the informed player (Player 1) has a categorical payoff type unknown to the uninformed player (Player 2). The goal of Player 1 is to minimize his…
This paper studies a system security problem in the context of observability based on a two-person noncooperative infinitely repeated game. Both the attacker and the defender have means to modify the dimension of the unobservable subspace,…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
We introduce a problem set-up we call the Iterated Matching Pennies (IMP) game and show that it is a powerful framework for the study of three problems: adversarial learnability, conventional (i.e., non-adversarial) learnability and…
In this paper we consider an infinite horizon zero-sum differential game where the dynamics of each player and the running cost are also depending on the evolution of some discrete (switching) variables. In particular, such switching…
The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…
We develop a hierarchical Bayesian dynamic game for competitive inventory and pricing under incomplete information. Two firms repeatedly choose order quantities and prices while facing two layers of uncertainty: unknown market demand and…
We formulate and analyze a general class of stochastic dynamic games with asymmetric information arising in dynamic systems. In such games, multiple strategic agents control the system dynamics and have different information about the…
In this work we investigate the information loss in (nonlinear) dynamical input-output systems and provide some general results. In particular, we present an upper bound on the information loss rate, defined as the (non-negative) difference…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
We consider a game-theoretic setting to model the interplay between attacker and defender in the context of information flow, and to reason about their optimal strategies. In contrast with standard game theory, in our games the utility of a…
In a situation where each player has control over the transition probabilities of each subsystem, we game-theoretically analyze the optimization problem of minimizing both the partial entropy production of each subsystem and a penalty for…
We provide a necessary and sufficient condition under which a convex set is approachable in a game with partial monitoring, i.e.\ where players do not observe their opponents' moves but receive random signals. This condition is an extension…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium…
In this work, conditional entropy is used to quantify the information loss induced by passing a continuous random variable through a memoryless nonlinear input-output system. We derive an expression for the information loss depending on the…
We propose InfoChess, a symmetric adversarial game that elevates competitive information acquisition to the primary objective. There is no piece capture, removing material incentives that would otherwise confound the role of information.…