Related papers: The Adversarial Stackelberg Value in Quantitative …

We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general \cadlag measurable processes. As a by-product of…

We develop an analytical Stackelberg game framework for optimal resource allocation in a sequential attacker--defender setting with a finite set of assets and probabilistic attacks. The defender commits to a mixed protection strategy, after…

We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges…

Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…

The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. Most of our assumptions…

In this paper we introduce and study {\em all-pay bidding games}, a class of two player, zero-sum games on graphs. The game proceeds as follows. We place a token on some vertex in the graph and assign budgets to the two players. Each turn,…

Two-player zero-sum repeated games are well understood. Computing the value of such a game is straightforward. Additionally, if the payoffs are dependent on a random state of the game known to one, both, or neither of the players, the…

Mutually beneficial behavior in repeated games can be enforced via the threat of punishment, as enshrined in game theory's well-known "folk theorem." There is a cost, however, to a player for generating these disincentives. In this work, we…

This paper examines finite zero-sum stochastic games and demonstrates that when the game's duration is sufficiently long, there exists a pair of approximately optimal strategies such that the expected average payoff at any point in the game…

Two-player games on graphs provide the mathematical foundation for the study of reactive systems. In the quantitative framework, an objective assigns a value to every play, and the goal of player 1 is to minimize the value of the objective.…

Anticipating the strategies of potential attackers is crucial for protecting critical infrastructure. We can represent the challenge of the defenders of such infrastructure as a Stackelberg security game. The defender must decide how to…

The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine…

A two-player finite horizon linear-quadratic Stackelberg differential game is considered. The feature of this game is that the control cost of a follower in the cost functionals of both players is small, which means that the game under…

We consider a repeated sequential game between a learner, who plays first, and an opponent who responds to the chosen action. We seek to design strategies for the learner to successfully interact with the opponent. While most previous…

This article considers a problem arising from a two-player game based on the classical secretary problem. First, Player 1 selects one object from a sequence as in the secretary problem. All of the other objects are then presented to Player…

The paper is concerned with a zero-sum Stackelberg stochastic linear-quadratic (LQ, for short) differential game over finite horizons. Under a fairly weak condition, the Stackelberg equilibrium is explicitly obtained by first solving a…

Two-player zero-sum "graph games" are a central model, which proceeds as follows. A token is placed on a vertex of a graph, and the two players move it to produce an infinite "play", which determines the winner or payoff of the game.…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

We analyze the Gambler's problem, a simple reinforcement learning problem where the gambler has the chance to double or lose the bets until the target is reached. This is an early example introduced in the reinforcement learning textbook by…

When opposing parties compete for a prize, the sunk effort players exert during the conflict can affect the value of the winner's reward. These spillovers can have substantial influence on the equilibrium behavior of participants in…