Related papers: Trapping the Ultimate Success
The orienteering problem is a well-studied and fundamental problem in transportation science. In the problem, we are given a graph with prizes on the nodes and lengths on the edges, together with a budget on the overall tour length. The…
Agents rarely act in isolation -- their behavioral history, in particular, is public to others. We seek a non-asymptotic understanding of how a leader agent should shape this history to its maximal advantage, knowing that follower agent(s)…
Individual sports competitions provide a natural setting for examining the relative importance of talent and luck/chance in achieving success. The belief that success is primarily due to individual abilities and hard work rather than…
We study the existence of optimal actions in a zero-sum game $\inf_{\tau}\sup_PE^P[X_{\tau}]$ between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem $\inf_{\tau}\mathcal{E}(X_{\tau})$…
We consider the Bilevel Knapsack with Interdiction Constraints, an extension of the classic 0-1 knapsack problem formulated as a Stackelberg game with two agents, a leader and a follower, that choose items from a common set and hold their…
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…
Game balancing is an important part of the (computer) game design process, in which designers adapt a game prototype so that the resulting gameplay is as entertaining as possible. In industry, the evaluation of a game is often based on…
This study presents a rigorous mathematical approach to the optimization of round and betting policies in Blackjack, using Markov Decision Processes (MDP) and Expected Utility Theory. The analysis considers a direct confrontation between a…
In a guessing game, players guess the value of a random real number selected using some probability density function. The winner may be determined in various ways; for example, a winner can be a player whose guess is closest in magnitude to…
We study the problem of online learning in a two-player decentralized cooperative Stackelberg game. In each round, the leader first takes an action, followed by the follower who takes their action after observing the leader's move. The goal…
This paper is concerned with the closed-loop solvability of one kind of linear-quadratic Stackelberg stochastic differential game, where the coefficients are deterministic. The notion of the closed-loop solvability is introduced, which…
We consider how an agent should update her uncertainty when it is represented by a set P of probability distributions and the agent observes that a random variable X takes on value x, given that the agent makes decisions using the minimax…
We consider graph games of infinite duration with winning conditions in parameterized linear temporal logic, where the temporal operators are equipped with variables for time bounds. In model checking such specifications were introduced as…
Ultimate Tic-Tac-Toe is a variant of the popular Tic-Tac-Toe game. Two players compete to win three aligned "fields," with each field constituting its own miniature tic-tac-toe game. Each move determines which field the next player must…
In this paper we study a linear pursuit differential game described by an infinite system of first-order differential equations in Hilbert space. The control functions of players are subject to geometric constraints. The pursuer attempts to…
Stackelberg games originate where there are market leaders and followers, and the actions of leaders influence the behavior of the followers. Mathematical modelling of such games results in what's called a Bilevel Optimization problem.…
This paper presents the design of a cooperative multi-player betting game, Trust-ya, as a model of some elements of status processes in human groups. The game is designed to elicit status-driven leader-follower behaviours as a means to…
The problem of guessing subject to distortion is considered, and the performance of randomized guessing strategies is investigated. A one-shot achievability bound on the guessing moment (i.e., moment of the number of required queries) is…
In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…