Related papers: Computational Complexity of Games and Puzzles
Noncooperative game-theoretic tools have been increasingly used to study many important resource allocation problems in communications, networking, smart grids, and portfolio optimization. In this paper, we consider a general class of…
In this paper we provide a case study of the use of relatively sophisticated mathematics and algorithms to redefine and adapt a simple traditional game/puzzle to exploit the computational power of smart devices. The focus here is not so…
In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two…
Human computation games (HCGs) are a crowdsourcing approach to solving computationally-intractable tasks using games. In this paper, we describe the need for generalizable HCG design knowledge that accommodates the needs of both players and…
In recent years, there has been a growing interest in games on graphs within the research community, fueled by their relevance in applications such as economics, politics, and epidemiology. This paper aims to comprehensively detail the…
There has been a remarkable increase in work at the interface of computer science and game theory in the past decade. In this article I survey some of the main themes of work in the area, with a focus on the work in computer science. Given…
We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…
This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill…
We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a…
Tasks of different nature and difficulty levels are a part of people's lives. In this context, there is a scientific interest in the relationship between the difficulty of the task and the persistence need to accomplish it. Despite the…
Recently, a standardized framework was proposed for introducing quantum-inspired moves in mathematical games with perfect information and no chance. The beauty of quantum games-succinct in representation, rich in structures, explosive in…
Negotiations, a model of concurrency with multi party negotiation as primitive, have been recently introduced in arXiv:1307.2145, arXiv:1403.4958. We initiate the study of games for this model. We study coalition problems: can a given…
Game theory is appropriate for studying cyber conflict because it allows for an intelligent and goal-driven adversary. Applications of game theory have led to a number of results regarding optimal attack and defense strategies. However, the…
We study the complexity of a particular class of board games, which we call `slide and merge' games. Namely, we consider 2048 and Threes, which are among the most popular games of their type. In both games, the player is required to slide…
Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria…