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Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
Usually, to apply game-theoretic methods, we must specify utilities precisely, and we run the risk that the solutions we compute are not robust to errors in this specification. Ordinal games provide an attractive alternative: they require…
We generalize a concept of classical finite extensive game to make it useful for application of quantum objects. The generalization extends a quantum realization scheme of static games to any finite extensive game. It represents an…
Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…
Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such…
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…
We propose the study of mathematical ludology, which aims to formally interrogate questions of interest to game studies and game design in particular. The goal is to extend our mathematical understanding of complex games beyond…
In this thesis, we survey techniques and results from the study of Complexity Theory and Games. We then apply these techniques to obtain new results for previously unstudied games. Our contributions in the games Hexiom, Cut the Rope, and…
Gamification applies game mechanics to non-game environments to motivate and engage users. Artificial Intelligence (AI) offers powerful tools for personalizing and optimizing gamification, adapting to users' needs, preferences, and…
We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…
Energy and pollution are urging problems of the 21th century. By gradually changing the actual power grid system, smart grid may evolve into different systems by means of size, elements and strategies, but its fundamental requirements and…
Correlated equilibria -- and their generalization $\Phi$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of…
It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, the most popular regularization approaches are Variational-type approaches, i.e.,…
Pebble games are popular models for analyzing time-space trade-offs. In particular, the reversible pebble game is often applied in quantum algorithms like Grover's search to efficiently simulate classical computation on inputs in…
Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…
The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and…
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…
Hybrid games are games played on a finite graph endowed with real variables which may model behaviors of discrete controllers of continuous systems. The synthesis problem for hybrid games is decidable for classical objectives (like LTL…
We revisit the complexity of deciding, given a {\it bimatrix game,} whether it has a {\it Nash equilibrium} with certain natural properties; such decision problems were early known to be ${\mathcal{NP}}$-hard~\cite{GZ89}. We show that…
With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…