Related papers: On the Complexity of Deciding Degeneracy in Games

We study alternating good-for-games (GFG) automata, i.e., alternating automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the suffix of the input word still to be read. We show…

We consider games with two antagonistic players --- \'Elo\"ise (modelling a program) and Ab\'elard (modelling a byzantine environment) --- and a third, unpredictable and uncontrollable player, that we call Nature. Motivated by the fact that…

Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…

We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm…

Although the definition of what empathetic preferences exactly are is still evolving, there is a general consensus in the psychology, science and engineering communities that the evolution toward players' behaviors in interactive…

We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable…

A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…

We develop a constrained bimatrix game framework that can be used to model many practical problems in many disciplines, including jamming in packetized wireless networks. In contrast to the widely used zero-sum framework, in bimatrix games…

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier)…

In this paper we study the computational complexity of the game of Scrabble. We prove the PSPACE-completeness of a derandomized model of the game, answering an open question of Erik Demaine and Robert Hearn.

Let D = { d_n } be a countable collection of Delta^1_3 degrees. Assuming that all co-analytic games on integers are determined (or equivalently that all reals have ``sharps''), we prove that either D has a Delta^1_3-minimal upper bound, or…

Interpreting three-leaf binary trees or {\em rooted triples} as constraints yields an entailment relation, whereby binary trees satisfying some rooted triples must also thus satisfy others, and thence a closure operator, which is known to…

We settle a long-standing open question in algorithmic game theory. We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed…

We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the…

We explore the power of semidefinite programming (SDP) for finding additive $epsilon$-approximate Nash equilibria in bimatrix games. We introduce an SDP relaxation for a quadratic programming formulation of the Nash equilibrium (NE) problem…

In this paper, we study the algorithmic complexity of the Mastermind game, where results are single-color black pegs. This differs from the usual dual-color version of the game, but better corresponds to applications in genetics. We show…

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…

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…

Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct definition of multipermutation solutions has not been…

The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…