Related papers: Dimension and codimension of simple games
This paper develops and analyses a novel quantum combinatorial game: quantum checkers (codenamed Cheqqers). The concepts of superposition, entanglement, measurements and interference from quantum mechanics are integrated into the game of…
We study a game for recognising formal languages, in which two players with imperfect information need to coordinate on a common decision, given private input words correlated by a finite graph. The players have a joint objective to avoid…
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…
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…
Game logic is a dynamic modal logic which models strategic two person games; it contains propositional dynamic logic (PDL) as a fragment. We propose an interpretation of game logic based on stochastic effectivity functions. A definition of…
We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.
We study the computational complexity of converting one representation of real numbers into another representation. Typical examples of representations are Cauchy sequences, base-10 expansions, Dedekind cuts and continued fractions.
Quantum games have proposed a new point of view for the solution of the classical problems and dilemmas in game theory. Certain quantization relationships can be proposed with the objective that a game can be generalized into a quantum…
A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given. Decoherence in other types of quantum games is…
The numbers game is a one-player game played on a finite simple graph with certain ``amplitudes'' assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…
In this speculative analysis, interdimensionality is introduced as the (co)existence of universes embedded into larger ones. These interdimensional universes may be isolated or intertwined, suggesting a variety of interdimensional intrinsic…
Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model…
Escalation is the fact that in a game (for instance an auction), the agents play forever. It is not necessary to consider complex examples to establish its rationality. In particular, the $0,1$-game is an extremely simple infinite game in…
We present a general way of defining various reduction games on \omega\ which "represent" corresponding topologically defined classes of functions. In particular, we will show how to construct games for piecewise defined functions, for…
If the influence diagram (ID) depicting a Bayesian game is common knowledge to its players then additional assumptions may allow the players to make use of its embodied irrelevance statements. They can then use these to discover a simpler…
Intransitivity is a critical issue in pairwise preference modeling. It refers to the intransitive pairwise preferences between a group of players or objects that potentially form a cyclic preference chain and has been long discussed in…
Decision making in modern large-scale and complex systems such as communication networks, smart electricity grids, and cyber-physical systems motivate novel game-theoretic approaches. This paper investigates big strategic (non-cooperative)…
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…
In addressing the challenge of exponential scaling with the number of agents we adopt a cluster-based representation to approximately solve asymmetric games of very many players. A cluster groups together agents with a similar "strategic…
We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also…