Related papers: A number game reconciliation
In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of…
We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the…
Game theory offers a powerful framework for analyzing strategic interactions among decision-makers, providing tools to model, analyze, and predict their behavior. However, implementing game theory can be challenging due to difficulties in…
Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…
In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…
Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and…
We present a unifying representation of computation as a two-player game between an \emph{Algorithm} and \emph{Nature}, grounded in domain theory and game theory. The Algorithm produces progressively refined approximations within a Scott…
In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum…
Game theory has been one of the most successful quantitative concepts to describe social interactions, their strategical aspects, and outcomes. Among the payoff matrix quantifying the result of a social interaction, the interaction…
Admissible strategies, i.e. those that are not dominated by any other strategy, are a typical rationality notion in game theory. In many classes of games this is justified by results showing that any strategy is admissible or dominated by…
After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an…
As interaction between autonomous agents, communication can be analyzed in game-theoretic terms. Meaning game is proposed to formalize the core of intended communication in which the sender sends a message and the receiver attempts to infer…
Schmidt's game, and other similar intersection games have played an important role in recent years in applications to number theory, dynamics, and Diophantine approximation theory. These games are real games, that is, games in which the…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
We consider the class of "well-tempered" integer-valued scoring games, which have the property that the parity of the length of the game is independent of the line of play. We consider disjunctive sums of these games, and develop a theory…
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…
When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning…
Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of…
This paper proposes a new approach to power in Game Theory. Cooperation and conflict are simulated with a mechanism of payoff alteration, called F-game. Using convex combinations of preferences, an F-game can measure players' attitude to…
A version of John Conway's game of Life is presented where the normal binary values of the cells are replaced by oscillators which can represent a superposition of states. The original game of Life is reproduced in the classical limit, but…