A Generalized Additive Game (GAG) (Cesari et al. in Int J Theory 46(4):919–939, 2017) is a Transferable Utility (TU) game (N, v), where each player N provided with an individual value, and the worth v(S) of coalition $$S \subseteq N$$ obtained as sum values players another subset $$\mathcal {M}(S)\subseteq . Based on conditions map {M}$$ (which associates to S set beneficial {M}(S)$$ not necess...

A generalization of the Möbius transform of games with finitely many players is introduced for games on MV-algebras. The variety of MValgebras subsumes most coalition models. We characterize the class of games for which the generalized Möbius transform exists. An application of the proposed transform to a Cimmino-type algorithm is shown for the core solution in games with finitely-many players.

In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized mean-payoff and energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be ...

We pursue a general theory of quantum games. We show that quantum games are more efficient than classical games, and provide a saturated upper bound for this efficiency. We also demonstrate how quantum games may be viewed simultaneously as both a generalized and yet restricted version of the corresponding classical games. We also deduce the quantum version of the Minimax Theorem and the Nash Eq...

We prove NP-hardness results for five of Nintendo’s largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pokémon. Our results apply to generalized versions of Super Mario Bros. 1–3, The Lost Levels, and Super Mario World; Donkey Kong Country 1–3; all Legend of Zelda games; all Metroid games; and all Pokémon role-playing games. In addition, we prove PSPACE-completenes...

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 games is PSPACE-complete, although it is fixed-parameter tractable with the number of reachability objectives as parameter. Moreover, we consider the memory r...

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 games is PSPACE-complete, although it is fixed-parameter tractable with the number of reachability objectives as parameter. Moreover, we consider the memory r...

Using coalgebraic methods, we extend Conway’s theory of games to possibly non-terminating, i.e. non-wellfounded games (hypergames). We take the view that a play which goes on forever is a draw, and hence rather than focussing on winning strategies, we focus on non-losing strategies. Hypergames are a fruitful metaphor for non-terminating processes, Conway’s sum being similar to shuffling. We dev...

Economic Models and Generalized Games 229 4.