Related papers: Roughly Weighted Hierarchical Simple Games

Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…

We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual…

Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two…

We establish relationships between various topological selection games involving the space of minimal cusco maps into the real line and the underlying domain. These connections occur across different topologies, including the topology of…

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…

Minority games where groups of agents remember, react or incorporate information with different timescales are investigated. We study how their respective gains depend on their timescales for standard models and games with no public…

We introduce open games as a compositional foundation of economic game theory. A compositional approach potentially allows methods of game theory and theoretical computer science to be applied to large-scale economic models for which…

Following Zhang and Grossi~(AAAI 2021), we study in more depth a variant of weighted voting games in which agents' weights are induced by a transitive support structure. This class of simple games is notably well suited to study the…

We unify standard frameworks for approachability both in full or partial monitoring by defining a new abstract game, called the "purely informative game", where the outcome at each stage is the maximal information players can obtain,…

Absolute Universes of combinatorial games, as defined in a recent paper by the same authors, include many standard short normal- mis\`ere- and scoring-play monoids. In this note we show that the class is categorical, by extending Joyal's…

We study discrete preference games in heterogeneous social networks. These games model the interplay between a player's private belief and his/her publicly stated opinion (which could be different from the player's belief) as a strategic…

The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propose a model called gamegraph, together with its generalization…

We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The…

We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category,…

Berlekamp proposed a class of impartial combinatorial games based on the moves of chess pieces on rectangular boards. We generalize impartial chess games by playing them on Young diagrams and obtain results about winning and losing…

Finite games in normal form and their mixed extensions are a corner stone of noncooperative game theory. Often generic finite games and their mixed extensions are considered. But the properties which one expects in generic games and the…

Matching games is a one-to-one two sided market model introduced by Garrido-Lucero and Laraki, in which coupled agents' utilities are endogenously determined as the outcome of a strategic game. They refine the classical pairwise stability…

One of the main results shown through Roughgarden's notions of smooth games and robust price of anarchy is that, for any sum-bounded utilitarian social function, the worst-case price of anarchy of coarse correlated equilibria coincides with…

Apportionment is the task of assigning resources to entities with different entitlements in a fair manner, and specifically a manner that is as proportional as possible. The best-known application is the assignment of parliamentary seats to…

In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical…