Related papers: The Penney's Game with Group Action

In this paper we show that the continuum time version of the Minority Game satisfies the criteria for the application of a theorem on the existence of an invariant measure. We consider the special case of a game with "sufficiently"…

This work is a contribution to the study of rewrite games. Positions are finite words, and the possible moves are defined by a finite number of local rewriting rules. We introduce and investigate taking-and-merging games, that is, where…

We introduce the class of pay or play games, which captures scenarios in which each decision maker is faced with a choice between two actions: one with a fixed payoff and an- other with a payoff dependent on others' selected actions. This…

A Subtraction-Division game is a two player combinatorial game with three parameters: a set S, a set D, and a number n. The game starts at n, and is a race to say the number 1. Each player, on their turn, can either move the total to n-s…

In a network game, players interact over a network and the utility of each player depends on his own action and on an aggregate of his neighbours' actions. Many real world networks of interest are asymmetric and involve a large number of…

The crossword-like patterns of tiles in Scrabble form connected graphs of occupied sites on a square lattice. We find the most structureless description that reproduces means and covariances observed in real Scrabble games by adapting a…

We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables…

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)…

We characterize all common notions of behavioral equivalence by one 6-dimensional energy game, where energies bound capabilities of an attacker trying to tell processes apart. The defender-winning initial credits exhaustively determine…

Players are arranged on a regular lattice and coded with a specific strategy for a pre-defined game. Each player sums their payoffs from playing the game with each of their neighbors, and then adopts the strategy of the most successful…

In this paper we study the notion of configuration for group actions. It is proved that some properties concerning configuration of groups can be extended for the case of group actions. The relationship between configuration and different…

This paper is inspired by the PQ penny flip game. It employs group-theoretic concepts to study the original game and also its possible extensions. We show that the PQ penny flip game can be associated with the dihedral group $D_{8}$. We…

We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an…

Strategic interactions between a group of individuals or organisations can be modelled as games played on networks, where a player's payoff depends not only on their actions but also on those of their neighbours. Inferring the network…

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…

Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…

In decision theory an act is a function from a set of conditions to the set of real numbers. The set of conditions is a partition in some algebra of events. The expected value of an act can be calculated when a probability measure is given.…

This brief paper describes the single-player card game called "Perpetual Motion" and reports on a computational analysis of the game's outcome. The analysis follows a Monte Carlo methodology based on a sample of 10,000 randomly generated…

Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…

In earlier work, we introduced the framework of language-based decisions, the core idea of which was to modify Savage's classical decision-theoretic framework by taking actions to be descriptions in some language, rather than functions from…