Related papers: SET! From Groups to Games
Quantitative measures of randomness in games are useful for game design and have implications for gambling law. We treat the outcome of a game as a random variable and derive a closed-form expression and estimator for the variance in the…
Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial properties, with connections to Stirling numbers, Dyck…
Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multi-person strategic decision making that can be used to model the interactions of decision makers in security problems who compete for…
The multilayer garbage disposal game is an evolution of the garbage disposal game. Each layer represents a social relationship within a system of finitely many individuals and finitely many layers. An agent can redistribute their garbage…
I consider a family of games with corresponding payoff matrices, parametrized by the parameter The informal question of interest is: what game is the best? Instead of attempting to suggest a more or less arbitrary definition of the best…
We introduce a two-player game, in which each player extends a given sequence by picking a free element in a domain D of the real line. The aim of the players is to control the parity of the number of transpositions necessary to put the…
This letter introduces an abstract learning problem called the "set embedding": The objective is to map sets into probability distributions so as to lose less information. We relate set union and intersection operations with corresponding…
Adding game elements to higher education is an increasingly common practice. As a result, many recent empirical studies focus on studying the effectiveness of gamified or game-based educational experiences. The findings of these studies are…
Under the assumptions that (i) gamification consists of various types of users that experience game design elements differently; and (ii) gamification is deployed in order to achieve some goal in the broadest sense, we pose the gamification…
Energy games are a well-studied class of 2-player turn-based games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the…
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
We present an algebraic framework for the analysis of combinatorial games. This framework embraces the classical theory of partizan games as well as a number of misere games, comply-constrain games, and card games that have been studied…
The main objective of this work is to describe games which fall under title of Potential and simplify the conditions for class of aggregative games. Games classified as aggregative are ones in which, in addition to the player's own action,…
The optimization of facility-based systems is considered. First, the congestion game is converted into a matrix form, so that the matrix approach is applicable. Then, a facility-based system with a system performance criterion is…
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…
This study employs gamified experiments to investigate and refine the Schelling Model of Segregation, a framework that demonstrates how individual preferences can lead to systemic segregation. Using a movement selection algorithm derived…
The aim of this paper is to describe the definitions and main properties of three generalizations of the group concept, namely: groupoid, generalized group and almost groupoid. Some constructions of these algebraic structures and…
J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games form a Group. However, Conway product is not well defined on…
Tournament solutions play an important role within social choice theory and the mathematical social sciences at large. We construct a tournament of order 36 for which the Banks set and the bipartisan set are disjoint. This implies that…
We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We…