Related papers: Tools for Mathematical Ludology
This article introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features…
We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of…
We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands…
A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem…
This paper introduces a geometric framework for analyzing power relations in games, independent of their strategic form. We define a canonical preference space where each player's relational stance is a normalized vector. This model…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person…
This paper investigates the rationality of large language models (LLMs) in strategic decision-making contexts, specifically within the framework of game theory. We evaluate several state-of-the-art LLMs across a spectrum of…
Inductions and game semantics are two useful extensions to traditional logic programming. To be specific, inductions can capture a wider class of provable formulas in logic programming. Adopting game semantics can make logic programming…
We present a game semantics for intuitionistic type theory. Specifically, we propose categories with families of a new variant of games and strategies for both extensional and intensional variants of the type theory with dependent function,…
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…
Although several methodologies for identifying the genealogy of video game genres and showing their relationships have been proposed in existing research, there have been few attempts to visualize the genealogy of a genre in a quantitative…
Long-distance relationships (LDRs) have become more common in the last few decades, primarily among young adults pursuing educational or employment opportunities. A common way for couples in LDRs to spend time together is by playing…
We argue for the use of active learning methods for player modelling. In active learning, the learning algorithm chooses where to sample the search space so as to optimise learning progress. We hypothesise that player modelling based on…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
Educational games can foster critical thinking, problem-solving, and motivation, yet instructors often find it difficult to design games that reliably achieve specific learning outcomes. Existing authoring environments reduce the need for…
Reflection is a critical aspect of the learning process. However, educational games tend to focus on supporting learning concepts rather than supporting reflection. While reflection occurs in educational games, the educational game design…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
Within the evolving field of digital intervention, serious games emerge as promising tools for evidence-based interventions. Research indicates that gamified therapy, whether employed independently or in conjunction with online…
In this paper we present a process for automatically generating manuals for board games within the Ludii general game system. This process requires many different sub-tasks to be addressed, such as English translation of Ludii game…