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Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the…
The need for data preservation and reproducible research is widely recognized in the scientific community. Yet, researchers often struggle to find the motivation to contribute to data repositories and to use tools that foster…
This paper concerns the design of a multidimensional Chebyshev interpolation based method for a differential game theory problem. In continuous game theory problems, it might be difficult to find analytical solutions, so numerical methods…
The Mathematization project investigates students' use of mathematical tools across the undergraduate physics curriculum. As a part of this project, we look at intermediate mechanics students' written homework solutions to understand how…
Concurrent and parallel programming (CPP) is an increasingly important subject in Computer Science Education. However, the conceptual shift from sequential programming is notoriously difficult to make. Currently, relatively little research…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
We introduce a class of resource games where resources and preferences are specified with the language of a resource-sensitive logic. The agents are endowed with a bag of resources and try to achieve a resource objective. For each agent, an…
Research has established increased engagement and positive behavioral, attitudinal, and learning outcomes from educational games. Although engagement begets these benefits, there is a lack of research on how students engage with educational…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically…
The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered…
We study an iteration approach to solve the coupled algebraic Riccati equations when they appear in general two player closed-loop type Nash differential games over an infinite time horizon. Also, we propose an effective algorithm for…
Children learn though play. We introduce the analogous idea of learning programs through play. In this approach, a program induction system (the learner) is given a set of tasks and initial background knowledge. Before solving the tasks,…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
We prove a theorem computing the number of solutions to a system of equations which is generic subject to the sparsity conditions embodied in a graph. We apply this theorem to games obeying graphical models and to extensive-form games. We…
In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…
A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…
We describe a study focusing on students' and faculty members' reasoning about problems of differing cognitive complexity related to the double-slit experiment (DSE) with single particles. In the first phase of the study, students in…
In competitive resource allocation formulations multiple agents compete over different contests by committing their limited resources in them. For these settings, contest games offer a game-theoretic foundation to analyze how players can…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…