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Grim Under A Compensation Variant, Aaron Davis, Aaron Davis

Honors College Theses

Games on graphs are a well studied subset of combinatorial games. Balance and strategies for winning are often looked at in these games. One such combinatorial graph game is Grim. Many of the winning strategies of Grim are already known. We note that many of these winning strategies are only available to the first player. Hoping to develop a fairer Grim, we look at Grim played under a slighlty different rule set. We develop winning strategies and known outcomes for this altered Grim. Throughout, we discuss whether our altered Grim is a fairer game then the original.

Providing Better Choices: An Exploration Of Solutions In Multi-Objective Optimization And Game Theory Using Variational Analysis, Glenn Matthew Harris

Graduate Research Theses & Dissertations

Multi-objective optimization problems and game theory problems have a wide array of

applications and because of this there are different types of solutions available. This dissertation

explores two areas of optimization and a solution type for each. First, substantial

efficiency (SE) as a type of solution to multi-objective optimization problems that extends

proper efficiency. Secondly, strong Nash equilibria (SNE) as a type of solution to game

theoretic problems that extends Nash equilibria. Substantial efficiency is demonstrated to

be a superior solution to the more rudimentary notion of proper efficiency in solving some

multi-objective financial market and economic problems. Using this …

A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler

Senior Independent Study Theses

Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.