Games People Play
Games People Play
Game Theory is one of the most challenging and controversial fields of applied Mathematics. Based on a robust theoretical framework, its applications range from analyzing simple board games and conflict situations to modeling complex systems and evolutionary dynamics.
This book is a short collection of introductory papers in the field, aimed primarily as reading material for graduate- and postgraduate-level lectures in Game Theory and/or Machine Learning. The four papers included here are all original works already published as open-access or conference publications, spanning a timeframe of several years apart and a wide range of topics. Hence, each paper is self-contained and can be studied on its own, without any prerequisite knowledge from the previous ones. However, their presentation order is consistent with going from the most elementary issues to the more advanced and experiment-rigorous topics.
The first paper presents an overview of Game Theory in general, its core issues and building blocks, game analysis and methods for identifying Minimax solutions and Nash equilibria, as well as a brief introduction to coalitional gaming and collective efficiency. There is also a short summary of other important elements like signaling, credibility, threats/promises, etc. The second paper extends some of the topics from coalitional gaming, focusing more on collective efficiency, optimal voting mechanisms and weighted voting, as well as a brief proposal for applying this gametheoretic framework to optimal combination of experts. The third paper builds upon this proposed framework and employs it in Pattern Recognition (Machine Learning) within the context of combining pattern classifiers. A “static” model for weighted majority voting with an analytical model for the voting weights is experimentally tested against other similar models. Finally, the forth paper presents an extension of this game-theoretic approach for classifier combination, employing “adaptive” voting weights via local accuracy estimates; in other words, the ensemble of classifiers is adapted to local efficiency priors (instead of static globals) but keeping the same analytical model for the voting weights, i.e., without the need to acquire them via training. This new approach is experimentally validated against state-of-the-art combination methods for pattern classifiers and it is proven highly competitive with much lower complexity overhead.