Application of Game Theory to Analysis of Machine versus Human Strategies

Operas combine story-lines, vocalizations, and instrumentation to map out a sequence of events caused by the decisions of their fictional characters. [1] This project aims to explore the underlying mathematical structure of these works of art by 1) examining whether their outcomes correspond to the laws of game theory and 2) analyzing how the music associated with each decision strengthens its meaning for the audience. We will then compare the outcomes to those made by different machine learning algorithms in an effort to understand how rationally and mathematically a machine “thinks” in comparison to characters in opera.

First, we map the sequence of decisions made by each character in the opera, along with the events that caused and resulted from these decisions. We then apply game theory concepts, such as Nash Equilibrium, to determine the optimal sequence of events and compare them to those made in the opera’s storyline, as well as those made by different machine learning algorithms. This will inform how accurate a machine versus a character is in making decisions with maximum positive results for every player.

By the end of this project, we expect to discover the decisions that bring characters maximum positive results in a variety of situations and to understand why those choices differ from those made by the characters in the opera and machine learning algorithms. Mathematical analysis of each opera’s music will help rationalize such decisions made by the characters.

1. Wolfman, Ursula Rehn. 2013. “Richard Wagner’s Concept of the ‘Gesamtkunstwerk.’” Interlude. March 11, 2013. https://interlude.hk/richard-wagners-concept-of-the-gesamtkunstwerk/.