Game Theory and Musical Interactions
Game theory is defined as “the analysis of strategies dealing with situations where the outcome of a participant’s choice of action depends on the actions of other participants.” Game theory has been applied to many different contexts including war, business, and science, but this paper utilizes the game theory model to create music. This paper analyzes musical interaction and proposes methods for generating music based on the results of the model. The origins of music were derived from interactions between players so in today’s age, it is apparent that you can produce natural music using mathematical processes that generate musical patterns.
The game theory presented in this paper relates to the game theory models discussed in class. In class, we talked about the Prisoner’s Dilemma model. In this model, two suspects are arrested and separated into different rooms. They are given two choices, to either confess or not confess. Based on the payoffs given, the strict dominant strategy is to always confess. In relation, the paper presents a game matrix that is very similar to the Prisoner’s Dilemma. There are two players and each player can either play a note or rest.
|
Same Melody |
Different Melodies |
|
|
Same Melody |
3,3 |
0,5 |
|
Different Melodies |
5,0 |
1,1 |
The strict dominant strategy in this case is to always play different melodies. In both cases, there is a Nash Equilibrium of (confess, confess) and (different melodies, different melodies). These games are also zero-sum games, meaning that the payoff of one player equals the losses of the other.
Source: http://quod.lib.umich.edu/cgi/p/pod/dod-idx/game-theoretical-model-for-musical-interaction.pdf?c=icmc;idno=bbp2372.2008.095