Neural Networks, Game Theory and Time Series Generation

TL;DR

This paper explores the interplay between neural networks, game theory, and time series generation, focusing on antipredictability and how neural networks can learn strategies in game-theoretic contexts.

Contribution

It introduces a framework connecting antipredictability in time series with game theory and proposes a neural network learning algorithm for zero-sum games.

Findings

Antipredictability is characterized for various prediction algorithms.

Extensions of the Minority Game are analyzed for time series properties.

A neural network-based learning algorithm for game strategies is developed.

Abstract

This dissertation highlights connections between the fields of neural networks, game theory and time series generation. The concept of antipredictability is explained, and the properties of time series that are antipredictable for several prototypical prediction algorithms (neural networks, Boolean funtions etc.) are studied. The Minority Game provides a framework in which antipredictability arises naturally. Several variations of the MG are introduced and compared, including extensions to more than two choices, and the properties of the generated time series are analysed. A learning algorithm is presented by which a neural network can find a good mixed strategy in zero-sum matrix games. In a certain limit, this algorithm is a stochastic variation of the "fictitious play" learning algorithm.