Impulse Balance Theory and its Extension by an Additional Criterion E-Book

Reinhard Selten

• Herausgeber: Books on Demand
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 26

Veröffentlichungsjahr: 2015

Beschreibung

In this paper I present a description of the theory of impulse balance. This theory predicts a mixed strategy for every player in an arbitrary n-person game in normal form. However, this mixed strategy is not interpreted as the result of a process of rational deliberation, but rather the behavioral distribution of pure strategies in a long section of a supergame of the normal form game. In a business problem not directly treatable by impulse balance the theory can be applied nevertheless with the help of an additional criterion 70% correct long term predictions of the future distribution of decision behavior were obtained in the evaluation of first experiements.

Leseprobe

Abstract

In this paper I present a description of the theory of impulse Balance. This theory predicts a mixed strategy for every player in an arbitrary n-person game in normal form. However, this mixed strategy is not interpreted as the result of a process of rational deliberation, but rather the behavioral distribution of pure strategies in a long section of a supergame of the normal form game. As the length of the section moves to infinity, the process of pure strategy choice approaches a stationary state with fixed mixed strategies attached to it. This is the basic idea guiding our theory construction. The theory has been first developed as a concept for 2 × 2 − games only (Selten and Chmura AER 2008). The theory can be easily generalized to normal forms with more than two pure strategies for some players. In the paper by Selten and Chmura a number of theories have been compared with experimental data on repeated 2 × 2 - games with anonymous interaction and changing opponents from one game to the next in the comparison the quadratic deviation between theoretical predictions and data is lowest for impulse balance theory. This was a surprising success of impulse balance theory. In a paper by Chmura, Goerg and Selten the theory of impulse balance is generalized to arbitrary normal forms. This paper also presents a learning model whose stationary distributions of pure strategies are impulse balance solutions and vice versa. The learning model opens the way for numerical computation of impulse balance predictions. Moreover the Chmura, Goerg and Selten paper also reports experimental data on a specific class of 3 × 3 − games (the class of bailiff and poacher games, see Selten. R., Anticipatory learning in n-person games, in: Game equilibrium models 1, Reinhard Selten (ed.) in Springer Verlag Berlin − Heidelberg −New York 1991). In the class of bailiff and poacher games every game has a unique Nash equilibrium and also a unique impulse balance solution. Therefore this class is well suited for the comparison of both concepts. The experiments on 3 × 3 − games reported in the paper by Chmura, Goerg, and Selten have been run on 12 games with completely mixed Nash equilibria and 14 games with partially mixed Nash equilibria. Nash equilibrium and impulse balance theory are both parameter free concepts which unlike most other concepts do not depend on parameters which have to be estimated from the experimental data and are not available before an experiment is run. Theories which are not parameter free in this sense are not truly predictive. The quadratic distance from the data is usually much smaller for impulse balance theory, than for Nash equilibrium. Impulse balance is clearly more successful in this comparison between the two parameter free theories. In a business problem not directly treatable by impulse balance the theory can be applied nevertheless with the help of an additional criterion 70% correct long term predictions of the future distribution of decision behavior were obtained in first experiments.

Keywords: impulse balance, Nash equilibrium, bailiff and poacher games.

Table of Contents

ABSTRACT

1 INTRODUCTION

2 PRELIMINARY DEFINITION AND NOTATIONS