Table of Contents
Game Theory
Volume 2014, Article ID 435092, 8 pages
Research Article

On Taxed Matrix Games and Changes in the Expected Transfer

Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany

Received 19 May 2014; Revised 11 August 2014; Accepted 13 August 2014; Published 31 August 2014

Academic Editor: X. Henry Wang

Copyright © 2014 Ingo Althöfer and Marlis Bärthel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In gambling scenarios the introduction of taxes may affect playing behavior and the transferred monetary volume. Using a game theoretic approach, we ask the following: How does the transferred monetary volume change when the winner has to pay a tax proportional to her win? In this paper we therefore introduce a new parameter: the expected transfer. For a zerosum matrix game with payoff matrix and mixed strategies and of the two players it is defined by . Surprisingly, it turns out that for small fair matrix games higher tax rates lead to an increased expected transfer. This phenomenon occurs also in analogous situations with tax on the loser, bonus for the winner, or bonus for the loser. Higher tax or bonus rates lead to overproportional expected revenues for the tax authority or overproportional expected expenses for the grant authority, respectively.