On Taxed Matrix Games and Changes in the Expected Transfer. (31st August 2014) - Althöfer, Ingo; Bärthel, Marlis
Abstract : 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 matrixA and mixed strategiesp andq of the two players it is defined byE T ( A ; p, q ) = ∑ ‍ ∑ ‍ p i q j | a i j | . 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.