A Novel Stochastic Game Via the Quantitative μ-calculus

Annabelle McIver, Carroll Morgan
2006 Electronical Notes in Theoretical Computer Science  
The quantitative μ-calculus qMμ extends the applicability of Kozen's standard μ-calculus [5] to probabilistic systems. Subsequent to its introduction [9,4] it has been developed by us [6, 7, 8 ] and by others [2] . Beyond its natural application to define probabilistic temporal logic [10], there are a number of other areas that benefit from its use. One application is stochastic two-player games, and the contribution of this paper is to depart from the usual notion of "absolute winning
more » ... s" and to introduce a novel game in which players can "draw". The extension is motivated by examples based on economic games: we propose an extension to qMμ so that they can be specified; we show that the extension can be expressed via a reduction to the original logic; and, via that reduction, we prove that the players can play optimally in the extended game using memoryless strategies.
doi:10.1016/j.entcs.2005.10.039 fatcat:mab7nnzibnbdpdjlka5fua7epi