Continuous Capacities on Continuous State Spaces

We propose axiomatizing some stochastic games, in a continuous state space setting, using continuous belief functions, resp. plausibilities, instead of measures. Then, stochastic games are just variations on continuous Markov chains. We argue that drawing at random along a belief function is the same as letting the probabilistic player P play first, then letting the non-deterministic player C play demonically. The same holds for an angelic C, using plausibilities instead. We then define a simple modal logic, and characterize simulation in terms of formulae of this logic. Finally, we show that (discounted) payoffs are defined and unique, where in the demonic case, P maximizes payoff, while C minimizes it.

• Type: Conference
• Year: 2007
• Where: ICALP
• Authors: Jean Goubault-Larrecq
• Keywords: Belief Function, Continuous Belief Functions, ICALP 2007, Stochastic Games, Theoretical Computer Science