2014/04/18 by Paul Hunter, Hunter, Paul, Jean-François Raskin +1 · 1 citation
Computer Science · #Computer Science and Game Theory (cs.GT) #F.1.1 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #cs.GT #cs.LO
paper · pdf · doi:10.48550/arxiv.1404.4856
Full version of CONCUR submission
arxiv created 2014/04/18 · arxiv updated 2014/04/21
Traditionally quantitative games such as mean-payoff games and discount sum games have two players -- one trying to maximize the payoff, the other trying to minimize it. The associated decision problem, "Can Eve (the maximizer) achieve, for example, a positive payoff?" can be thought of as one player trying to attain a payoff in the interval (0,∞). In this paper we consider the more general problem of determining if a player can attain a payoff in a finite union of arbitrary intervals for various payoff functions (liminf, mean-payoff, discount sum, total sum). In particular this includes the interesting exact-value problem, "Can Eve achieve a payoff of exactly (e.g.) 0?"