We consider Markov decision processes (MDP) as generators of sequences of probability distributions over states. A probability distribution is psynchronizing if the probability mass is at least p in a single state, or in a given set of states. We consider four temporal synchronizing modes: a sequence of probability distributions is always p-synchronizing, eventually p-synchronizing, weakly psyn...

We consider two-player zero-sum stochastic games on graphs with ω-regular winning conditions specified as parity objectives. These games have applications in the design and control of reactive systems. We survey the complexity results for the problem of deciding the winner in such games, and in classes of interest obtained as special cases, based on the information and the power of randomizatio...

The probability of winning a game, a set, and a match in tennis are computed, based on each player’s probability of winning a point on serve, which we assume are independent identically distributed (iid) random variables. Both two out of three and three out of five set matches are considered, allowing a 13-point tiebreaker in each set, if necessary. As a by-product of these formulas, we give an...

We analyze the chances of winning a tournament under assumption that probabilities individual matches follow Bradley-Terry model [2]. present an exact solution and show few examples its use. The are from California volleyball tournaments, round sixteen in World Cup Champions League, group stage Association Tennis Professionals tournament, SuperLega Italy.
 computational complexity grows ex...

We consider two-players stochastic reachability games with partial observation on both sides and finitely many states, signals and actions. We prove that in such games, either player 1 has a strategy for winning with probability 1, or player 2 has such a strategy, or both players have strategies that guarantee winning with non-zero probability (positively winning strategies). We give a fix-poin...

In this paper we will fully characterize all types of winning moves in the “takeaway” game of Fibonacci Nim. We prove the known winning algorithm as a corollary of the general winning algorithm and then show that no other winning algorithms exist. As a by-product of our investigation of the game, we will develop useful properties of Fibonacci numbers. We conclude with an exploration of the prob...

Strategic bidding in joint energy and spinning reserve markets is a challenging task from the viewpoint of generation companies (GenCos). In this paper, the interaction between energy and spinning reserve markets is modeled considering a joint probability density function for the prices of these markets. Considering pay-as-bid pricing mechanism, the bidding problem is formulated and solved as a...