On payoff allocations for assignment games and on algorithms for stochastic games

This thesis study concentrates on computing efficiently the Shapley value for assignment games, a model of a two-sided market where each agent either supplies or demands exactly one good. In each iteration, we compute the Shapley value of two games whose worth have special monotonicity properties. These monotonicity properties allow for efficient data mining pruning strategies for the search space of essential coalitions. By utilizing the additivity property of the Shapley value we reduce the exponentially costly computation.; In the second part of this work, we show that the nucleolus, another well-known single point solution concept is pairwise monotonic for assignment games. In an assignment games, pairwise monotonicity implies that when the worth of a buyer-seller coalition is increased, then the payoff allocation for both the buyer and the seller does not decrease.; Finally, we examine in detail a special class of stochastic games, two-person perfect information stochastic games. A counterexample is given which resolves an open question posed on solving average reward two-person zero-sum perfect information stochastic games via a policy-improvement algorithm. In the last section, we show that nonzero discounted perfect information games can be solved via an Extended Linear Complementarity problem. Hence, showing such class of stochastic games possess the orderfield property.