We study Blackwell's approachability in repeated games with vector payoffs when the approaching player is restricted to use strategies with bounded memory: either strategies with bounded recall, or strategies that can be implemented by finite automata. Our main finding is that the following...

An absorbing game is a repeated game where some of the action combinations are absorbing, in the sense that whenever they are played, there is a positive probability that the game terminates, and the players receive some terminal payoff at every future stage. We prove that every n-player...

"There is no place where espionage is not possible." -Sun Tzu, The Art of War, approximately 500BC We consider extensive form games in which players decide on their strategies before the start of play and can purchase noisy information about their opponents' decisions concerning future response...

Randomization may add beneficial flexibility to the construction of optimal simple decision rules in dynamic environments. A decision maker, restricted to the use of simple rules, may find a stochastic rule that strictly outperforms all deterministic ones. This is true even in highly separable...