We consider a finite two-player zero-sum game with vector-valued rewards. We study the question of whether a given polyhedral set D is "approachable," that is, whether Player 1 (the "decision maker") can guarantee that the long-term average reward belongs to D, for any strategy of Player 2 (the...

We consider a finite-state, finite-action, infinite-horizon, discounted reward Markov decision process and study the bias and variance in the value function estimates that result from empirical estimates of the model parameters. We provide closed-form approximations for the bias and variance,...

Regret minimization in repeated matrix games has been extensively studied ever since Hannan's seminal paper [Hannan, J., 1957. Approximation to Bayes risk in repeated play. In: Dresher, M., Tucker, A.W., Wolfe, P. (Eds.), Contributions to the Theory of Games, vol. III. Ann. of Math. Stud., vol....

We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on...

We show that when a one-supplier/one-newsvendor supply chain is capacity-constrained, wholesale price contracts have some flexibility in allocating the channel-optimal profit. We analyze how this flexibility changes as we change the supply chain׳s capacity constraint and market demand. We also...