We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership – at least temporarily. We show that leapfrogging occurs in...

We define a class of dynamic Markovian games that we call directional dynamic games (DDG) in which directionality is represented by a partial order on the state space. We propose a fast and robust state recursion algorithm that can find a Markov perfect equilibrium (MPE) via backward induction...

Dynamic programming (DP) is a powerful tool for solving a wide class of sequential decision-making problems under uncertainty. In principle, it enables us to compute optimal decision rules that specify the best possible decision in any situation. This article reviews developments in DP and...