The linear-quadratic-Gaussian control paradigm is well-known in literature. The strategy of minimizing the cost function is available, both for the case where the state is fully known and where it is estimated through an observer. The situation is different when the cost function has an exponential discount factor, also known as a prescribed degree of stability. In this case, the optimal contro...

We present a proportional reaction strategy in a repeated Cournot duopoly game with discounting. The strategy is based on increasing the total output quantity in proportion to deviations from a cartel point. Such a strategy was originally proposed by Osborne (1976) for a static oligopoly. We show that the resulting equilibrium is subgame perfect and weakly renegotiation proof when the possible ...

The e↵ectiveness of monetary promotions has been well reported in the literature to a↵ect shopping decisions for products in real life experience [3]. Nowadays, e-commerce retailers are facing more fierce competition on price promotion in that consumers can easily use a search engine to find another merchant selling an identical product for comparing price. We study e-commerce data — shopping r...

Cooperation between upstream suppliers and downstream manufacturers in technology investment is a popular way to improve production for reducing suppliers’ costs of key components. The cooperation strategies are mainly influenced by manufacturers’ investments wholesale price discount contracts provided suppliers. This paper explores whether supplier should cooperate with two competing accept th...

Based on the fact that T-mall and JD.com, two major e-commerce platforms, reduce prices significantly every year in shopping festival, but still can obtain high profits, this paper explains causes profit mechanism from perspective of game theory. Meanwhile, article builds a Bertrand model to analyze firms. The Nash equilibrium is (Discount, Discount) until they drop their 0, which obviously aga...

A Blackwell ε-optimal strategy in a Markov Decision Process is a strategy that is ε-optimal for every discount factor sufficiently close to 1. We prove the existence of Blackwell ε-optimal strategies in finite Markov Decision Processes with partial observation. 1. Introduction. A well-known result by Blackwell [3] states that, in any Markov Decision Process (MDP hereafter) with finitely many st...