We consider a dynamic pricing problem where customer response to the current price is impacted by the customer price expectation, aka reference price. We study a simple and novel reference price mechanism where reference price is the average of the past prices offered by the seller. As opposed to the more commonly studied exponential smoothing mechanism, in our reference price mechanism the prices offered by seller have a longer term effect on the future customer expectations. We show that under this mechanism, a markdown policy is near-optimal irrespective of the parameters of the model. This matches the common intuition that a seller may be better off by starting with a higher price and then decreasing it, as the customers feel like they are getting bargains on items that are ordinarily more expensive. For linear demand models, we also provide a detailed characterization of the near-optimal markdown policy along with an efficient way of computing it. We then consider a more challenging dynamic pricing and learning problem, where the demand model parameters are apriori unknown, and the seller needs to learn them online from the customers' responses to the offered prices while simultaneously optimizing revenue. The objective is to minimize regret, i.e., the $T$-round revenue loss compared to a clairvoyant optimal policy. This task essentially amounts to learning a non-stationary optimal policy in a time-variant Markov Decision Process (MDP). For linear demand models, we provide an efficient learning algorithm with an optimal $\tilde{O}(\sqrt{T})$ regret upper bound.

Users of public permissionless blockchains can modify the shared state of the network through transactions that are executed by a set of nodes with limited computational resources. To allocate resources among competing transactions most blockchains use transaction fees. Initial transaction fee mechanisms in the Bitcoin and Ethereum blockchains relied on users bidding for transaction inclusion as the main way of pricing congestion. Moreover, all computational resources were bundled into a unique virtual resource ("gas") with fixed relative prices hardcoded in the protocol. Current R&D efforts are focused on improving transaction fee markets along two directions: (1) setting a minimum dynamic base fee (henceforth also called price) that is adjusted by the protocol as function of user demand and (2) unbundling resources so that different resources can be individually priced and their relative prices can also efficiently adjust with demand. In this paper, we propose a new framework for choosing a resource pricing policy that makes significant progress across both directions. We consider the practical problem of a blockchain protocol that has to jointly update the prices of multiple resources at every block. We assume that the type of resources being metered and priced, as well as the block limits and sustainable targets for each resource, are pre-determined.

We study the problem of how to optimize a cloud service provider's pricing policy so as to better compete with other providers. Different from previous work, we take both the evolution of the market and the competition between multiple cloud providers into consideration while optimizing the pricing strategy for the provider. Inspired by the real situations in today's cloud market, we consider a situation in which there is only one provider who actively optimizes his/her pricing policy, while other providers adopt a follow-up policy to match his/her price cut. To compute optimal pricing policy under the above settings, we decompose the optimization problem into two steps: (1) When the market finally becomes saturated, we use Q-learning, a method of reinforcement learning, to derive an optimal pricing policy for the stationary market; (2) Based on the optimal policy for the stationary market, we use backward induction to derive an optimal pricing policy for the situation of competition in an evolutionary market. Numerical simulations demonstrate the effectiveness of our proposed approach.

We study the problem of how to optimize a cloud service provider's pricing policy so as to better compete with other providers. Different from previous work, we take both the evolution of the market and the competition between multiple cloud providers into consideration while optimizing the pricing strategy for the provider. Inspired by the real situations in today's cloud market, we consider a situation in which there is only one provider who actively optimizes his/her pricing policy, while other providers adopt a follow-up policy to match his/her price cut. To compute optimal pricing policy under the above settings, we decompose the optimization problem into two steps: (1) When the market finally becomes saturated, we use Q-learning, a method of reinforcement learning, to derive an optimal pricing policy for the stationary market; (2) Based on the optimal policy for the stationary market, we use backward induction to derive an optimal pricing policy for the situation of competition in an evolutionary market. Numerical simulations demonstrate the effectiveness of our proposed approach.