Kimmo Berg

Continuous learning methods in two-buyer pricing problem

This paper presents continuous learning methods in a monopoly pricing problem where the firm has uncertainty about the buyers’ preferences. The firm designs a menu of quality-price bundles and adjusts them using only local information about the buyers’ preferences. The learning methods define different paths, and we compare how much profit the firm makes on these paths, how long it takes to learn the optimal tariff, and how the buyers’ utilities change during the learning period. We also present a way to compute the optimal path in terms of discounted profit with dynamic programming and complete information. Numerical examples show that the optimal path may involve jumps where the buyer types switch from one bundle to another, and this is a property which is difficult to include in the learning methods. The learning methods have, however, the benefit that they can be generalized to pricing problems with many buyers types and qualities.

Elementary Subpaths in Discounted Stochastic Games

AbstractThis paper examines the subgame-perfect equilibria in discounted stochastic games with finite state and action spaces. The fixed-point characterization of equilibria is generalized to unobservable mixed strategies. It is also shown that the pure-strategy equilibria consist of elementary subpaths, which are repeating fragments that give the acceptable action plans in the game. The developed methodology offers a novel way of computing and analyzing equilibrium strategies that need not be stationary nor Markovian.

Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games

This paper examines how to construct subgame-perfect mixed-strategy equilibria in discounted repeated games with perfect monitoring. We introduce a relatively simple class of strategy profiles that are easy to compute and may give rise to a large set of equilibrium payoffs. These sets are called self-supporting sets, since the set itself provides the continuation payoffs that are required to support the equilibrium strategies. Moreover, the corresponding strategies are simple as the players face the same augmented game on each round but they play different mixed actions after each realized pure-action profile. We find that certain payoffs can be obtained in equilibrium with much lower discount factor values compared to pure strategies. The theory and the concepts are illustrated in 2 × 2 games.

Critical Discount Factor Values in Discounted Supergames

This paper examines the subgame-perfect equilibria in symmetric 2×2 supergames. We solve the smallest discount factor value for which the players obtain all the feasible and individually rational payoffs as equilibrium payoffs. We show that the critical discount factor values are not that high in many games and they generally depend on how large the payoff set is compared to the set of feasible payoffs. We analyze how the stage-game payoffs affect the required level of patience and organize the games into groups based on similar behavior. We study how the different strategies affect the set of equilibria by comparing pure, mixed and correlated strategies. This helps us understand better how discounting affects the set of equilibria and we can identify the games where extreme patience is required and the type of payoffs that are difficult to obtain. We also observe discontinuities in the critical values, which means that small changes in the stage-game payoffs may affect dramatically the equilibrium payoffs.

A game-theoretic evaluation of an ISP business model in caching

Internet traffic volume is increasing and this causes scalability issues in content delivery. This problem can be addressed with different types of caching solutions. The incentives of different stakeholders to pay for these solutions are not known. However, it has been identified that Internet service providers (ISPs) need to be involved in the process of cache deployment due to their ownership of the network. This work evaluates a new business model where ISPs charge content providers (CPs) for a caching service because CPs benefit from more efficient content distribution. We provide conditions for sustainable paid in-network caching and their numerical evaluation in order to aid strategic decision-making by CPs, ISPs, and Cloud storage providers (CSPs). Although ISP caching as a paid service may not be an equilibrium, it turns out to be Pareto optimal at the right pricing. This encourages cooperation between CPs and ISPs. CSPs may choose cache friendly physical locations for their facilities in order to provide the necessary capacity to the ISPs. However, the required amounts are in all likelihood too small to be an incentive for the CSPs. ISP caching as a paid service can be an equilibrium when future benefits are considered and when the ISPs terminate caching-related improvements of service quality for clients who do not pay for caching.

Priority-based classification of spectrum access models [Accepted From Open Call]

The reforms in spectrum management aim toward more efficient, flexible, and shared use of spectrum, while fostering innovation and competition in mobile communications. The goal is to have affordable wireless broadband and make Internet access a human right. To achieve this goal, the regulators need to identify, evaluate, and decide between the different spectrum access models. This article presents a taxonomy of the models, which is based on priorities between the different users of spectrum. For example, the low priority systems may be allowed to use the spectrum only if the high priority systems are not occupying the frequency. The hierarchy of the systems can be implemented using different technologies such as centralized databases or distributed sensing devices. The taxonomy clarifies the regulatory alternatives and emphasizes the differences in ownership and usage rights. The new models can be incorporated in the auction design in order to estimate their value to the companies, and this reflects the recent trend of supporting spectrum management with market- based methods.