Arnob Ghosh

Quality sensitive price competition in spectrum oligopoly

We investigate a spectrum oligopoly where primary users allow secondary access in lieu of financial remuneration. Transmission qualities of the licensed bands fluctuate randomly. Each primary needs to select the price of its channel with the knowledge of its own channel state but not that of its competitors. Secondaries choose among the channels available on sale based on their states and prices. We formulate the price selection as a non-cooperative game and prove that a symmetric Nash equilibrium (NE) strategy profile exists uniquely. We explicitly compute this strategy profile and analytically and numerically evaluate its efficiency. Our structural results provide certain key insights about the unique symmetric NE.

Quality-sensitive price competition in secondary market spectrum oligopoly: single location game

We investigate a spectrum oligopoly market where each primary seeks to sell its channel to a secondary. Transmission rate of a channel evolves randomly. Each primary needs to select a price depending on the transmission rate of its channel. Each secondary selects a channel depending on the price and the transmission rate of the channel. We formulate the above problem as a noncooperative game. We show that there exists a unique Nash equilibrium (NE) and explicitly compute it. Under the NE strategy profile, a primary prices its channel to render the channel that provides high transmission rate more preferable; this negates the perception that prices ought to be selected to render channels equally preferable to the secondary regardless of their transmission rates. We show the loss of revenue in the asymptotic limit due to the noncooperation of primaries. In the repeated version of the game, we characterize a subgame perfect NE where a primary can attain a payoff arbitrarily close to the payoff it would obtain when primaries cooperate.

Nash Equilibrium for Femto-Cell Power Allocation in HetNets with Channel Uncertainty

We propose power allocation among femto-base stations (femto-BSs) in a heterogeneous network (HetNet) based on non cooperative games. A minimum level of quality of service has to be guaranteed at macro-user terminals (macro-UTs). Femto-BSs are unaware of the exact values of the channel parameters between them and macro-UTs because of the lack of cooperation and fading. First, we consider the design criterion where the outage probability has to be below a certain threshold at macro-UTs. The equilibrium concept is based on the Normalized Nash Equilibrium (NNE) since it caters to the distributed setting. NNE is unique only for a few strictly concave utility functions in this case. We introduce the concept of Weakly Normalized Nash Equilibrium (WNNE) which keeps the most of the appealing features of NNE but can be extended to a wide class of utility functions and can be incorporated with low complexity. Finally, we consider the design criterion where the expected SINR at a macro-UT has to be greater than a threshold. In this case, the NNE is always unique for any strictly concave utility functions.

Quality sensitive price competition in spectrum oligopoly over multiple locations

We investigate a spectrum oligopoly market where each primary seeks to sell secondary access to channels at multiple locations. Transmission qualities of a channel evolve randomly. Each primary needs to select a price and a set of non-interfering locations (which is the independent set in the conflict graph of the region) at which to offer its channel without knowing the transmission qualities of the channels of its competitors. Secondaries select a channel depending on the price and the quality the channel offers. We formulate the above problem as a non-cooperative game theoretic problem. We focus on a class of conflict graphs, known as mean valid graphs which commonly arise in practice. We explicitly compute a symmetric Nash equilibrium (NE) that selects only a small number of independent sets with positive probability. The NE is threshold type in that primaries do not choose independent sets whose cardinality fall below a certain threshold. The threshold on the cardinality increases with increase in quality of the channel on sale.

Control of charging of electric vehicles through menu-based pricing under uncertainty

We propose an online pricing mechanism for electric vehicle (EV) charging. A charging station decides prices for each arriving EV depending on the energy and the time within which the EV will be served (i.e., deadline). The user selects either one of the contracts by paying the prescribed price or rejects all depending on their surpluses. The charging station can serve users using renewable energy and conventional energy. Users may select longer deadlines as they may have to pay less because of the less amount of conventional energy, however, they have to wait a longer period. We consider a myopic charging station and show that there exists a pricing mechanism which jointly maximizes the social welfare and the profit of the charging station when the charging station knows the utilities of the users. However, when the charging station does not know the utilities of the users, the social welfare pricing strategy may not maximize the expected profit of the charging station and even the profit may be 0. We propose a fixed profit pricing strategy which provides a guaranteed fixed profit to the charging station and can maximize the profit in practice. We empirically show that our proposed mechanism reduces the peak-demand and utilizes the limited charging spots in a charging station efficiently.

The Value of Side-Information in Secondary Spectrum Markets

We consider a secondary spectrum market where primaries set prices for their unused channels. The payoff of a primary then depends on the availability of channels for its competitors, which a primary might not have information about. We study a model where a primary can acquire this competitor’s channel state information (C-CSI) at a cost. We formulate a game between two primaries, where each primary decides whether to acquire the C-CSI or not and then selects its price based on that. We first characterize the Nash equilibrium of this game for a symmetric model where the C-CSI is perfect. We show that the payoff of a primary is independent of the C-CSI acquisition cost. We then generalize our analysis to allow for imperfect estimation and cases, where the two primaries have different C-CSI costs or different channel availabilities. Our results show interestingly that the payoff of a primary increases when there is estimation error. We also show that surprisingly the expected payoff of a primary may decrease when the C-CSI acquisition cost decreases or primaries have different availabilities.

Secondary spectrum market: To acquire or not to acquire side information?

In a secondary spectrum market primaries set prices for their unused channels to the secondaries. The payoff of a primary depends on the channel state information (CSI) of its competitors. We consider a model where a primary can acquire its competitors CSI at a cost. We formulate a game between two primaries where each primary decides whether to acquire its competitors CSI or not and then selects its price based on that. Our result shows that no primary decide to acquire its competitors CSI with an absolute certainty. When the cost of acquiring the CSI is above a threshold, there is a unique Nash Equilibrium (NE) where both the primaries remain uninformed of their respective competitors CSI. When the cost is below the threshold, in the unique NE each primary randomizes between its decision to acquire the CSI or not. Our result reveals that irrespective of the cost of acquiring the CSI, the expected payoff of a primary remains the same.

Pricing for profit in internet of things

We investigate the economics of internet of things (IoT). An economic model of IoT consists of end users, advertisers and three different kinds of providers. We model different kinds of interaction among the providers as a combination of sequential and parallel non-cooperative games. We characterize the equilibrium pricing strategy and payoff of providers and corresponding demands of end users in each such setting. We quantify the impact of advertising revenue on the equilibrium pricing and demands, and compare the payoffs and demands for different interaction models.

Tiered cloud storage via two-stage, latency-aware bidding

In cloud storage, the digital data is stored in logical storage pools, backed by heterogeneous physical storage media and computing infrastructure that are managed by a cloud service provider (CSP). One of the key advantages of cloud storage is its elastic pricing mechanism, in which the users need only pay for the resources/services they actually use, e.g., depending on the storage capacity consumed, the number of file accesses per month, and the negotiated service level agreement. To balance the tradeoff between service performance and cost, CSPs often employ different storage tiers, for instance, cold storage and hot storage. Storing data in hot storage incurs high storage cost yet delivers low access latency, whereas cold storage is able to inexpensively store massive amounts of data and thus provides lower cost with higher latency. In this paper, we address a major challenge confronting the CSPs utilizing such tiered storage architecture—how to maximize their overall profit over a variety of storage tiers that offer distinct characteristics, as well as file placement and access request scheduling policies. To this end, we propose a scheme where the CSP offers a two-stage auction process for: 1) requesting storage capacity and 2) requesting accesses with latency requirements. Our two-stage bidding scheme provides a hybrid storage and access optimization framework with the objective of maximizing the CSP’s total net profit over four dimensions: file acceptance decision, placement of accepted files, file access decision and access request scheduling policy. The proposed optimization is a mixed-integer nonlinear program that is hard to solve. We propose an efficient heuristic to relax the integer optimization and to solve the resulting nonlinear stochastic programs. The algorithm is evaluated under different scenarios and with different storage system parameters, and insightful numerical results are reported by comparing the proposed approach with other profit-maximization models. We see a profit increase of over 60% of our proposed method compared to other baseline algorithms in certain simulation scenarios.

Secondary spectrum oligopoly market over large locations

We investigate a secondary spectrum market where each primary owns a channel over large number of locations. Each primary sells its channel to the secondaries in exchange of a price. However, the secondaries can not transmit simultaneously at interfering locations. A primary must select a price and a set on non-interfering locations for its available channel where the availability of a channel for sale evolves randomly. The set of non-interfering locations turns out to be an independent set in the conflict graph representation of the region. The primary needs to find a strategy for each possible channel state vector. We consider node symmetric conflict graphs which arise frequently in practice when the number of locations is large (potentially, infinite). Since there is a symmetry in the interference relationship, we also consider a symmetric relationship among the joint probability distribution of the channel state vectors. We show that that a symmetric NE exists and explicitly compute it. In the symmetric NE a primary randomizes equally among the maximum independent sets at a given channel state vector. The symmetric NE exhibits several important structural differences compared to the symmetric NE strategy for small number of locations which we have obtained in our earlier works. The conflict graph representation depends on the channel state vector, thus, it is a random graph. We also empirically and theoretically investigate the expected component size in random conflict graphs which governs the computation of maximum independent sets. Our analysis shows that the mean component size is in general moderate, however, it can be high when the channel availability probability is very high. We show that with random sampling method, a primary can govern the mean component size. We numerically evaluate the ratio of the expected payoff attained by primaries in the game and the payoff attained by primaries when all the primaries collude.