Pricing in Social Networks with Negative Externalities

We study the problems of pricing an indivisible product to consumers who are embedded in a given social network. The goal is to maximize the revenue of the seller. We assume impatient consumers who buy the product as soon as the seller posts a price not greater than their values of the product. The product's value for a consumer is determined by two factors: a fixed consumer-specified intrinsic value and a variable externality that is exerted from the consumer's neighbors in a linear way. We study the scenario of negative externalities, which captures many interesting situations, but is much less understood in comparison with its positive externality counterpart. We assume complete information about the network, consumers' intrinsic values, and the negative externalities. The maximum revenue is in general achieved by iterative pricing, which offers impatient consumers a sequence of prices over time. We prove that it is NP-hard to find an optimal iterative pricing, even for unweighted tree networks with uniform intrinsic values. Complementary to the hardness result, we design a 2-approximation algorithm for finding iterative pricing in general weighted networks with (possibly) nonuniform intrinsic values. We show that, as an approximation to optimal iterative pricing, single pricing can work rather well for many interesting cases, but theoretically it can behave arbitrarily bad

Optimal Pricing Effect on Equilibrium Behaviors of Delay-Sensitive Users in Cognitive Radio Networks

This paper studies price-based spectrum access control in cognitive radio networks, which characterizes network operators' service provisions to delay-sensitive secondary users (SUs) via pricing strategies. Based on the two paradigms of shared-use and exclusive-use dynamic spectrum access (DSA), we examine three network scenarios corresponding to three types of secondary markets. In the first monopoly market with one operator using opportunistic shared-use DSA, we study the operator's pricing effect on the equilibrium behaviors of self-optimizing SUs in a queueing system. %This queue represents the congestion of the multiple SUs sharing the operator's single \ON-\OFF channel that models the primary users (PUs) traffic. We provide a queueing delay analysis with the general distributions of the SU service time and PU traffic using the renewal theory. In terms of SUs, we show that there exists a unique Nash equilibrium in a non-cooperative game where SUs are players employing individual optimal strategies. We also provide a sufficient condition and iterative algorithms for equilibrium convergence. In terms of operators, two pricing mechanisms are proposed with different goals: revenue maximization and social welfare maximization. In the second monopoly market, an operator exploiting exclusive-use DSA has many channels that will be allocated separately to each entering SU. We also analyze the pricing effect on the equilibrium behaviors of the SUs and the revenue-optimal and socially-optimal pricing strategies of the operator in this market. In the third duopoly market, we study a price competition between two operators employing shared-use and exclusive-use DSA, respectively, as a two-stage Stackelberg game. Using a backward induction method, we show that there exists a unique equilibrium for this game and investigate the equilibrium convergence.Comment: 30 pages, one column, double spac

Tolling, Capacity Selection and Equilibrium Problems with Equilibrium Constraints

An Equilibrium problem with an equilibrium constraint is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium regarding competition in toll pricing on a network utilising 2 alternative algorithms. In the first algorithm, we utilise a Gauss Siedel fixed point approach based on the cutting constraint algorithm for toll pricing. In the second algorithm, we extend an existing sequential linear complementarity approach for finding Nash equilibrium subject to Wardrop Equilibrium constraints. Finally we consider how the equilibrium may change between the Nash competitive equilibrium and a collusive equilibrium where the two players co-operate to form the equivalent of a monopoly operation

llc: a collection of R functions for fitting a class of Lee-Carter mortality models using iterative fitting algorithms

We implement a specialised iterative regression methodology in R for the analysis of age-period mortality data based on a class of generalised Lee-Carter (LC) type modelling structures. The LC-based modelling frameworks is viewed in the current literature as among the most efficient and transparent methods of modelling and projecting mortality improvements. Thus, we make use of the modelling approach discussed in Renshaw and Haberman (2006), which extends the basic LC model and proposes to make use of a tailored iterative process to generate parameter estimates based on Poisson likelihood. Furthermore, building on this methodology we develop and implement a stratified LC model for the measurement of the additive effect on the log scale of an explanatory factor (other than age and time). This modelling methodology is implemented in a publically available collection of programming functions that facilitate both the preparation of mortality data and the fitting and analysis of the given log-linear modelling structures. Also, the package incorporates methods to produce forecasts of future mortality rates and to compute the corresponding future life expectancy

Communication-efficient Distributed Multi-resource Allocation

In several smart city applications, multiple resources must be allocated among competing agents that are coupled through such shared resources and are constrained --- either through limitations of communication infrastructure or privacy considerations. We propose a distributed algorithm to solve such distributed multi-resource allocation problems with no direct inter-agent communication. We do so by extending a recently introduced additive-increase multiplicative-decrease (AIMD) algorithm, which only uses very little communication between the system and agents. Namely, a control unit broadcasts a one-bit signal to agents whenever one of the allocated resources exceeds capacity. Agents then respond to this signal in a probabilistic manner. In the proposed algorithm, each agent makes decision of its resource demand locally and an agent is unaware of the resource allocation of other agents. In empirical results, we observe that the average allocations converge over time to optimal allocations.Comment: To appear in IEEE International Smart Cities Conference (ISC2 2018), Kansas City, USA, September, 2018. arXiv admin note: substantial text overlap with arXiv:1711.0197