How to Run a Campaign: Optimal Control of SIS and SIR Information Epidemics

Information spreading in a population can be modeled as an epidemic. Campaigners (e.g. election campaign managers, companies marketing products or movies) are interested in spreading a message by a given deadline, using limited resources. In this paper, we formulate the above situation as an optimal control problem and the solution (using Pontryagin's Maximum Principle) prescribes an optimal resource allocation over the time of the campaign. We consider two different scenarios --- in the first, the campaigner can adjust a direct control (over time) which allows her to recruit individuals from the population (at some cost) to act as spreaders for the Susceptible-Infected-Susceptible (SIS) epidemic model. In the second case, we allow the campaigner to adjust the effective spreading rate by incentivizing the infected in the Susceptible-Infected-Recovered (SIR) model, in addition to the direct recruitment. We consider time varying information spreading rate in our formulation to model the changing interest level of individuals in the campaign, as the deadline is reached. In both the cases, we show the existence of a solution and its uniqueness for sufficiently small campaign deadlines. For the fixed spreading rate, we show the effectiveness of the optimal control strategy against the constant control strategy, a heuristic control strategy and no control. We show the sensitivity of the optimal control to the spreading rate profile when it is time varying.Comment: Proofs for Theorems 4.2 and 5.2 which do not appear in the published journal version are included in this version. Published version can be accessed here: http://dx.doi.org/10.1016/j.amc.2013.12.16

Modeling Inflation in India: The Role of Money

This paper studies the role of the real money gap- the deviation of real money balance from its long-run equilibrium level- for predicting inflation in India. Using quarterly data on manufacturing inflation from 1982 to 2007, we find that the real money gap is a significant predictor of inflation in India. Our results show that this variable is a better predictor of future inflation at quarterly horizon than the deviation of broad money growth from its target for the whole sample period. We also document a break in the overall predictability of inflation in the last quarter of 1995. We find that except for the real money gap, the forecasting power of other predictors under study has declined considerably after 1995.Inflation. Monetary Policy, Indian Economy

Data Revisions in India and its Implications for Monetary Policy

This paper studies data revision properties of GDP growth and inflation as measured by the Wholesale Price Index (WPI) for the Indian economy. We find that data revisions to GDP growth and WPI inflation in India are significant. The results show that revisions to GDP growth and WPI inflation can not be characterized as either containing pure news or pure noise. We also find that there is a significant predictable component in revisions to GDP growth and inflation. Our findings suggest that if the Reserve Bank of India were to follow a Taylor rule for its monetary policy formulation, then the interest rate based on the preliminary data would be much lower than the one based on the fully revised data.Data Revisions, Real-Time Data, Monetary Policy

Game Theoretic Analysis of Tree Based Referrals for Crowd Sensing Social Systems with Passive Rewards

Participatory crowd sensing social systems rely on the participation of large number of individuals. Since humans are strategic by nature, effective incentive mechanisms are needed to encourage participation. A popular mechanism to recruit individuals is through referrals and passive incentives such as geometric incentive mechanisms used by the winning team in the 2009 DARPA Network Challenge and in multi level marketing schemes. The effect of such recruitment schemes on the effort put in by recruited strategic individuals is not clear. This paper attempts to fill this gap. Given a referral tree and the direct and passive reward mechanism, we formulate a network game where agents compete for finishing crowd sensing tasks. We characterize the Nash equilibrium efforts put in by the agents and derive closed form expressions for the same. We discover free riding behavior among nodes who obtain large passive rewards. This work has implications on designing effective recruitment mechanisms for crowd sourced tasks. For example, usage of geometric incentive mechanisms to recruit large number of individuals may not result in proportionate effort because of free riding.Comment: 6 pages, 3 figures. Presented in Social Networking Workshop at International Conference on Communication Systems and Networks (COMSNETS), Bangalore, India, January 201

Optimal Resource Allocation Over Time and Degree Classes for Maximizing Information Dissemination in Social Networks

We study the optimal control problem of allocating campaigning resources over the campaign duration and degree classes in a social network. Information diffusion is modeled as a Susceptible-Infected epidemic and direct recruitment of susceptible nodes to the infected (informed) class is used as a strategy to accelerate the spread of information. We formulate an optimal control problem for optimizing a net reward function, a linear combination of the reward due to information spread and cost due to application of controls. The time varying resource allocation and seeds for the epidemic are jointly optimized. A problem variation includes a fixed budget constraint. We prove the existence of a solution for the optimal control problem, provide conditions for uniqueness of the solution, and prove some structural results for the controls (e.g. controls are non-increasing functions of time). The solution technique uses Pontryagin's Maximum Principle and the forward-backward sweep algorithm (and its modifications) for numerical computations. Our formulations lead to large optimality systems with up to about 200 differential equations and allow us to study the effect of network topology (Erdos-Renyi/scale-free) on the controls. Results reveal that the allocation of campaigning resources to various degree classes depends not only on the network topology but also on system parameters such as cost/abundance of resources. The optimal strategies lead to significant gains over heuristic strategies for various model parameters. Our modeling approach assumes uncorrelated network, however, we find the approach useful for real networks as well. This work is useful in product advertising, political and crowdfunding campaigns in social networks.Comment: 14 + 4 pages, 11 figures. Author's version of the article accepted for publication in IEEE/ACM Transactions on Networking. This version includes 4 pages of supplementary material containing proofs of theorems present in the article. Published version can be accessed at http://dx.doi.org/10.1109/TNET.2015.251254

Robust Power Allocation and Outage Analysis for Secrecy in Independent Parallel Gaussian Channels

This letter studies parallel independent Gaussian channels with uncertain eavesdropper channel state information (CSI). Firstly, we evaluate the probability of zero secrecy rate in this system for (i) given instantaneous channel conditions and (ii) a Rayleigh fading scenario. Secondly, when non-zero secrecy is achievable in the low SNR regime, we aim to solve a robust power allocation problem which minimizes the outage probability at a target secrecy rate. We bound the outage probability and obtain a linear fractional program that takes into account the uncertainty in eavesdropper CSI while allocating power on the parallel channels. Problem structure is exploited to solve this optimization problem efficiently. We find the proposed scheme effective for uncertain eavesdropper CSI in comparison with conventional power allocation schemes.Comment: 4 pages, 2 figures. Author version of the paper published in IEEE Wireless Communications Letters. Published version is accessible at http://dx.doi.org/10.1109/LWC.2015.249734

The Instability in the Monetary Policy Reaction Function and the Estimation of Monetary Policy Shocks

This paper uses the conventional wisdom about the shift in the monetary policy stance in 1979 to compute monetary policy shocks by estimating different monetary policy reaction functions for the pre-1979 and post-1979 time periods. We use the information from the internal forecasts of the Federal Reserve to derive monetary policy shocks. The results in this paper show that a monetary policy shock in the pre-1979 period affects output and prices much more strongly and quickly than what has been reported in the literature for the full sample. Our findings suggest that the dynamic response of output and prices to a monetary policy shock declined significantly between 1980-2001. We argue that this diminished response to the monetary policy shock is the result of a successful monetary policy that has led to a less volatile economy.Monetary Policy Shocks, Greenbook data, Reaction Function

Is the East African Community an Optimum Currency Area?

This paper investigates whether the East African Community (EAC) constitutes an optimum currency area (OCA) by estimating the degree and evolution of business cycle synchronization between the EAC countries. We also investigate whether the degree of business cycle synchronization has improved after signing of the EAC treaty in 1999. The degree of business cycle synchronization is estimated using an unobserved components model of structural shocks obtained from a structural VAR model. We then use a time-varying parameter model to estimate the evolution of business cycle synchronization. Our results indicate that the proportion of shocks that is common across different countries is small, implying weak synchronization. However, we also find that the degree of synchronization has improved after signing of the EAC treaty in 1999.East African Community, Optimum Currency Area, Business Cycle Synchronization, Structural VAR, State-Space Model