arXiv subjects

Nagarajan Krishnamurthy

Publications and source records attributed to Nagarajan Krishnamurthy.

5 recordsLinked to original sources

arXiv2021

Resource Availability in the Social Cloud: An Economics Perspective

This paper focuses on social cloud formation, where agents are involved in a closeness-based conditional resource sharing and build their resource sharing network themselves. The objectives of this paper are: (1) to investigate the impact of agents' decisions of link addition and deletion on their local and global resource availability, (2) to analyze spillover effects in terms of the impact of link addition between a pair of agents on others' utility, (3) to study the role of agents' closeness in determining what type of spillover effects these agents experience in the network, and (4) to model the choices of agents that suggest with whom they want to add links in the social cloud. The findings include the following. Firstly, agents' decision of link addition (deletion) increases (decreases) their local resource availability. However, these observations do not hold in the case of global resource availability. Secondly, in a connected network, agents experience either positive or negative spillover effect and there is no case with no spillover effects. Agents observe no spillover effects if and only if the network is disconnected and consists of more than two components (sub-networks). Furthermore, if there is no change in the closeness of an agent (not involved in link addition) due to a newly added link, then the agent experiences negative spillover effect. Although an increase in the closeness of agents is necessary in order to experience positive spillover effects, the condition is not sufficient. By focusing on parameters such as closeness and shortest distances, we provide conditions under which agents choose to add links so as to maximise their resource availability.

cs.GT↗

arXiv2019

Externalities in Endogenous Sharing Economy Networks

This paper investigates the impact of link formation between a pair of agents on the resource availability of other agents (that is, externalities) in a social cloud network, a special case of endogenous sharing economy networks. Specifically, we study how the closeness between agents and the network size affect externalities. We conjecture, and experimentally support, that for an agent to experience positive externalities, an increase in its closeness is necessary. The condition is not sufficient though. We, then, show that for populated ring networks, one or more agents experience positive externalities due to an increase in the closeness of agents. Further, the initial distance between agents forming a link has a direct bearing on the number of beneficiaries, and the number of beneficiaries is always less than that of non-beneficiaries.

cs.GT↗

arXiv2018

Stability, Efficiency, and Contentedness of Social Storage Networks

Social storage systems are a good alternative to existing data backup systems of local, centralized, and P2P backup. In this paper, we look at two untouched aspects of social storage systems. One aspect involves modelling social storage as an endogenous social network, where agents themselves decide with whom they want to build data backup relation. The second aspect involves studying the stability of social storage systems, which would help reduce maintenance costs and further, help build efficient as well as contented networks. We have a four fold contribution that covers the above two aspects. We, first, model the social storage system as a strategic network formation game. We define the utility of each agent in the network under two different frameworks. Second, we propose the concept of bilateral stability which refines the pairwise stability concept defined by Jackson et. al. 1996, by requiring mutual consent for both addition and deletion of links, as compared to mutual consent just for link addition. Mutual consent for link deletion is especially important in the social storage setting. Third, we prove necessary and the sufficient conditions for bilateral stability of social storage networks. For symmetric social storage networks, we prove that there exists a unique neighborhood size, independent of the number of agents (for all non-trivial cases), where no pair of agents has any incentive to increase or decrease their neighborhood size. We call this neighborhood size as the stability point. Fourth, given the number of agents and other parameters, we discuss which bilaterally stable networks would evolve and also discuss which of these stable networks are efficient --- that is, stable networks with maximum sum of utilities of all agents. We also discuss ways to build contented networks, where each agent achieves the maximum possible utility.

cs.GT↗

arXiv2017

Data Backup Network Formation with Heterogeneous Agents

Social storage systems are becoming increasingly popular compared to the existing data backup systems like local, centralized and P2P systems. An endogenously built symmetric social storage model and its aspects like the utility of each agent, bilateral stability, contentment, and efficiency have been extensively discussed in Mane et. al. (2017). We include heterogeneity in this model by using the concept of Social Range Matrix from Kuznetsov et. al (2010). Now, each agent is concerned about its perceived utility, which is a linear combination of its utility as well as others utilities (depending upon whether the pair are friends, enemies or do not care about each other). We derive conditions when two agents may want to add or delete a link, and provide an algorithm that checks if a bilaterally stable network is possible or not. Finally, we take some special Social Range Matrices and prove that under certain conditions on network parameters, a bilaterally stable network is unique.

cs.MA↗

arXiv2010

Some Tractable Win-Lose Games

Determining a Nash equilibrium in a $2$-player non-zero sum game is known to be PPAD-hard (Chen and Deng (2006), Chen, Deng and Teng (2009)). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and Valiant (2005)). However, there do exist polynomial time tractable classes of win-lose bimatrix games - such as, very sparse games (Codenotti, Leoncini and Resta (2006)) and planar games (Addario-Berry, Olver and Vetta (2007)). We extend the results in the latter work to $K_{3,3}$ minor-free games and a subclass of $K_5$ minor-free games. Both these classes of games strictly contain planar games. Further, we sharpen the upper bound to unambiguous logspace, a small complexity class contained well within polynomial time. Apart from these classes of games, our results also extend to a class of games that contain both $K_{3,3}$ and $K_5$ as minors, thereby covering a large and non-trivial class of win-lose bimatrix games. For this class, we prove an upper bound of nondeterministic logspace, again a small complexity class within polynomial time. Our techniques are primarily graph theoretic and use structural characterizations of the considered minor-closed families.

cs.GT↗