A semi-dynamic model for competition over popularity and over advertisement space in social networks

We consider in this paper competition of content creators in routing their content through various media. The routing decisions may correspond to the selection of a social network (e.g. twitter versus facebook or linkedin) or of a group within a given social network. The utility for a player to send its content to some medium is given as the difference between the dissemination utility at this medium and some transmission cost. We model this game as a congestion game and compute the pure potential of the game. In contrast to the continuous case, we show that there may be various equilibria. We show that the potential is M-concave which allows us to characterize the equilibria and to propose an algorithm for computing it. We then give a learning mechanism which allow us to give an efficient algorithm to determine an equilibrium. We finally determine the asymptotic form of the equilibrium and discuss the implications on the social medium selection problem.Proposition 5. For any setting Γ, the number of Nash equilibria is upper bounded. More precisely, let E Γ be the set of the loads of the Nash equilibria of Γ. Then:Further, this bound is tight. Indeed, let J ≥ 2, m ∈ N * and γ ∈ R + . We define the game Γ by K = J 2 and ∀j ∈ J, N j = m, γ j = γ. Then |E Γ | = J ⌊ J 2 ⌋ . The proof of Proposition 5 is given in Appendix A. Note that the bound is in

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“…This implies the structure of point (ii). The use of this type of utility in competition for resources in social networks can be found in [2].…”

Section: Model and Notationsmentioning

confidence: 99%

“…A similar game as the one in this paper was already studied in [2] and [3], but there the players control rates of creation of contents and/or decide how to split the rates. The resulting games are simpler than ours as they possess a single equilibrium.…”

Section: Introductionmentioning

confidence: 99%

The Social Medium Selection Game

Lebeau

Touati

Altman

et al. 2019

Static &Amp; Dynamic Game Theory: Foundations &Amp; Applications

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“…We have studied such problems in [4], [3]. In those problems, however, the costs turn out to be linear in the state, which allows one to reduce the complexity of the problem and to obtain some characteristics of the equilibrium policies.…”

Section: Related Workmentioning

confidence: 99%

An epidemic game between contents in a wireless network

Altman

2012

2012 International Symposium on Wireless Communication Systems (ISWCS)

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Abstract-Consider a town with N competing sources of content where each one wishes to disseminate its own content and thus to make its content available to as many destination users as possible. A content here may stand for information about somoe cultural event or the list of hotels in town or the wheather report. The dissemination to the potential destination is done through a fleet of M mobile relays. The rate of dissemination of content of a given source to its potential destinations depends on how many relays have a copy of the content. We therefore focus on the problem of competition over the access to relays. Each source has to trade between the access costs and and the availability of his content in the relays. As access cost we consider here the transmission power used by the source. The power used determines the coverage of the transmission and thus the probability of reaching some relay. We model the competition using stochastic game approaches and then obtain the structure of the equilibrium strategies.

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“…Both fully dynamic [5] models as well as semi-dynamic [6] models have been proposed. It has been noted that these problems are similar in nature to the problem of competition over shelf space, a problem well studied in Operations Research (see [7]).…”

Section: Introductionmentioning

confidence: 99%

Competition over timeline in social networks

Altman

Kumar

Venkatramanan

et al. 2013

Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining

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Social networking sites pervade the World Wide Web and have millions of users worldwide. This provides ample opportunity for brands and organisations to reach out to a large and diverse audience. They do so by creating content and spreading it across the social network. Most popular social networks follow a timeline based homepage to display such content to the end users. Content once posted on the timeline, remains visible for a limited time, determined by the rate of content generation in the network. There are various ways by which brands can become more visible on the timeline of their followers, for instance by retransmitting/advertising their content from time to time. Hence, with multiple content creators in the network, there is a competition over a user's timeline, which we analyse in this paper. We first characterise the occupancy distribution of a given user's timeline and then use queueing techniques to analyse the period of time a content is present on a given timeline. We then study the competition between different content creators and characterise the equilibrium rate of content generation. We finally provide some numerical results, which provide insights into the effect of various system parameters.

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A semi-dynamic model for competition over popularity and over advertisement space in social networks

Cited by 10 publications

References 12 publications

The Social Medium Selection Game

The Social Medium Selection Game

An epidemic game between contents in a wireless network

Competition over timeline in social networks

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