Optimal Investment Strategies for Competing Camps in a Social Network: A Broad Framework

Abstract

We study the problem of optimally investing in nodes of a social network in a competitive setting, where two camps aim to maximize adoption of their opinions by the population. In particular, we consider the possibility of campaigning in multiple phases, where the final opinion of a node in a phase acts as its initial biased opinion for the following phase. Using an extension of the popular DeGroot-Friedkin model, we formulate the utility functions of the camps, and show that they involve what can be interpreted as multiphase Katz centrality. Focusing on two phases, we analytically derive Nash equilibrium investment strategies, and the extent of loss that a camp would incur if it acted myopically. Our simulation study affirms that nodes attributing higher weightage to initial biases necessitate higher investment in the first phase, so as to influence these biases for the terminal phase. We then study the setting in which a camp's influence on a node depends on its initial bias. For single camp, we present a polynomial time algorithm for determining an optimal way to split the budget between the two phases. For competing camps, we show the existence of Nash equilibria under reasonable assumptions, and that they can be computed in polynomial time.

A two phase investment game for competitive opinion dynamics in social networks

“…To the best of our knowledge, there has not been an analytical study on a rich model such as Friedkin-Johnsen, for opinion dynamics in two phases (not even for single camp). The most relevant to this study is our earlier work [47] where, however, a camp's influence on a node is assumed to be independent of the node's bias. In this paper, we consider a more realistic setting by relaxing this assumption.…”

“…In this paper, we consider a more realistic setting by relaxing this assumption. An interesting outcome of relaxing this assumption is that, while the camps' optimal strategies turn out to be mutually independent in [47], these strategies get coupled in our setting. In other words, the setting in [47] results in a competition, while the one in this paper results in a game.…”

“…(The terminologies 'good' and 'bad' camps are used only for the ease of interpretation that one camp holds a positive opinion while the other camp holds a negative opinion on the real number line; it does not necessarily imply that one camp is more virtuous than the other.) We consider a well-accepted quantification of the overall opinion of a network: the average or equivalently, the sum of opinion values of the nodes in the social network [4,5,6]. Hence, the good and bad camps simultaneously aim to maximize and minimize this sum, respectively.…”

Spread of Information With Confirmation Bias in Cyber-Social Networks

“…In [19], every individual updates her belief as an average of her neighbors. In [20], the model further involves innate opinions, see also [22], [23]. In this paper, we focus on the topology inference problem of networks with known information dynamics such as the ones in [19]- [21], with the important explicit consideration of confirmation bias.…”

“…It is well known that machine learning algorithms that filter news on social media feeds automatically utilize and foster this bias, see e.g., [24]- [26], hence contribute to the polarizations of public opinions. We consider this work as a part of comprehensive exploration of mathematical underpinnings of the misinformation spread in networks, see e.g., [22], [27]- [31].…”