Bayesian Security Games for Controlling Contagion

Abstract

Influence blocking games have been used to model adversarial domains with a social component, such as counterinsurgency. In these games, a mitigator attempts to minimize the efforts of an influencer to spread his agenda across a social network. Previous work has assumed that the influence graph structure is known with certainty by both players. However, in reality, there is often significant information asymmetry between the mitigator and the influencer. We introduce a model of this information asymmetry as a two-player zero-sum Bayesian game. Nearly all past work in influence maximization and social network analysis suggests that graph structure is fundamental in strategy generation, leading to an expectation that solving the Bayesian game exactly is crucial. Surprisingly, we show through extensive experimentation on synthetic and real-world social networks that many common forms of uncertainty can be addressed near-optimally by ignoring the vast majority of it and simply solving an abstracted game with a few randomly chosen types. This suggests that optimal strategies of games that do not model the full range of uncertainty in influence blocking games are typically robust to uncertainty about the influence graph structure. I INTRODUCTIONSocial contagion has long been of great interest in the literature on marketing, the spread of rumors, and, recently, in the context of Arab Spring [1][2][3]. Our specific focus is on counterinsurgency, which we view as a competition for the support of local leaders. Counterinsurgency can be modeled as a game with two strategic players, the insurgents and the peacekeepers, in which the insurgents aim to spread their views, unrest, etc. among the local population, while the peacekeepers wish to minimize the resulting contagion by engaging in their own influence campaign [4][5][6]. The key computational question we address is: given limited resources, how to select which of the local leaders to influence to minimize the global impact of the insurgency.These 'influence blocking' games have received recent attention in the security games literature [6], where they have been modeled using graphs with nodes representing the tribal leaders and edges representing possible transmission of influence. However, this line of work has assumed that full information about network structure is available to both players. In practice, informational challenges abound in counterinsurgency, where the insurgents are typically an indigenous group that has an informational advantage, and the mitigators are often uncertain about the the social network [4].We model counterinsurgency as an influence blocking game with asymmetric information. Specifically, we assume that the influencer (an insurgent group) has perfect knowledge of the influence graph structure, while the mitigator is uncertain about it. In the resulting Bayesian game, an influencer type is a particular instantiation of the influence graph, and the mitigator must reason over the distribution over these graphs (i.e., influencer types...

Computational Game Theory for Security and Sustainability

“…Moreover, multiple intelligent parties attempt to leverage the same social network to spread their message, necessitating an adversary-aware approach to strategy generation. Game-theoretic approaches can be used to generate resource allocations strategies for such large-scale, real world networks [36], [37]. This interaction can be modeled as a graph with one player attempting to spread influence while another player attempts to stop the probabilistic propagation of that influence by spreading their own influence.…”

Game-Theoretic Target Selection in Contagion-Based Domains

“…DOPL requires more time than DOLP because of the fact that the defender PAGERANK oracle explicitly adapts to the attacker's strategy (only uses nodes adjacent to attacker nodes), while the attacker PAGERANK oracle does not. Previous work explored scaling to larger graphs with more resources, but since this is not the focus of our work, we refer the interested reader to Tsai et al [30]. Figure 8b shows the impact on solution quality as the graph size is scaled up.…”

Strategic analysis of complex security scenarios.

“…[66] introduce an important restricted class of Stackelberg games specifically targeted at security settings; they refer to these as Stackelberg security games, and demonstrate that extremely scalable algorithms can be devised for this class of games. Since then, a number of follow-up papers have emerged, studying, for the most part, computational aspects of the problem and aiming to scale the algorithms to larger and larger instances [75,106,109,61,69,62,38,105], as well as illustrating their actual deployment in the field, such as the LAX airport [94], Federal Air Marshall Service [63], and the US Coast Guard [101]. Of these approaches, [105] presents the most similar model to ours.…”

“…Since then, a number of follow-up papers have emerged, studying, for the most part, computational aspects of the problem and aiming to scale the algorithms to larger and larger instances [75,106,109,61,69,62,38,105], as well as illustrating their actual deployment in the field, such as the LAX airport [94], Federal Air Marshall Service [63], and the US Coast Guard [101]. Of these approaches, [105] presents the most similar model to ours. The principal difference is in the game structure and motivation: Tsai et al model both the defender and attacker as agents who aim to influence contagion of ideas in a simultaneous move game; thus, the two players actually have symmetric roles.…”