A Survey on Interdependent Privacy <s> Game Theory <s> This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published "Theory of Games and Economic Behavior." In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. <s> BIB001 </s> A Survey on Interdependent Privacy <s> Game Theory <s> This survey provides a structured and comprehensive overview of research on security and privacy in computer and communication networks that use game-theoretic approaches. We present a selected set of works to highlight the application of game theory in addressing different forms of security and privacy problems in computer networks and mobile applications. We organize the presented works in six main categories: security of the physical and MAC layers, security of self-organizing networks, intrusion detection systems, anonymity and privacy, economics of network security, and cryptography. In each category, we identify security problems, players, and game models. We summarize the main results of selected works, such as equilibrium analysis and security mechanism designs. In addition, we provide a discussion on the advantages, drawbacks, and future direction of using game theory in this field. In this survey, our goal is to instill in the reader an enhanced understanding of different research approaches in applying game-theoretic methods to network security. This survey can also help researchers from various fields develop game-theoretic solutions to current and emerging security problems in computer networking. <s> BIB002 </s> A Survey on Interdependent Privacy <s> Game Theory <s> Users share massive amounts of personal information and opinion with each other and different service providers every day. In such an interconnected setting, the privacy of individual users is bound to be affected by the decisions of others, giving rise to the phenomenon which we term as interdependent privacy. In this paper we define online privacy interdependence, show its existence through a study of Facebook application permissions, and model its impact through an Interdependent Privacy Game (IPG). We show that the arising negative externalities can steer the system into equilibria which are inefficient for both users and platform vendor. We also discuss how the underlying incentive misalignment, the absence of risk signals and low user awareness contribute to unfavorable outcomes. <s> BIB003 </s> A Survey on Interdependent Privacy <s> Game Theory <s> Risks faced by information system operators and users are not only determined by their own security posture, but are also heavily affected by the security-related decisions of others. This interdependence between information system operators and users is a fundamental property that shapes the efficiency of security defense solutions. Game theory is the most appropriate method to model the strategic interactions between these participants. In this survey, we summarize game-theoretic interdependence models, characterize the emerging security inefficiencies, and present mechanisms to improve the security decisions of the participants. We focus our attention on games with interdependent defenders and do not discuss two-player attacker-defender games. Our goal is to distill the main insights from the state of the art and to identify the areas that need more attention from the research community. <s> BIB004 </s> A Survey on Interdependent Privacy <s> Game Theory <s> Existing online social networks (OSNs) only allow a single user to restrict access to her/his data but cannot provide any mechanism to enforce privacy concerns over data associated with multiple users. This situation leaves privacy conflicts largely unresolved and leads to the potential disclosure of users' sensitive information. To address such an issue, a MultiParty Access Control (MPAC) model was recently proposed, including a systematic approach to identify and resolve privacy conflicts for collaborative data sharing in OSNs. In this paper, we take another step to further study the problem of analyzing the strategic behavior of rational controllers in multiparty access control, where each controller aims to maximize her/his own benefit by adjusting her/his privacy setting in collaborative data sharing in OSNs. We first formulate this problem as a multiparty control game and show the existence of unique Nash Equilibrium (NE) which is critical because at an NE, no controller has any incentive to change her/his privacy setting. We then present algorithms to compute the NE and prove that the system can converge to the NE in only a few iterations. A numerical analysis is also provided for different scenarios that illustrate the interplay of controllers in the multiparty control game. In addition, we conduct user studies of the multiparty control game to explore the gap between game theoretic approaches and real human behaviors. <s> BIB005 </s> A Survey on Interdependent Privacy <s> Game Theory <s> Over the last few years, the vast progress in genome sequencing has highly increased the availability of genomic data. Today, individuals can obtain their digital genomic sequences at reasonable prices from many online service providers. Individuals can store their data on personal devices, reveal it on public online databases, or share it with third parties. Yet, it has been shown that genomic data is very privacy-sensitive and highly correlated between relatives. Therefore, individuals’ decisions about how to manage and secure their genomic data are crucial. People of the same family might have very different opinions about (i) how to protect and (ii) whether or not to reveal their genome. We study this tension by using a game-theoretic approach. First, we model the interplay between two purely-selfish family members. We also analyze how the game evolves when relatives behave altruistically. We define closed-form Nash equilibria in different settings. We then extend the game to N players by means of multi-agent influence diagrams that enable us to efficiently compute Nash equilibria. Our results notably demonstrate that altruism does not always lead to a more efficient outcome in genomic-privacy games. They also show that, if the discrepancy between the genome-sharing benefits that players perceive is too high, they will follow opposite sharing strategies, which has a negative impact on the familial utility. <s> BIB006 </s> A Survey on Interdependent Privacy <s> Game Theory <s> Most popular location-based social networks, such as Facebook and Foursquare, let their users post location and co-location information (with other users). Such posts bring social benefits to the users who post them but also to their friends, who view them. Yet, they represent a severe threat to the users’ (location) privacy, as co-location information introduces interdependence between users. In this paper, we propose a game theoretical framework for analyzing and predicting the strategic behaviours of users of social networks regarding (co)-location information sharing. In addition, in order to design parametric utility functions as representative as possible of the users’ actual preferences, we conduct a survey targeted at Facebook users and rely on conjoint analysis for quantifying the users benefits of sharing vs. viewing (co)-location information and their preference for privacy vs. benefits.We evaluate our framework through data-driven numerical simulations. We show how users’ individual preferences influence each others’ decisions and identify several factors that significantly impact these decisions, specifically the considered adversary and the preference for privacy vs. benefits. <s> BIB007
Game theory is the study of the interaction between multiple rational decision makers (referred to as players) who aim to optimize their utility (referred to as payoff)  BIB001 . It has been successfully applied to fields such as economics and political science but also in computer science and more specifically computer security and privacy BIB004 BIB002 . A key concept of game theory is the notion of equilibrium, more precisely Nash equilibrium (NE), that enables the modeling and prediction of stable states where, given other players' strategies, no player has an incentive to deviate from his strategy. The optimal strategy given others' strategies is formalized with the so-called best response. Mathematically, the best response br i (s −i ) of player i to the profile of others' strategies s −i is defined as follows: (2) Fig. 2 . Two-player information sharing game where each player chooses between two strategies (install app vs. not install app or share information vs. not share information): (a) a simultaneous game represented in its normal form. Both players play at the same time. Each cell of the matrix represents the respective payoffs of the players for the corresponding strategies; the best responses are framed and the dominant strategies are underlined, (b) a sequential game represented in its extensive form. The second player plays after the first player. The values at the leaves (right) represent the respective payoffs of the players for the corresponding sequence of strategies. The thick lines represent the best moves in the backward induction procedure. where u i (s i , s −i ) represents player i's payoff, given the strategy profile s = (s i , s −i ) encompassing all players. 6 From this definition, the notion of NE can be defined as the case where all players' strategies are the mutual best responses to each other. Formally, the strategy profile s * is a NE if, for each player i, (3) There exist two main types of games: simultaneous games (static) and sequential games (dynamic). In simultaneous games, players move at the same time and are not aware of the move(s) of the other(s), whereas in sequential games players have some knowledge about the other players' previous moves. A main difference between these game types is in their representation (see Figure 2) . Normal-form (also called strategic-form) representation is used for simultaneous games (see Figure 2 (a)), whereas extensive-form representation is used for sequential games (see Figure 2 (b)). The normal form is represented by a matrix of payoff of all players for all strategy profiles, whereas the extensive form is represented by a decision tree. Finally, repeated games are an extension of sequential games and, as such, also use the extensive-form representation. They consist in the repetition of a single-stage game multiple times and capture the effect of players on the future payoffs and moves of other players (which is a key feature of the extensive form, as discussed below). More subtle notions of NE are needed for reasoning about extensive-form/sequential games. For instance, a sub-game perfect Nash equilibrium (SPNE) is an equilibrium derived by considering a smaller part of the whole game tree and by eliminating incredible risks (i.e., strategies that would not rationally be chosen). A common method for finding SPNE in finite games is referred to as backward induction. It first considers the last actions of the game and derives the best decision of the last player given all other previous possible decisions in the game. It then considers the second to last actions and again derives the utility-maximizing decision of the corresponding player. The same process is applied to all tree levels, until one reaches the root of the tree. Figure 2 depicts simple examples of the two main game types discussed above. Figure 2 (a) shows a two-player simultaneous game with (the same) two strategies for each player. We can immediately notice that the "install" strategy is the best response for both players, regardless of the other player's strategy. Strategy "not install" is said to be strictly dominated by "install." In this example, ("install," "install") is the unique NE. Figure 2 (b) shows a two-player sequential game with (the same) two strategies for each player. Using backward induction, we first define the second player's best moves given the possible history. If the first player (Player 1) chooses "share," then Player 2's best move is to not share, as 4 is larger than 2. Similarly, if Player 1 decides to not share, then Player 2's best move is to not share either, as 3 is larger than 2. Then, given the best moves of Player 2, player 1 chooses her best moves too, which is to share (2 > 1). Hence, they reach a NE ("share," "not share"). Software libraries implementing game-theoretical analysis tools (e.g., backward induction and finding NE) include Gambit (Python binding) 7 and MatTuGames (MATLAB), 8 to name a couple. Application to interdependent privacy. Because game theory can well model and capture the interactions between individuals with potentially conflicting interests, it is very helpful for predicting the strategies adopted by individuals and the stable states in interdependent privacy settings. Various game-theoretic models have been used in the context of interdependent privacy, such as simultaneous games BIB003 BIB006 , sequential games BIB007 , and repeated games BIB005 ] (see Section 5.1.1 and more specifically Table 3 on page 24).