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Interdependent Security Games Under Behavioral Probability Weighting

Part of the Lecture Notes in Computer Science book series (LNSC,volume 9406)


We consider a class of interdependent security games where the security risk experienced by a player depends on her own investment in security as well as the investments of other players. In contrast to much of the existing work that considers risk neutral players in such games, we investigate the impacts of behavioral probability weighting by players while making security investment decisions. This weighting captures the transformation of objective probabilities into perceived probabilities, which influence the decisions of individuals in uncertain environments. We show that the Nash equilibria that arise after incorporating probability weightings have much richer structural properties and equilibrium risk profiles than in risk neutral environments. We provide comprehensive discussions of these effects on the properties of equilibria and the social optimum when the players have homogeneous weighting parameters, including comparative statics results. We further characterize the existence and uniqueness of pure Nash equilibria in Total Effort games with heterogeneous players.


  • Probability Weighting
  • Social Optimum
  • Interior Equilibrium
  • Investment Level
  • Successful Attack

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  1. 1.

    In a related class of security games known as Stackelberg security games with two players, one attacker and one defender, there have been recent studies [4, 13, 17, 31, 32] that incorporate behavioral decision theoretic models, including prospect theory and quantal response equilibrium. However, this class of games is very different from interdependent security games [20], which is the focus of the current work.

  2. 2.

    Both positive and negative externalities have been studied in the literature. Negative externalities capture settings where more investment by others makes a player more vulnerable, and this is usually the case where the attack is targeted towards individuals who have invested less in security. Most of the literature in security games has focused on positive externalities [20].

  3. 3.

    There are also various behavioral characteristics that affect the perceived values of gains and losses [12, 16]. However, as the values of the gains and losses are not strategy-dependent in the games that we consider here, behavioral value functions would not affect the equilibria that arise.

  4. 4.

    While we focus on the Prelec weighting function here, many of our results will also hold under a broader class of weighting functions with similar qualitative properties as the Prelec weighting function.


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Correspondence to Shreyas Sundaram .

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Hota, A.R., Sundaram, S. (2015). Interdependent Security Games Under Behavioral Probability Weighting. In: Khouzani, M., Panaousis, E., Theodorakopoulos, G. (eds) Decision and Game Theory for Security. GameSec 2015. Lecture Notes in Computer Science(), vol 9406. Springer, Cham.

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