Strategic defense and attack for series and parallel reliability systems

In the contest-theoretic literature on the attack and defense of networks of targets the focus has primarily been on pure-strategy equilibria. In a prominent class of these models, we show that for much of the parameter space examined pure-strategy equilibria do not exist. Therefore, all such “characterizations” of the pure-strategy equilibria over these parameter configurations are invalid. One example that typifies the issues is Hausken (2008a). For that model, we provide necessary conditions for the “solution” given in that article to form a pure-strategy Nash equilibrium. Many of the existing results in the contest-theoretic literature on the attack and defense of networks of targets rely upon Hausken’s (2008a) characterization and require corresponding parameter restrictions. When these restrictions are not met, the analysis of Clark and Konrad (2007) and Kovenock and Roberson (2010a) provides a foundation for constructing mixed-strategy Nash equilibria. JEL Classification: C72, D74, H56