The Optimal Defense of Networks of Targets

Abstract

This paper examines a game‐theoretic model of attack and defense of multiple networks of targets in which there exist intranetwork strategic complementarities among targets. The defender's objective is to successfully defend all the networks and the attacker's objective is to successfully attack at least one network of targets. Although there are multiple equilibria, we characterize correlation structures in the allocations of forces across targets that arise in all equilibria. For example, in all equilibria the attacker utilizes a stochastic “guerrilla warfare” strategy in which a single random network is attacked. (JEL C72, D74)

Strategic and experimental analyses of conflict and terrorism

“…In the first contribution, Kovenock et al (2018) study the allocations of defensive resources and choices of attack venues over a weakest-link network of targets, for which the aggressor has the objective of attacking successfully any one of the possible targets, while the defender has the objective of guarding all targets. Theoretical analyses of such an environment were provided earlier by Clark and Konrad (2007), under the assumption that the contest success function (CSF) at each target is a lottery CSF, and by Kovenock and Roberson (2017), who assumed that the contest success function at each target is an auction CSF. The present paper by Kovenock, Roberson and Sheremeta provides a complete characterization of the equilibrium in the lottery CSF version of the game and then provides an experimental test of the implications of both models.…”

The attack and defense of weakest-link networks

“…Although the attacker"s objective is to win at least one target, due to the decreasing returns to expenditure exhibited by the lottery CSF, the optimal strategy is actually to attack each and every target with an identical strictly positive level of resources. Kovenock and Roberson (2010a) Table 1 summarizes the experimental parameters. We employ a two-by-two design with four treatments, by varying the rules that determine the winner of a target (Lottery and Auction treatments), and by varying the values that determine whether the attacker or the defender receives a higher expected payoff (A and D treatments).…”

“…allocation to a target wins that target with certainty, and the "lottery" CSF, in which the probability of winning a target equals the ratio of a player"s resource allocation to the sum of the players" resource allocations to that target (with randomization independent across targets). Clark and Konrad (2007) and Kovenock and Roberson (2010a) theoretically analyze this two-player game of attack and defense of a weakest-link network of targets under the lottery and auction CSFs, respectively. 3 Under the lottery CSF, if ( ), the ratio of the attacker"s valuation of success to the defender"s valuation of success, is below a threshold (determined by the number of targets, ), the defender plays a pure strategy that allocates the same positive level of the resource to each target.…”

Strategic Network Disruption and Defense

“…Kovenock and Roberson () recently looked in a similar way at network defense, yet their paper is less relevant to our model, because network structure is not taken into account. Instead, in their paper network vulnerability arises because of the production function generated by the nodes in the network, where in one extreme one node suffices to obtain full production, and in the other case all nodes are necessary for full production.…”

“…For a justification in terms of applications, seeArguilla and Ronfeldt (2000), who find that many networked groups are actually without leaders. Whereas this does not mean that all members of such a group are actually equal, it goes a long way in justifying the assumption of homogeneity of the nodes we use here.5 Kovenock and Roberson (2010) recently looked in a similar way at network defense, yet their paper is less relevant to our model, because network structure is not taken into account. Instead, in their paper network vulnerability arises because of the production function generated by the nodes in the network, where in one extreme one node suffices to obtain full production, and in the other case all nodes are necessary for full production.…”