Analysis of indirect effect for ground-based air-defence


  • Tam Beran
  • Mika Cohen

Publish date: 2020-01-24

Report number: FOI-R--4818--SE

Pages: 34

Written in: Swedish


  • Weapon system assessment
  • ground-based air defence
  • combat effectiveness
  • indirect effect
  • simulation
  • OPaL
  • decision theory
  • game theory


The aim of this report is to investigate methods to analyse the indirect effect of ground-based air-defence (GBAD) on a tactical level. Combat effectiveness can be defined as a measure of how well a combat task has been performed. There are direct and indirect effects. The direct effect is caused by an action, i.e. by interception of the threats. The indirect effect is on the other hand not preceded by an action. The existence of the GBAD unit and its capability to act are sufficient to affect the adversary's choice of tactics to achieve his goals. For analysis of the direct effect, GBAD scenarios can be simulated in the tool Opal, but for the indirect effect, simulations need to be complemented with other methods. A method to analyse the indirect effect is to use decision and game theory. The GBAD scenario is formulated as a game consisting of two players with opposite goals; the GBAD unit who is the defender and the adversary who is the attacker. Each player has a number of alternative actions and combinations of these alternatives are set up as GBAD scenarios in Opal. The simulation results, i.e. hit count or detection time, are parameters that measure the direct effect. In order to quantify the indirect effect, the outcomes from the simulations are used as input data to a game theoretical analysis. Consequently, there is a relationship between the direct and indirect effect. The direct effect is a prerequisite for an indirect effect, but is not necessarily proportional to it. Depending on whether the decision of the GBAD is open or hidden to the adversary, the game theory analysis results in different optimal strategies for the adversary. An open decision implies a strategy where the adversary makes a deterministic decision, that is choosing the alternative action that gives the best result based on the GBAD's decision. A hidden decision can on the other hand imply choosing a stochastic decision, that is not necessarily a specific alternative action, but can consist of a probability distribution of alternative actions. The indirect effect arises when the adversary has to use an optimal strategy to adapt the mission to the GBAD's decision. The consequences can be loss of time or larger resources being allocated. A hidden decision affects the adversary more compared with an open decision, and accordingly implies a larger indirect effect. For illustration of the method, examples of simplified GBAD scenarios with few entities are given in this report. The analysis can be extended to include more complex scenarios with many alternative actions and including not only one decision, but a chain of decisions. A game can also be formulated to include other domains and operational levels.