Game Theoretic Validation of Air Combat Simulation Models

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Game Theoretic Validation of Air Combat
Simulation Models

• Jirka Poropudas and Kai Virtanen
• Systems Analysis Laboratory
• Helsinki University of Technology
• jirka.poropudas_at_hut.fi, kai.virtanen_at_hut.fi

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Air combat simulation

• Air combat is analyzed to compare effectiveness
  of tactics and ways for conducting missions as
  well as system performance
• Test flights are expensive and time consuming ?
  constructive simulation
• Discrete event simulation models provide a
  controlled and reproducible environment that may
  be complex and convoluted with many levels of
  sub-models

• Air combat simulation model
• Aircraft, weapon systems, radars, other
  apparatus
• Pilot decision making and situation awareness
• Uncertainties

Validation of the model?
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Existing validation and optimization approaches

• Simulation metamodels
• Mappings from simulation input to output
• - Response surface methods, regression models,
  neural networks, etc.
• Validation methods
• Real data, expert knowledge, statistical methods,
  sensitivity analysis
• Simulation-optimization methods
• Ranking and selection, stochastic gradient
  approximation, metaheuristics, sample path
  optimization

One-sided approaches ? Action of the adversary
is not taken into account
The game theoretic approach!
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The game theoretic approach

• Definition of the scenario
• Aircraft, weapons, sensory and other systems
• Initial geometry
• Objectives ? Measures of effectiveness (MOEs)
• Available tactics and systems Tactical
  alternatives
• Simulation of the scenario using the simulation
  model
• Input tactical alternatives
• Output MOE estimates
• Estimation of games from the simulation data
  using statistical techniques
• Use of the games in validation

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Games in validation

• Goal Confirming that the simulation model
  performs as intended
• Comparison of the scenario and properties of the
  game
• Symmetry
• Symmetric scenarios gt symmetric games
• Dependence between decision variables and payoffs
• Dependence between tactical alternatives and MOEs
• Best responses and Nash equilibria
• Explanation and interpretation based on the
  scenario
• Initiative
• Making ones decision before or after the
  adversary gt Advantageous/disadvantageous?
• Explanation and interpretation based on the
  scenario

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Validation example Aggression level

• Two-on-two air combat scenario
• Identical aircraft, air-to-air missiles, radars,
  data links, etc.
• Symmetric initial geometry
• Identical tactical alternatives
• - Aggression levels of pilots Low, Medium, High
• Objectives gt MOEs
• - Blue kills, red kills, difference of kills
• Simulation using X-Brawler
• Many versus many air combat simulation
• Discrete event simulation methodology
• Aircraft, weapons and other hardware models
• Elements describing pilot decision making and
  situation awareness

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Validation results
Payoff Blue kills

• Expert knowledge
• Increasing aggressiveness ?
• Increasing causality rates
• MOE blue kills
• Low aggressiveness for red
• High aggressiveness for blue

• Dependence
• Increasing aggressiveness
• gt Increase of blue kills
• Best responses Nash equilibria
• Medium or high for blue, low for red
• Medium and high leading to the same outcome gt
  Possible shortcoming

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Validation results
Payoff Blue kills Red kills
RED, min

• Expert knowledge
• Increasing aggressiveness
• gt Increasing causality rates
• Symmetric scenario
• gt Symmetric game

BLUE, max

• Symmetry
• MOE estimates approximately zero when the
  decisions coincide
• E.g., low, high gt best, worst AND high, low gt
  worst, best
• Dependence
• Increasing aggressiveness gt Increasing causality
  rates for both sides
• Medium and high for blue leading to the same
  outcome gt Possible shortcoming
• Best responses Nash equilibrium
• Low for blue, low for red

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Conclusions

• Novel way to analyze air combat
• Combination of discrete event simulation and game
  theory
• Extension of one-sided validation and
  optimization approaches
• Validation
• Properties of games ? Air combat practices
• Simulation data in an informative form
• Comparison of tactical alternatives using games
• Systematic means for analyzing air combat
• - Single simulation batch
• Other application areas involving game settings