Game Theoretic Approach to Air Combat Simulation

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Game Theoretic Approach to Air Combat Simulation

• 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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Outline

• Air combat simulation
• The new approach to air combat simulation
• Discrete event simulation
• Game theory
• Estimation of games from simulation data
• Games in validation
• Games in optimization
• Conclusions

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Air combat simulation

• Analysis of air combat
• Effectiveness of tactics and ways for conducting
  missions
• System performance
• Expensive time consuming

? Constructive simulation

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

Discrete event simulation methodology
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Discrete event simulation model

• Controlled and reproducible environment
• Complex and convoluted
• Many levels of sub-models

Air combat simulation model

• Simulation output
• Sample of observations
• gt Estimates for output

• Validation of the model?
• Optimization of output?

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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 gt 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 and optimization

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Estimation of games - Discrete decision variables
Game
Simulation
Discrete tactical alternatives x and y
Discrete decision variables x and y
Analysis of variance
MOE estimates
Payoff
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Estimation of games - Continuous decision
variables
Game
Simulation
Continuous tactical alternatives x and y
Continuous decision variables x and y
Regression analysis
MOE estimates
Payoff
Payoff
MOE estimate
Blue x
Blue x
Red y
Red y
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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 Aggression Level
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 Aggression Level
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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Validation example Missile support time
Phase 3 Locked
Phase 1 Support Relay radar information on the
adversary to the missile
Phase 2 Extrapolation

• Symmetric one-on-one scenario
• Tactical alternatives Support times x and y
• Objective gt MOE combination of kill
  probabilities
• Simulation using X-Brawler

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Payoffs of the support time game

• Regression models for kill probabilities
• Payoff Weighted sum of kill probabilities
• Blue WBBlue kill prob. (1-WB)Red kill prob.
• Red WRRed kill prob. (1-WR)Blue kill prob.
• Weights ? Measure of aggressiveness

Probability of Blue kill
Probability of Red kill
Reds support time y
Blues support time x
Blues support time x
Reds support time y
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Best responses of the support time game

• Best responses
• Optimal support times against a given support
  time of the adversary

WB0.75
WB0.25
WB0.5
WB0
Best responses with different weights
WR0.75
WR0.5
Nash equilibria Intersections of the best
responses
Reds support time y
WR0.25
WR0
Blues support time x
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Validation results Missile support time

• Expert knowledge
• Increasing support time gt Higher kill
  probability and probability of being kill
• Increasing aggressiveness gt Longer support times
• Symmetry
• Symmetric kill probabilities
• Symmetric best responses
• Dependence
• Increasing support times gt Increase of kill
  probabililties
• Best responses Nash equilibria
• Increasing weights Increasing aggressivenes gt
  Longer support times

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Games in optimization

• Comparison of effectiveness of tactical
  alternatives using properties of games
• Best responses and Nash equilibria
• Optimal tactical alternatives against actions of
  the adversary
• Dominance between alternatives
• Simplification of analysis
• Different payoffs
• Analysis from several viewpoints
• Max-min solutions
• Uncertainty on objectives of the adversary

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Optimization example Aggression level
Payoff Blue kills Red kills

• Dominance between alternatives
• Medium and high dominated alternatives
• Best responses Nash equilibrium
• Low, low
• Max-min solution
• Low, low
• Synthesis Launch the missile and disengage

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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
• Optimization
• Comparison of tactical alternatives using games
• Systematic means for analyzing air combat
• - Single simulation batch
• Other application areas involving game settings
• Application to simulation studies beyond game
  settings
• Random factor of a simulation model ? Decision
  variable of a virtual adversary
• Overview of the impact of uncertainties presented
  by the random factor