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Game theory in the popular press.

Putting the Pawn into Rocket Science

Beyond 2000
July 12, 2000
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Anybody out there remember the old Atari game "Missile Command"? The idea was that you had to intercept an incoming ballistic missile shower by predicting the path of the weapons and then detonating an explosion in front of them. A near miss would bring fragmentation of the falling warhead and double your trouble. Well, after the Pentagon's billion-dollar test failure last week of their National Missile Defense interceptor, an Israeli academic thinks that we should be looking towards games to find a better and cheaper solution.

Global thermonuclear warfare is obviously no game, but the idea of using game theory (a mathematical field) to help intercept incoming missiles came to Professor Josef Shinar as Sadaam Hussein's Scuds rained down on Israel during the Gulf War. Those Scuds were jerry-built affairs; ungainly combinations lashing together components from two missiles in order to extend the range. As they re-entered the atmosphere they tended to break apart and follow unpredictable trajectories, making clean interception difficult.

This randomness was terrifying enough, but Shinar, a professor of Aerospace Engineering at the Technion-Israel Institute of Technology, realised that while existing tactical ballistic missiles (TBM's) such as the Scud are compelled to follow a fixed trajectory, it would not require a great technological leap to develop TBM's that could maneuver intentionally.

By performing evasive maneuvers as they homed in on their targets, such weapons would be considerably more difficult to catch than their fixed trajectory brethren, and defensive missiles designed to intercept passive targets would be virtually useless against them. Besides, hitting a missile even on a predictable ballistic trajectory has proved incredibly hard to do, as last week's test failure illustrates.

Play the Game

Game theory is an umbrella term to cover an area of mathematics concerned with predicting outcomes in real-world scenarios. It is mostly used in economic forecasting, but one specialised branch deals with real games such as chess and Go. This is known as 'combinatorial game theory' and involves determining the endgame position in advance by continually examining all possible moves as play progresses.

In true board game fashion, Shinar applied the gambit of anticipating the development of maneuverable TBM's, and went about creating what he calls a "guidance law" that considers the most dramatic evasive moves they could possibly make. In doing so, Shinar applied what is known as "zero-sum pursuit-evasion game theory."

"A pursuit-evasion game is an intuitive notion indicating that one of the players of the game, called the pursuer, is chasing and wants to capture the other, called the evader. It is a game of two players only. Since the gain of one player is the loss of the other, the game is called a zero-sum game," explains Shinar.

"This notion is well suited to an interception scenario, where the pay-off is the probability of destruction of the ballistic missile," he adds. The interceptor missile (pursuer) wants to maximise this pay-off and the TBM (evader) wants to minimise it.

Armed with this new guidance law, an interceptor would be provided with a set of equations covering all possibilities and generating a gradually shortening list of end co-ordinates. By knowing exactly where its prey must be at a certain point in time, the kill vehicle would have a vastly improved chance of homing in on its target. It could even ignore certain evasive actions by knowing that they wouldn't affect the outcome.

Current aircraft and cruise missile interceptors, like the Patriot, have only a limited ability to think ahead, generally being reduced to reacting after every maneuver and then playing catch-up. They rely on pure speed to get close to their targets and then detonate, hopefully knocking down the enemy in the process.

However, despite plenty of media hype and government propaganda, the much-vaunted Patriot missiles were unable to even do this during the Gulf War. An independent expert called in by a Senate committee investigating the Patriot's performance found that upon closer examination, none of the claimed interceptions had actually taken place. The best result was a couple of near-misses, which had just caused the Scuds to break up a bit and spread the damage over a wider area.

Clearly the missile wasn't quite smart enough.

Playing for keeps

For the National Missile Defense (NMD) interceptor, hits are even more difficult to achieve. This concept doesn't use proximity detonation to take out its target, but depends on actual impact between its Exoatmospheric Kill Vehicle (EKV) (pictured) and the enemy warhead. That has quite rightly been compared to using one bullet to shoot down another one. The need for accurate path prediction is paramount. Missing by an inch is as good as a mile.

(To be fair, last week's missed interception was not due to any failure in guidance, but rather to an abortive stage separation in the booster rocket.)

The NMD program is however dealing with ICBM's and not intermediate-range missiles like the Scud. Shinar says though that despite being conceived against TBM's , there is no theoretical reason why his guidance law could not eventually be applied to longer-range rocket threats. Additionally, if someone were to come up with a maneuverable ICBM or re-entry vehicle, the magic bullet of the NMD interceptor would be rendered impotent since it depends largely on data and predictions made before it's even launched.

While Shinar's idea is still at the theoretical investigation level, computer simulations of his law have offered "very impressive results." He asserts that the law could be easily incorporated into any existing or developing missile system.

And parents, take note! All that time he spent playing video games as a kid may eventually pay off.

Copyright 2001 Beyond Online Limited