Los Angeles County sheriff's deputies say the incident began when a man backed his car into Brady's vehicle Sunday night in the 21200 block of Pacific Coast Highway.
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The two drivers began exchanging information but when the other driver heard sirens approaching he reportedly tried to run away on foot, according to a sheriff's statement. Brady tried to stop him from fleeing and a scuffle broke out, deputies say.
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The other driver was able to run away but deputies found him a short time later in a nearby neighborhood. They arrested the driver, whose name was not released, for suspicion of driving under the influence of alcohol, hit and run (property damage only), and battery.
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Anyone who witnessed the confrontation or who has more information is asked to call the Malibu/Lost Hills Sheriff's Station at (818)878-1808.
Brady, 51, is an actor, singer, comedian and host of the game show "Let's Make A Deal."