These strategies are only basic ideas. Creativity is encouraged, and often necessary, in order to succeed in a chase. You cannot use the same strategy twice in the same chase.
Chasers
Barricade - Physically prevent the runners from escaping by closing gates, standing in the way etc. this could be represented by an initiative check to slip in through the gates before they close, acrobatics to scale over obstacles/evade AoOs.
Runners
Diversion - You attempt to create loud noises elsewhere, or make your footprints change direction to misdirect your opponent.
Both Parties
Secret Passage - Typically represented by an opposed knowledge check based on the environment (local, nature, planes).
CC - Via bolas, nets, traps or spells, you attempt to slow your opponent down. Usually represented by attacks or saves.
Mad Dash - Roll opposed luck checks. For every 10 speed faster your party is, gain a +2 bonus.
Hide/Ambush - This could mean stealth or disguise. You try and give your opponent the slip or pretend to be someone unimportant. Typically opposed to perception.