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Game-Theoretic Selection of Paths in Motion-based
Games
Joseph JaegerDr. Kostas BekrisAndrew Kimmel1 August 2013
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Game Theory
• Game Theory
• Max-Min (Shoham & Leyton-Brown 2009)• Regret Minimization (Halpern & Pass 2012)
Player 2 Helps Player 2 Lazy
Player 1 Helps 400 300
Player 1 Lazy 500 0
Player 2 Helps Player 2 Lazy
Player 1 Helps 400, 400 300, 500
Player 1 Lazy 500, 300 0, 0
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Motion-based Games
• Motion-based Games
• Motion Planning
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Proposed Framework
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Benchmark Game: Bomberman
• Actions: Move around and drop bombs to destroy the environment/other agents• Goal: Be the last agent not destroyed by a bomb
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Variation
• Random Goals• Periodic Bomb Placement• Continuous Environments
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Example Video
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Strategies & Experiments
Stategies• Regret-Min (RM)• Horizon-Regret-Min (HorizonRM)• Max-Min (MM)• Horizon-Max-Min (HorizonMM)
• Greedy• Greedy-Avoidance (GA)
Experiments• 1-on-1• Free-for-All (4 Player and 8 Player)
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1-on-1 Results
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Free-for-All Results
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Free-for-All Results
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1-on-1 Results
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Free-for-All Results
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New Experiments
New Strategies• RM+• HorizonRM+• MM+• HorizonMM+
Prior Strategies• RM• HorizonRM• MM• HorizonMM• Greedy• GA
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1-on-1 Results
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1-on-1 Results
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Questions?