game-theoretic selection of paths in motion-based games joseph jaeger dr. kostas bekris andrew...

Game-Theoretic Selection of Paths in Motion-based

Games

Joseph JaegerDr. Kostas BekrisAndrew Kimmel1 August 2013

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

Motion-based Games

• Motion-based Games

• Motion Planning

Proposed Framework

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

Variation

• Random Goals• Periodic Bomb Placement• Continuous Environments

Example Video

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)

1-on-1 Results

Free-for-All Results

Free-for-All Results

1-on-1 Results

Free-for-All Results

New Experiments

New Strategies• RM+• HorizonRM+• MM+• HorizonMM+

Prior Strategies• RM• HorizonRM• MM• HorizonMM• Greedy• GA

1-on-1 Results

1-on-1 Results

Questions?