Golden Balls Game

• Content map: SMU H3 Game Theory Map

Setup

Definition:

Golden Balls Game

• Players: Player 1 and Player 2.
• Strategies: Each player chooses Split or Steal.
• Rules: Players move simultaneously; stealing while the other splits wins the prize.

Payoff Matrix

Derivation (Best Response Analysis)

• If the opponent plays Split, then Steal yields $P>\tfrac{P}{2}$.
• If the opponent plays Steal, then both Split and Steal yield $0$.

Nash Equilibrium

Result:

Steal is a weakly dominant strategy for each player. A Nash equilibrium is:

Insights

Insight:

Pareto superior strategy profiles might not be stable, each player has an incentive to deviate to Steal when expecting Split.