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Centipede Game

A sequential game where players alternate deciding to take the current pot or pass it to the opponent (who grows it). Backward induction predicts immediate defection, but cooperation yields much higher payoffs.

Your Turn

Round 1 of 6
$4
If you take: You get $1, AI gets $0
If you pass: Pot grows to $8

Current Game

Round 1 / 6
Current Pot $4
Max Possible $256

Session Statistics

Games Played 0
Avg Rounds -
Reached Final Round 0
Avg Total Payoff -

About the Centipede Game

The Setup: Two players alternate turns. On each turn, a player can either "take" the current pot (ending the game) or "pass" to the other player. When passed, the pot grows (typically doubles).

Example Sequence:

• Round 1 (P1): Pot = $4. Take → (P1: $1, P2: $0). Pass → Pot grows to $8

• Round 2 (P2): Pot = $8. Take → (P1: $0, P2: $2). Pass → Pot grows to $16

• Round 3 (P1): Pot = $16. Take → (P1: $4, P2: $0). Pass → Pot grows to $32

• ... continues until final round or someone takes

Backward Induction Paradox: Game theory predicts Player 1 should take immediately in Round 1, because:

• In the final round, the last player will always take

• Knowing this, the second-to-last player should take on their turn

• Working backward, Player 1 should take immediately

Experimental Reality: People rarely take immediately! Most pass multiple rounds, achieving much higher total payoffs. This demonstrates limits of backward induction and importance of trust and bounded rationality.

Applications: Sequential bargaining, investment decisions, contract negotiations, and any situation requiring trust in future reciprocity.