Complexity Explorer Santa Fe Institute

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Game Theory II- Dynamic Games

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2.2 Representation and Strategies in a Sequential Game » Quiz Solution

 In the game depicted below, how many strategies does player 2 (P2) have?

 

 (a) 2

(b) 4

(c) 8

(d) 16

Explanation: Remember a strategy is an "if" statement that specifies what a player would do for all possible observations. Therefore one of player 2's strategies is

"If player 1 plays A, then play L;

if player 1 plays B, then play R;

if player 1 plays C, then play R;

if player 1 plays D, then play L."

Listing all strategies in this way shows that there are 16 strategies for player 2.