Ultimate Writer
In Centipede Game, there are two players take turns choosing either continue to play the game and pass the choice to the other player, or stop playing. In this particular centipede game, there are two players called player A and player B and there are total 20 rounds which is divided into 2 parts (the first 10 rounds and the last 10 rounds). In each part, the player A was the first mover, and the Player B was the second mover. Players’ payoffs in the first 10 rounds is less than the last 10 rounds when players choosing to stop play the game. The unique point of this game is that whoever controls the game by choosing stop playing achieves higher payoffs than the other player achieves.
Assuming there are 42 participants in our lab and consider there are 21 player A and 21 player B. At the start of each round, there are 21 pairs that are matched out of all 42 players. The matching is done randomly in each round and ever player has equal possibility to be selected to match with another player. This matching rule may make each player play with a new person in each round. In each round, there are two moves (continue playing and stop playing) available for each matching pair. The decision has to be done in alternating order. The game continues for a fixed number of rounds (automatic stop) or until a player decides to end the game by choosing stop playing.
For the rounds 1to10 (the game display in Fig.1.)We start with a total payoff $2.5 divided into $2 for player A and $0.5 for player B.
Player A starts the game by choosing either to continue or to stop, if player A chooses to stop the game at node 1, then the player B would have no chance to choose to continue or to stop which means the game will be ended. When the game ends in the first round, player A will earn $2 and player B will earn $0.5. Player B only gets opportunity to make a move when player A chooses to continue the game. If player B decides to stop the game in round 2, player A will earn $1 and player B will earn $4. However, if player B chooses to continue the game in round 2 and Player A decides to stop playing in round 3, Player A will get $6 and Player B will get $1.5. In the round 3, if player A chooses to continue the game, the choices now passes to player B in round 4. If player B decides to stop the game in round 4, player A will earn $2 and player B will earn $8. On the other hand, if player B chooses to continue playing in round 4, it will be player A’s turn to make decision in round 5. Player A will earn $10 and player B will earn $2.5 if player A chooses to stop the game in round 5. If player A decides to continue the game in round 5, then player B have to makes the move in round 6, at this time, there is an automatic stop. So player B has to stop. As result, Player A will get $3 and player B will get $12 in round 6 which when player B reaches automatic stop. Therefore, at the first 10 rounds, the total payoff for player A is $2+$1+$6+$2+$10+$3=$24 and the payoff for player B is $0.5+$4+$1.5+$8+$2.5+$12=$28.5
FIG.1. (The Centipede Game for round 1to10)
For the second part of this experiment consists rounds 11 to 20 (the game display in Fig.2.). We also start with a total payoff $2.5 divided into $2 for player A and $0.5 for player B if player A selects stop at node 1. If player A chose to continue, then player B will make a decision at node 2. If player B select to stop, the payoff for player A is $1.5 and for player B is $6. If player B continues the game, the player A have a chance to make a decision. If player A stops, the payoff for player A is $10 and for player B is $2.5 at node 3. If player A decides to continue, again player B will make a decision, the payoff for player A is $3.5 and for player B is $14 if B ends the game at node 4. If player B choose to continue the game, player A will have to determine. Payoff for Player A is $18 for player B is $4.5 if player A select stop at node 5. If player A selects to continue it, the game will move on to the round 6, which is a final automatic stop, payoff for player A is $5.5 and for B is $22.5.
FIG.2. (The Centipede Game for round 11 to 20)