INTRODUCTION 5: DYNAMIC GAMES

1
INTRODUCTION 5 DYNAMIC GAMES
2
Centipede game

• Rosenthal 1981, McKelvey and Palfrey 1992
• Unique SPNE (S, S, S, S, S)

J1
J2
J1
J2
J1
3 12
C
C
C
C
C
S
S
S
S
S
1 4
6 1.5
2 8
10 2.5
2 0.5
3
BI Instructions

• You are involved in a two-person game.
• In stage 1, you have to choose between
  terminating the game (S) or continuing (C) to
  stage 2.
• In stage 2, your opponent has to choose between
  terminating the game (S) or continuing (C).
• In case you both continue, you will receive
  1.347892045 and your opponent receives
• 48,976206903.

4
BI Instructions

• Representation of the game

Player 1
C
S
Player 2
X
C
S
Y
1,347892045 - 48,976206903
5
BI Instructions

• The information about the payoffs in the event
  you stop the game and in the event your opponent
  stops the game is concealed. You are allowed to
  see this information only once. Click button X if
  you want to see first the information on event X
  and button Y if you want to read first the
  information on event Y.
• What is your choice? X or Y?

Player 1
C
S
Player 2
X
C
S
Y
1,347892045 - 48,976206903
6
Backward induction Results

• About 65 of the subjects choose X.
• References Camerer et al. 1994, Rubinstein
  1999
• Conclusion People tend to analyze an extensive
  game forward rather than backward.

Player 1
C
S
Player 2
X
C
S
Y
1,347892045 - 48,976206903
7
Dollar auction Instructions

• A dollar bill is auctioned with these rules
• The dollar bill goes to the highest bidder, who
  pays whatever the high bid was.
• Each new bid has to be higher than the current
  high bid, and the game ends when there is no new
  bid within a specified time limit.
• The second-highest bidder also has to pay the
  amount of his last bid and gets nothing in
  return.
• Let us start the auction

8
Dollar auction

• Martin Shubik 1971
• Results The highest bidder pays far more than a
  dollar for a dollar and the second-highest bidder
  pays far more than a dollar for nothing!
• Game of escalation (war of attrition)
• SPNE? ? ONeill 1986, Leininger 1989
• Applications
• Dollar auctions in real life (phone calls, bus
  stop, etc.)
• Arms race
• Patent race

9
FI Instructions

• Two players play the following game
• What is your prediction?

Player 1
A
300, 300
C
10
Forward induction Results

• Cooper et al. 1993
• About 75 predict (C, L, L).

Player 1
A
300, 300
C
11
Forward induction

• Cooper et al. 1993
• Two SPNE (A, R, R) and (C, L, L)
• Forward induction ? (C, L, L)

Player 1
A
300, 300
C