Introduction to Experimental Games
Experimental Evidence on Games and Anomaly
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Environments, Institution, and Behavior
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Environments, Institution
• Environment
– agent
• with preference, risk attitude, knowledge (learning behavior),
skill, endowment, cost structure, ...
– resources
• commodities, inputs
• Institution
– rules of transaction/exchange
(incentive, i.e., reward/punishment)
– rules of communication (information
transmission/cost)/contract
– structures of the game
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Reasons for conducting experiments
• Test a theory, or discriminate between theories
– 荷式、英式拍賣, double-auction, post-offer auction
• Explore the causes of a theory’s failure
– real/experimental data 可能包含太多變因, e.g., ultimatum
game
• Establish empirical regularities as a basis for new theory
– 利用實驗結果建立新理論, 或可解決問題的模型, e.g.,
emission permit, airport slot
• Compare environments
– 不同偏好 (效用, 風險, 公平正義認知), 不同知識
• Compare institutions
– 比較不同之交易制度, 資訊傳遞...
• Evaluate policy proposals
• The laboratory as a testing ground for institutional design
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A Note on the Design of Experiments
• Benchmark (對照組, 或理論值)
• Treatment
– environment
– institution
e.g., 學習效果, 資訊傳遞, 交易制度, 動機設計, 風險態度
• Joint hypothesis
– randomness/anonymity of players
– information(knowledge) necessary to the Subjects
• Tools of analyzing observations in the Lab.
– percentage/distribution
– ANOVA/MANOVA
– econometric model
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Matching Pennies
• Previous Matching Pennies Game and Best Response f()
q
1-q
Head
Tail
p
Head
1, -1
-1,1
(1-p)
Tail
-1,1
1,-1
0


p*  B1 (q)  {p : 0  p  1} if

1

1


q*  B2 (p)  {q : 0  q  1} if

0

q  1/ 2
q  1/ 2
q  1/ 2
p
B
1-p
S
q
B
1-q
S
80 ,40
40, 80
40, 80
80, 40
Player 2’s
best response
q
1
Player 1’s
best response
1/2
p  1/ 2
p  1/ 2
p  1/ 2
0
1/2
1
p
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Modified Matching Pennies Game
p
B
1-p
S
q
B
1-q
S
80 ,40
40, 80
40, 80
80, 40
• If Payoff of player 1 on {B,B} is raised to 320 !!!!!
q
1-q
B
S
p
B
320,40
40, 80
(1-p)
S
40, 80
80, 40
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Modified Matching Pennies Game
• Payoff of player 1 on {B,B} is raised to 320 !!!!!
p
1-p
B
S
q
B
1-q
S
80 ,40
40, 80
40, 80
80, 40
0


p*  B1 (q)  {p : 0  p  1} if

1

1


q*  B2 (p)  {q : 0  q  1} if

0

q
1-q
B
S
p
B
320,40
40, 80
(1-p)
S
40, 80
80, 40
q  1/ 8
q  1/ 8
q  1/ 8
p  1/ 2
p  1/ 2
p  1/ 2
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Modified Matching Pennies Game
• Best Response f() of modified matching pennies game
Player 2’s
best response
q
1
Player 1’s
best response
1/8
0
1/2
1
p
• Mixed strategy equil. (1, 2) = ({1/2,1/2},{1/8,7/8})
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Experimental Design of Matching Pennies
• Goeree and Holt (2001, AER)
• 50 subjects in a one-shot game
• Subjects were randomly matched and assigned row or
column players.
• Repeated games were investigated and the results were
persistent
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Experimental Evidence on Matching Pennies
• Goeree and Holt (2001, AER)
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The BoS game: A coordination game
• A typical coordination game
(84%)
0,
(96%)
• A modified version with an option S: when x = 0
• What are the Nash equil. ?
– “S” is to be eliminated
– (L,L) and (H, H) and a mixed strategy
(1, 2) = ({1/3, 2/3}, {1/3, 2/3})
• Experimental Evidence
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The BoS game: A coordination game
• When x = 400
• What are the Nash equil. ?
– (L,L) and (H, H)
(76%)
400,
(64%)
• With this change (x =0 to x=400)
• Player 1’s choice on H reduces from 96% to 64% while
Player 2’s choice on L also reduces from 84% to 76%.
• When x =0 , coordination on (H,H) is 80%
When x =400 , coordination on (H,H) drops to 32%
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The Ultimatum Game (最後通牒賽局)
• Distribution Game
• Two player to split $ c
– Player 1 offers player 2 $x (up to $c)
– if player 2 accept this amount, the payoffs are (c-x, x)
if player 2 reject, the payoffs are (0,0)
1
• Subgame Perfect Equilibrium?
x
– min. increnment = 0.01
0
Y
cx, x
2
c
N
0,0
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Experiments on the Ultimatum Game
• 1970s in Germany (GSS,1982) in textbook
• Players
– 42 graduate students of economics
– split into 2 groups and seated on different sides of a room
– Player 1 wrote down x on a form
This form was then given to a randomly determined player 2
• Payoff:
c  (4 , 10) DM
(2~5 USD)
minimum increment 1 cent (0.01 DM)
• Each player had 10 min. to make her decision
– The entire game was repeated a week later.
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Experimental Results (GSS,1982)
Exp. 1
Exp. 2
mean of x
0.65 c
0.69 c
Rejection %
20%
20%
• Mean of x is not close to 0.01 DM
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Experimental Evidence on the Ultimatum Game
• Hoffman (1994) cited by Smith (2002)
(分配)
(角色是買
賣雙方,
出價者是
賣方)
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Trust Game
• A simple two-stage game
– Trust the other player? Go on next step could get more!
• What is the Subgame Perfect Equilibrium?
1
R
(10,10)
L
2 R
(15, 25)
L
(0,40)
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Experimental Evidence on Trust Game
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Experimental Evidence on Trust Game
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3-stage Trust Game
R
1
(7, 14)
L
2 R
L
1
R
SPE payoffs
(8, 8)
(10, 10)
L
(12, 6)
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Voluntary vs Involuntary Trust Game
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Robustness in the Trust Game
• By Goeree and Holt (2001, AER)
• randomly paired 50 subjects who play this game only once
• Treatment
– Robustness of the backward induction
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Robustness in the Trust Game: A benchmark
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Robustness in the Trust Game: A Treatment
• The cost of irrationality is small?
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Incredible Threat ?
• That 1st player chooses R signals a “win-win” message
• That 1st player chooses R signals a “selfish” message?
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Incredible Threat: A Treatment
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Incredible Threat after Many Rounds
Cooperation payoffs
SPE payoffs
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Experiments of Competitive Market Behavior
• By Vernon L. Smith (1962, JPE)
• Competitive Market
– 買賣雙方人數眾多 (皆為 price taker)
– 價格機能:供不應求, 則價漲; 供過於求, 則價跌
– 市場愈敏感 (供需曲線愈平緩), 則收歛愈快
• Design of the Experiment
– The subjects are randomly assigned to buyer/supplier with
privately given Value and Cost of one-unit (virtual) good.
– Incentive: maxmizing V-P and P-C (no monetary rewards)
– Information transmission: Verbal offer/acceptance
– Information history: observable
– Transaction: Double-Auction
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Benchmark
coefficient of convergence
=(P0)/P0
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Sensitivity of Demand/Supply (flat curves)
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Sensitivity of Demand/Supply (steep curves)
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A Parallel Shift in Demand with Horizontal Supply
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A Changed Slope in Demand
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A Decrease in Demand with Vertical Supply
A decrease in
demand
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A Change in Market Organization
Sellers only
bidding
Buyers and
Sellers
bidding
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Summary of Smith’s (1962) findings
• Small numbers of buyers/sellers can achieve competitive
equilibrium (as long as prohibited collusion with publicity
of all bids
• Competitive equilibrium works in changes in demand
except overshooting
• When supply curve is perfectly elastic (horizontal line),
empirical equilibrium > theoretical equilibrium
• Seller-only market exhibits weaker tendencies toward
equilibrium
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What we have learned from Experiments?
• Institutions matters
– posted offer pricing converges more slowly and erratically
and is less than continuous double auction
• Unconscious optimization in market interactions
– learning by doing
• Information: less can be better
– Incomplete or asymmetric info. often leads to sub-optimum
• Common information is not sufficient to yield common
expectations or “knowledge”
– you are not sure others how to use the common info.
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What we have learned from Experiments?
• Dominated strategies are for playing, not for eliminating
– Dominant strategies should only occur in the common
knowledge
• Efficiency and under-revelation are compatible
– the UPDA auction game (股市交易) is efficient than the
blind 2-sided auction
• The endowment effect
– willingness to pay  willingness to accept
• Fairness: Taste or Expectation?
– The ultimatum game:
A monopoly can extract all surplus of consumers?
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Application of Experimental Games
•
•
•
•
Auction designs
Deregulation of Airline Route
Electricity Market
Iowa Electronic (Futures) Market
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