Introduction to Experimental Games Experimental Evidence on Games

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Introduction to Experimental Games Experimental Evidence on Games and Anomaly 1

Introduction to Experimental Games Experimental Evidence on Games and Anomaly 1

Environments, Institution, and Behavior 2

Environments, Institution, and Behavior 2

Environments, Institution • Environment – agent • with preference, risk attitude, knowledge (learning behavior),

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 3

Reasons for conducting experiments • Test a theory, or discriminate between theories – 荷式、英式拍賣,

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 4

A Note on the Design of Experiments • Benchmark (對照組, 或理論值) • Treatment –

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 5

Matching Pennies • Previous Matching Pennies Game and Best Response f() 6

Matching Pennies • Previous Matching Pennies Game and Best Response f() 6

Modified Matching Pennies Game • If Payoff of player 1 on {B, B} is

Modified Matching Pennies Game • If Payoff of player 1 on {B, B} is raised to 320 !!!!! 7

Modified Matching Pennies Game • Payoff of player 1 on {B, B} is raised

Modified Matching Pennies Game • Payoff of player 1 on {B, B} is raised to 320 !!!!! 8

Modified Matching Pennies Game • Best Response f() of modified matching pennies game •

Modified Matching Pennies Game • Best Response f() of modified matching pennies game • Mixed strategy equil. ( 1, 2) = ({1/2, 1/2}, {1/8, 7/8}) 9

Experimental Design of Matching Pennies • Goeree and Holt (2001, AER) • 50 subjects

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 10

Experimental Evidence on Matching Pennies • Goeree and Holt (2001, AER) 11

Experimental Evidence on Matching Pennies • Goeree and Holt (2001, AER) 11

The Bo. S game: A coordination game • A typical coordination game (84%) 0,

The Bo. S 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 12

The Bo. S game: A coordination game • When x = 400 • What

The Bo. S 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% 13

The Ultimatum Game (最後通牒賽局) • Distribution Game • Two player to split $ c

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) • Subgame Perfect Equilibrium? – min. increnment = 0. 01 14

Experiments on the Ultimatum Game • 1970 s in Germany (GSS, 1982) in textbook

Experiments on the Ultimatum Game • 1970 s 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. 15

Experimental Results (GSS, 1982) • Mean of x is not close to 0. 01

Experimental Results (GSS, 1982) • Mean of x is not close to 0. 01 DM 16

Experimental Evidence on the Ultimatum Game • Hoffman (1994) cited by Smith (2002) (分配)

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) 17

Trust Game • A simple two-stage game – Trust the other player? Go on

Trust Game • A simple two-stage game – Trust the other player? Go on next step could get more! • What is the Subgame Perfect Equilibrium? 18

Experimental Evidence on Trust Game 19

Experimental Evidence on Trust Game 19

Experimental Evidence on Trust Game 20

Experimental Evidence on Trust Game 20

3 -stage Trust Game SPE payoffs 21

3 -stage Trust Game SPE payoffs 21

Voluntary vs Involuntary Trust Game 22

Voluntary vs Involuntary Trust Game 22

Robustness in the Trust Game • By Goeree and Holt (2001, AER) • randomly

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 23

Robustness in the Trust Game: A benchmark 24

Robustness in the Trust Game: A benchmark 24

Robustness in the Trust Game: A Treatment • The cost of irrationality is small?

Robustness in the Trust Game: A Treatment • The cost of irrationality is small? 25

Incredible Threat ? • That 1 st player chooses R signals a “win-win” message

Incredible Threat ? • That 1 st player chooses R signals a “win-win” message • That 1 st player chooses R signals a “selfish” message? 26

Incredible Threat: A Treatment 27

Incredible Threat: A Treatment 27

Incredible Threat after Many Rounds Cooperation payoffs SPE payoffs 28

Incredible Threat after Many Rounds Cooperation payoffs SPE payoffs 28

Experiments of Competitive Market Behavior • By Vernon L. Smith (1962, JPE) • Competitive

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 29

Benchmark coefficient of convergence = (P 0)/P 0 30

Benchmark coefficient of convergence = (P 0)/P 0 30

Sensitivity of Demand/Supply (flat curves) 31

Sensitivity of Demand/Supply (flat curves) 31

Sensitivity of Demand/Supply (steep curves) 32

Sensitivity of Demand/Supply (steep curves) 32

A Parallel Shift in Demand with Horizontal Supply 33

A Parallel Shift in Demand with Horizontal Supply 33

A Changed Slope in Demand 34

A Changed Slope in Demand 34

A Decrease in Demand with Vertical Supply A decrease in demand 35

A Decrease in Demand with Vertical Supply A decrease in demand 35

A Change in Market Organization Sellers only bidding Buyers and Sellers bidding 36

A Change in Market Organization Sellers only bidding Buyers and Sellers bidding 36

Summary of Smith’s (1962) findings • Small numbers of buyers/sellers can achieve competitive equilibrium

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 37

What we have learned from Experiments? • Institutions matters – posted offer pricing converges

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. 38

What we have learned from Experiments? • Dominated strategies are for playing, not for

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? 39

Application of Experimental Games • • Auction designs Deregulation of Airline Route Electricity Market

Application of Experimental Games • • Auction designs Deregulation of Airline Route Electricity Market Iowa Electronic (Futures) Market 40