Introduction to Experimental Games Experimental Evidence on Games
- Slides: 40
Introduction to Experimental Games Experimental Evidence on Games and Anomaly 1
Environments, Institution, and Behavior 2
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, 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 – 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
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 to 320 !!!!! 8
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 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
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 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 – 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 • 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 DM 16
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 next step could get more! • What is the Subgame Perfect Equilibrium? 18
Experimental Evidence on Trust Game 19
Experimental Evidence on Trust Game 20
3 -stage Trust Game SPE payoffs 21
Voluntary vs Involuntary Trust Game 22
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 Treatment • The cost of irrationality is small? 25
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 after Many Rounds Cooperation payoffs SPE payoffs 28
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
Sensitivity of Demand/Supply (flat curves) 31
Sensitivity of Demand/Supply (steep curves) 32
A Parallel Shift in Demand with Horizontal Supply 33
A Changed Slope in Demand 34
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
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 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 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 Iowa Electronic (Futures) Market 40
- Experimental vs non experimental
- Descriptive vs correlational vs experimental research
- Experimental vs non experimental research
- Experimental vs non experimental
- Nonexperimental study
- Dyribal
- What is a primary source
- Primary evidence vs secondary evidence
- Primary evidence vs secondary evidence
- Primary evidence vs secondary evidence
- Primary evidence vs secondary evidence
- Are fibers class evidence
- Class vs individual evidence
- Difference between physical and testimonial evidence
- Class vs individual evidence
- The ecological fallacy
- Describe peeta's injuries
- Types of games outdoor
- Hunger games literary analysis
- Introduction paragraph structure
- Experimental procedure example
- What is an independent variable in an experiment
- Experimental design independent and dependent variables
- Universidad nacional experimental de yaracuy
- Experimental design xo1
- Evidencia experimental
- Placement sae examples
- Quasi experimental design example
- How to calculate experimental uncertainty
- Experiment in probability
- 11-2 probability
- El control experimental
- Variables de diseño
- Experimental unit stats
- Experimental study design
- Example of experiment research
- Non experimental design
- Types of experimental studies
- Evidencia experimental
- Quasi experimental
- Experimental cause and effect