Alternative-offer bargainging 2009 Alternative-offer bargainging -An Experiment based on the students of Peking University Yang Cao, Bachelor candidate for Economics, PKU Yang He, Bachelor candidate for Finance, PKU Lisha Fu, Bachelor candidate for Economics, PKU Aug. 6th, 2009

Agenda 2009 Background Review Experiment Design Purpose & Innovation 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Agenda 2009 Background Review Experiment Design Purpose & Innovation Make sense of the Data Drawbacks & Improvement Q & A 9

Stahl/Rubinstein prediction 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Background Review 2009 Standard Model Ultimatum Game Binmore,Shaked & Sutton(1982) Guth & Tieze(1987) Neelin, Sonnenschein & Spiegel(1988) Ochs & Roth(1989) Developed by Stahl(1972)&Rubinstein(1982): (1)Two bargainers decide how to divide K . (2) Discount factors:δ1 and δ2 (represent the time value of the bargainers) Solution: (Two-period Game) (1) The solution of the bargain strictly follows the logic of the backward induction; (2) The game would end in the first period; (3) Only the discount factors influence the division outcome. Standard Model Stahl/Rubinstein prediction 9

Background Review 2009 Ultimatum Game Standard Model Ultimatum Game Binmore,Shaked & Sutton(1982) Guth & Tieze(1987) Neelin, Sonnenschein & Spiegel(1988) Ochs & Roth(1989) One-period bargaining game designed by Guth et.al. The results deviated from the theoretical prediction. The subjects often rely on what they consider a fair or justified result. Furthermore, the ultimatum aspect cannot be completely exploited since subjects do not hesitate to punish if their opponents ask for “too much”. ——Guth Consideration of fairness and being afraid of the punishment. (further proved by Dictator Game) Ultimatum Game

Background Review 2009 Binmore,Shaked & Sutton(1982) Standard Model Ultimatum Game Binmore,Shaked & Sutton(1982) Guth & Tieze(1987) Neelin, Sonnenschein & Spiegel(1988) Ochs & Roth(1989) Two-period game experiment; At the beginning of the experiment, the results are similar to the Ultimatum Game conducted by Guth; when the experiment was conducted again with the role of the players reversed , most of the opening offers become very close to the prediction of the theoretical model.; some simple learning experience would help the results approach the theoretical model. Binmore,Shaked & Sutton(1982)

Background Review 2009 Guth & Tieze(1987) Standard Model Ultimatum Game Binmore,Shaked & Sutton(1982) Guth & Tieze(1987) Neelin, Sonnenschein & Spiegel(1988) Ochs & Roth(1989) It is because the discount factor applied by Binmore et.al. is too moderate that the results of the experiments could be close to the theoretical prediction. ——Guth & Tieze Introduce two treatments with two extreme discount factors---0.1 and 0.9 into their design to test the predictive power of the Stahl/Rubinstein through the comparison between the two treatments. The results of the second treatment seriously deviate from the Stahl/Rubinstein prediction. Guth & Tieze(1987)

Background Review 2009 Neelin, Sonnensc- -hein& Spiegel(1988) Standard Model Ultimatum Game Binmore,Shaked & Sutton(1982) Guth & Tieze(1987) Neelin, Sonnenschein & Spiegel(1988) Ochs & Roth(1989) 2-period, 3-period and 5-period experiments; Nor the Stahl/Rubinstein or the equal-split model predict the bargaining behavior observed in our experiments. A convenient summary of what we observed is that in each game the sellers offer the buyers the value of the second-round pie.” ——Neelin et.al Neelin, Sonnensc- -hein& Spiegel(1988)

Background Review 2009 Ochs & Roth(1989) Standard Model Ultimatum Game Binmore,Shaked & Sutton(1982) Guth & Tieze(1987) Neelin, Sonnenschein & Spiegel(1988) Ochs & Roth(1989) A consistent first-mover advantage is observed in both of the first-period and subgames in all the treatments; The discount factor of player1 was observed to influence the outcome of the two-period game ,which contradict the prediction of the mainstream theory; Though, according to the theoretical prediction, the game should end in the first period, a large percentage of opening offers were rejected in the experiments; The observed mean agreements deviate from the equilibrium predictions in the direction of equal split; A substantial rejected opening offers were followed by disadvantageous counterproposals, which means that the rejection in the first period is impossible to bring the buyer a larger utility in the subgames. Ochs & Roth(1989)

Agenda 2009 Background Review Experiment Design Purpose & Innovation 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Agenda 2009 Background Review Experiment Design Purpose & Innovation Make sense of the Data Drawbacks & Improvement Q & A 9

Experiment Design 2009 4 treatments 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Experiment Design 2009 Experiment A Experiment B Experiment C Experiment D Period Player 1 Player 2 1 10 2 3 7 - 0.9 4 0.27 5 0.081 Discount factor 0.3 0.7 Nash equilibrium (7, 3) (3, 7) (7.9, 2.1) (7.7, 2.3) 4 treatments Randomization 16 participants (students from different departments) 60 observations for each treatment 9

Agenda 2009 Background Review Experiment Design Purpose & Innovation 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Agenda 2009 Background Review Experiment Design Purpose & Innovation Make sense of the Data Drawbacks & Improvement Q & A 9

2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Purpose & Innovation 2009 Through the comparison among treatment A, B and C to observe people’s decisions in experiments involving different periods. (Neelin et.al,1988) Innovation: discount factor & Revenue chart Through the comparison between treatment A and B to observe people’s decisions in experiments involving different discount factors. (Guth & Tieze,1987) Innovation: design of our discount factor (0.3/0.7) Replicate the alternative-offer experiment in China to observe whether there are culture differences among participants from different countries. Test the behavior routines established by Ochs & Roth(1989), and make our own conclusions about the opening-offers, rejection rate, disadvantageous counterproposals, first-mover advantages and the differences of decisions among people having different genders and degrees. 9

Agenda 2009 Background Review Experiment Design Purpose & Innovation 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Agenda 2009 Background Review Experiment Design Purpose & Innovation Make sense of the Data Drawbacks & Improvement Q & A 9

Opening Offers in Experiments A,C and D 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Opening Offers Analysis 2009 Opening Offers in Experiments A,C and D Most offers of player 1 are between the subgame perfect Nash equilibrium offer and even division, and the closer to subgame perfect Nash equilibrium offer it is, the higher for the rejection rate. In three-period game, player 1 are more likely to offer fifty-fifty, while player 1 in five-period game are more likely to choose subgame perfect Nash equilibrium offer. 1

Opening Offers in Experiments A and B 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Opening Offers Analysis 2009 Opening Offers in Experiments A and B In Experiment A, discount factor for players are both 0.3, while in Experiment B, the discount factor for player 1 is 0.3 and for player 2 is 0.7. Player 2 in Experiment B is more powerful than those in Experiment A. Because subgame perfect Nash equilibrium for Experiment A and B is (7,3) and (3,7), respectively. The results for each experiment are closer to their own equilibrium. In Experiment B, player 1 has first-move advantage, so even subgame perfect Nash equilibrium is (3,7), he will not get less earnings than player 2 1

perfect equilibrium offer ————————— actual offer 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Opening Offers Analysis 2009 Opening Offers of the experienced players ·········· perfect equilibrium offer ————————— actual offer Figures show the opening offers of experienced players. Experienced players refer to the one who have played the specific game for the most time. the subgame perfect Nash equilibrium may not be a good prediction. Because most offers tend to move to equal division, and only the player in Experiment D tend to offer as subgame perfect Nash equilibrium. 5

Source: Euromonitor International 2007 data 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Opening Offers Analysis 2009 Testing predictive power of Nash equilibrium Test for the opening offers in each experiment The direction of the difference corresponds to the theoretically predicted direction in 5 of the 6 groups. Source: Euromonitor International 2007 data 5

2009 Rejected Opening Offers Analysis Offers &Responses in Experiments 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Rejected Opening Offers Analysis 2009 Offers &Responses in Experiments Disadvantageous counters are referred to the situation that player rejects the opening offer and make a counterproposal, he will not get as much as he can if has been accepted. In Experiment A,C,D, the subgame perfect Nash equilibrium is (7,3), (7.9,2.1), (7.7,2.3), respectively. our subjects failed to reach equilibrium prediction in the first period, with 8 percent of opening offers rejected. 5

2009 Rejected Opening Offers Analysis 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Rejected Opening Offers Analysis 2009 Rejection rate and disadvantageous counterproposal rate in previous experiments The pattern of rejections and counterproposals observed in the experiments is quite similar to those in the previous experiment discussed above. One explanation is that players usually have limited calculation ability, they cannot figure out where Nash equilibrium locates. Another is that players’ utility is not measured by their monetary payoff. 5

Average opening offers and Average earnings 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt First-move advantage and earnings 2009 Average opening offers and Average earnings Although player 1 has first-move advantage, it doesn’t mean that he can get highest earnings when making most generous offers, because the reject rate is also very high The fitted line between average earnings and average offers, we find that it’s like cubic polynomial, which indicates that average earnings increase first and then decrease as average offers increase 1

2. Data after semicolon mean percentage in the row Legend: 1. Data before semicolon mean percentage in the column 2. Data after semicolon mean percentage in the row 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt Other factors analysis——Gender and Education 2009 Variance Table of Opening Offers Opening Offers Rejection Rate These two factors both have significant influence on the opening offers, no matter separately or as a whole Men and postgraduates usually leave themselves less earnings in the first period and are also more likely reject opening offers, while women and graduates usually leave themselves more earnings and seldom reject opening offers 5

Agenda 2009 Background Review Experiment Design Experiment Process 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt 2009 Agenda Background Review Experiment Design Experiment Process Make sense of the Data Drawbacks & Improvement Q & A 9

Agenda 2009 Background Review Experiment Design Experiment Process 2019年2月1日星期五6时11分5秒 0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt 2009 Agenda Background Review Experiment Design Experiment Process Make sense of the Data Drawbacks & Improvement Q & A 9