Does Social Pressure Affect Decision Making?

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Does Social Pressure Affect Decision Making? An Experimental Analysis of Increasing-Sum Centipede Game Among Top Level College Students of Turkey

Mert Bakcacı Ali Eren Çamur Tugay Dilikoğlu

May 2018 Boğaziçi University

INTRODUCTION

People often have difficulty in making decision when they face a situation where their decisions have a direct effect on others. The most important feature that distinguishes we, humans, from other living beings is to live in societies with cooperating and trusting each other. We have developed this trust and cooperation awareness even with stranger people that we have never seen before or we will never see again. Starting from childhood caring about others, altruism, is one of the main virtues that society tries to instill in us. Therefore; in such complicated situations, people may take decisions which may damage their gainings. The behavior of people in situations where decisions they made are in opposition to maximize their utility has been one of the popular research topics in behavioral economics. Several studies have been made to try to understand the decision way of people. Centipede game is a good example to bring people the dilemma in decision process. The Centipede Game is proposed by Rosenthal in 1981. The game is a classic since it provides the question whether people behave rationally for self-interest or think of others’ benefit also. The game is an extensive form game where two player decide for their actions sequentially for several rounds. They decide between continuing the game and ending it. If the player continues the game then it is for other player to make the decision: continue or end the game. But if the player ends the game, she will get the bigger share from the pie leaving the other player remaining smaller portion of the payoff. The arrangements are made such that if one player continues the game and the opponents finishes it on the next round, player 1 gets less than the amount if she had finished the game on her round. Also, the payoff structure is made such that they are increasing as the games continues. Thus, it gives also an incentive to players to trust the opponent by hoping that she can reach higher stakes.

The unique subgame perfect Nash equilibrium, by using backward induction, suggests that the first player ends the game and takes the payoff in first round. However, previous researches showed us a contrary situation in real life: players often continue the game several rounds. Several experiments have done to understand the decisions process in Centipede Game.

(Figure 1 : Rosenthal’s Centipede Game)

Rosenthal has introduced the game of 10 rounds where payoff sums increase in each round. Megiddo (1986) and Aumann (1988) designed a shorter game which they called the decision options as “Share or quit”. The payoff sums increased exponentially in each round. Binmore (1987) introducing a 100-round version gave the game the name of Centipede. McKelvey and Palfrey (1992) conducted the experiment of centipede game using a similar version of Aumann. The results showed that only 37 out of 662 games ended in first round in accordance with SPNE prediction. 23 people continued the game until the final round and most of people finished it in the middle of the game, mostly in rounds closer to end. Behavioral economists still try to understand the behavioral reasons of this divergence from the equilibrium. While the Nash Equilibrium predicts that the game must end in the first round, will the game last more than one round in real life? If not, what are the reasons of this divergence between theory and real life?

PROCEDURES

The experiment was designed to be conducted with two participants. Participants made their decisions sequentially; one player goes after the other. First players were the ones who start the game and second players were the other player who made their decisions if first player decides to continue game in first round. Their roles don’t change along the game. The experiment is based on a modified version of Centipede Game. It is a two-player extensive-form game, the players make decisions in sequential order. First player starts the game by deciding whether she prefers to continue or finish the game. If she finishes the game, she receives a payoff of 4/5 of the stake and the second player gets remaining 1/5 of the stake. If first player decides to continue the game, the decision turn passes to second player and she faces with the same decision and payoff options: continue or finish the game. The game lasts 10 rounds. And for every continuing rounds, the stake in the middle is multiplied with a decided multiplication coefficient. The experiment consisted of four treatments. Treatment A was conducted online with low multiplier coefficient between rounds with 48 participants out of which were 20 female and 28 male. Treatment B was conducted online online with high multiplier between rounds with 42 participants out of which were 19 female and 23 male . Treatment C was conducted in field with low multiplier coefficient with 36 participant out of which were 13 female and 23 male. Treatment D was conducted in field with high multiplier with 36 participants out of which were 14 female and 22 male. All participants of experiments were Turkish native speaker students in Boğaziçi University ranging in age 19-23 whose nationality were Turkey . The online experimental design was constructed using Google Forms and available between 01/05/2018 and 16/05/2018. The link of the form is shared on Facebook groups of Boğaziçi

University students. The field experiment was conducted by three authors of this paper in Boğaziçi University North Campus on 16/05/2018. Treatment A and B were conducted online by using Google Forms. The language used in the form was Turkish. Randomization between two treatments in online experiment design was done by the initial question, in which participants were asked to select in which month range they were born i.e. the options were January-February-March, April-May-June, July-AugustSeptember and October-November-December. Individual who chose first option were assigned to Treatment A as first player, the ones who chose second option were assigned to Treatment A as second player, the ones who chose third option were assigned to Treatment B as first player, whereas the ones who chose fourth option were assigned to Treatment B as second player. After the subjects answered the randomization question, the instructions about the game appeared on their screen: They are told that this game is a dynamic game which is played by two players, which played sequentially and there is an initial hypothetic stake of 100 TL in the middle. The instructions continued as each round, they are faced with two decisions: continue the game or finish the game. They are also told that if they stop the game at their turn, they get 4/5 of the stake in the middle and their opponents gets the remaining 1/5, and if they choose to continue, the decision turn passes to their opponent, and at the same time, the stake in the middle multiplies by a multiplier factor. The value of that multiplier factor is randomly determined (equals to 2 or 3) according to which treatment they are in. For example, a participant that was born in December is the second player in his/her game and s/he faces with a high multiplier factor which equals to 3. They are told that the game consists of 10 rounds. When they finish playing the game, Google Forms redirected them to a questionnaire in which there are 3 cognitive-skill testing questions, a question about their gender, a question about how many siblings that they have, a question which asks if they love playing chess, a question which asks how many economics courses that they had and finally, a

question whether if they have participated in an economics experiment. All the questions were mandatory to fill. After they filled the questionnaire, the online part of the experiment is over. The estimated duration of the online part of that experiment was approximately 4 to 6 minutes. The matching of first and second players in each treatments was made randomly in excel by using “RAND” command after the data has been gathered. Treatment C and D were conducted in field. The language used was Turkish. The experiment was held on 16/05/2018. It was a sunny and warm day. Participations are selected randomly from common areas in the campus. The sample size was 36 for both Treatment C (13 females and 23 males) and D (14 females and 22 males). Experimenters first asked kindly to participants whether they want to participate an economics experiment if they have time. If they accepted, they are told that this was an experiment about centipede game which is a twoplayer and sequential game and the instructions of the game were given verbally. The standardized dialog of experimenters is presented at the Appendix. The player who begins, i.e. first player, was selected by a fair flip coin. The instructions continued as each player will face two decision in each round as the game kept going: continue or finish the game. If a player finishes the game she would get 4/5 of the existing stake in the middle which was a hypothetical 100 TL for both Treatment C and D, and their opponents will get the remaining 1/5. If they choose to continue, the decision turn passes to their opponent, and at the same time, the stake in the middle multiplies by a multiplier factor. The value of that multiplier factor which randomly determined as 2 for Treatment C and as 3 for Treatment D is said to subjects. They also informed that there were 10 rounds in total. It was forbidden for participants to talk each other and bargain to reach further rounds. To begin the game first participant is asked as she is in first round and whether she continue or finish the game if there is a stake of 100 TL in the middle. If the game continued, the same question was asked to second player and the game went on until one of the player finished the game. The

decisions of participants were noted by experimenters. When the game ended, the same questionnaire sheet with the same question in the online experiment was given to participants and they are asked kindly to answer these question. The game period depending on the rounds played in the game generally lasted 1 to 2 minutes and the participants spend about 3 to 5 minutes to answer the questionnaire. Participation both in online and field experiments were completely voluntary, no real payment was made in the end.

(Figure 2: Centipede Game with Low Multiplier Factor C: Continue, F: Finish the game)

THEORY AND HYPOTHESIS

Theory The Centipede Game is first proposed by Rosenthal (1981). The game is an extensive form game with 2 players where two players for their actions sequentially for several rounds. Players make decisions about sharing of the stake in the middle. They have two option in each round: continue or finish the game. If the player continues, the decision turn passes to the opponent who will also faces with same options: continue or finish the game. If the player finishes the game, she will get the bigger share, while the opponent gets remaining smaller portion of the payoff. The payoff sums increase for each round as the games continues; however, a player’s payoff is lower in the following round of her continue decision if the opponent ends the game. Probable future gains because of the increasing sums gives an incentive to players to trust the opponent by hoping that she can reach higher stakes. In our setup, the initial amount of the stake was 100 TL for all treatments. The stake is multiplied by a multiplier factor after each round as the game continues. The game length is restricted to 10 round. Treatments differ only in multiplier factor which was 2 for Treatment A and C; and it was 3 for Treatment B and D. Players know the payoffs, multipliers, initial stake, structure of the game, in which node they are when playing and the number of rounds that game has. The subgame perfect Nash equilibrium in Centipede Game indicates that the player who plays must end the game and take the higher payoff in every round. By using backward induction, we can reach this answer. As can be seen in Figure 2, the game must necessarily end by rule of the game in 10th round and second player gets 40960 whereas first player gets 10240. Therefore, first player knowing this must end the game since her payoff in 9th round is

higher (20480 > 10240). It is second player’s turn in 8th node and she knows that first player finishes the game in the next round since she knows that she gets lower payoff otherwise. The same strategy applies for other rounds and this leads us finally to that first player finishes game in the first round. In the unique subgame perfect Nash equilibrium, each player finishes the game at every opportunity. This means the games must end in the first round by first player taking the decision finishing the game.

Hypotheses In this experiment, the participants were expected to prefer to continue or to finish the game for a share as 4/5 for the player who decided and 1/5 for the opponent from the stake which is multiplied by a factor for each round the game continued. There are 4 treatments in our experiment. Treatment A and B were online form-based experiments. The initial stake was 100 TL for both, but it is multiplied by 2 in Treatment A while it is multiplied by 3 in Treatment B. Treatment C and D were field experiments where the participants were face to face. The initial amount of stake was again 100 TL for both, but it is multiplied by 2 in Treatment C while it is multiplied by 3 in Treatment D. It is expected that the higher multiplier factor of the stakes between rounds results in player finishes the game in earlier rounds. It is also expected that players will take the game to the further rounds when they are face to face in opposition to playing the game in front of a computer screen. In the experiment, the hypotheses below are tested: I: Players finish the game earlier when the multiplier factor is higher. II: The game continues until further rounds if players play the game face to face instead of playing without seeing each other.

RESULTS

Descriptive Statistics

Field Experiment Gender

27, 37%

Female Male

45, 63%

Online Experiment Gender

Female

39, 43%

Male

51, 57%

Graph 1.1

Field Experiment Number of Siblings 8, 11%

7, 8% 7, 8%

8, 11% 11, 15%

Only Child One sibling

45, 63%

Only child One sibling

22, 24%

Two sibling 2+ sibling

Graph 1.2

Online Experiment Number of siblings

Two siblings 54, 60%

2+ siblings

Field Experiment Chess

Online Experiment Chess

Likes chess

Likes chess 31, 43%

44, 49% 41, 57%

46, 51%

Doesn't like chess

Doesn't like chess

Graph 1.3

Field Experiment Cognitive Reflection

Online Experiment Cognitive Reflection 2, 2%

10, 14% 10, 14% 16, 22%

Graph 1.4

1, 1%

3 out of 3 2 out of 3 36, 50%

1 out of 3 0 out of 3

3 out of 3 24, 27%

2 out of 3 63, 70%

1 out of 3 0 out of 3

Field Experiment Econ. classes taken

Online Experiment Econ. classes taken

18, 25% 0-3

31, 34%

3+

0-3 59, 66%

54, 75%

3+

Graph 1.5

Field Experiment Prior participation

22, 31% 50, 69%

Online Experiment Prior participation

28, 31%

Yes No

62, 69%

Yes No

Graph 1.6

Here we have the descriptive statistics for both online and field portion of our experiment. As you can see participants in both treatments have similar characteristics and we failed to reject that these two samples are from different populations except when we compare these two samples based on their cognitive reflection test results (p