Magi

The Game of the ‘Magi’: Effect of Compromise & Reciprocity in Battle of Sexes

_______________________________________

Mainak Sarkar Dept. of Economics, Jadavpur University

Manali Barman Dept. of Economics, Jadavpur University

Jayati Das Dept. of Economics, Jadavpur University

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This paper is based on a lab-run experiment conducted by a group of experimenters from Jadavpur University, by taking a sample of 15 different pairs and playing a simple Battle of Sexes game to predict what the real-life outcomes are for such a cooperative game. We also have tried to figure out the reasons and the extent to which they affect the divergence of the actual outcomes from the socially optimum ones. We also have modified a few conditions one after another of the general game and considered the impact, if there is any.

I. The Battle of Sexes: An Elementary Note to Begin With A couple living in a metropolis were planning an outing on a Saturday evening. The husband was excited about the football match scheduled in the stadium nearby, whereas the wife wanted to visit the movie theater for the newest flick. Both of them prefer their own choices more than the other’s, but only if they go together. What is important here is that being together matters for both of them. If by somehow the duo chooses to visit different locations, not being together, gets no satisfaction at all. The couple has to decide simultaneously without communicating with each other and we assume this to be a single-shot game. (Well, how often you get a Saturday night off in these days of abrupt urban life, out of your busy schedule?) The simple game could be represented through a 2x2 normal form matrix, where the strategy set available to both the husband and wife is (Football, Movie).The payoffs in the matrix consists of a pair, the first being the payoff (ordinally measured in utility terms) of the husband for choosing action m, the other is of the wife for choosing action n; m, n = (Football, Movie). Wife

Football

Movie

Football

(4,2)

(0,0)

Movie

(0,0)

(2,4)

Husband

2

For a 2- person game, we can define a Nash Equilibrium as a strategic profile (si*, s-i*) for which ui (si*, s-i*)>=ui (si’, s-i*); i= 1, 2, where si’ belongs to the available strategy set to individual i. For this game, there exists two different Nash equilibria, (Football, Football) and (Movie, Movie). (We have not taken into account the case of mixed strategy Nash equilibrium here intentionally, & concentrated only on pure strategies) From this result, we can conclude that Nash solutions are those where both players stay together. Also, there are multiple Nash equilibria present in this context, out of which, any one could be reached at the expense of any one player’s compromise. The last line is being elaborated here. To reach any one of the two available N.E’s, which are social optima too, one player has to stick with his own preference while the other must compromise. If one of them compromises or decides to follow his/her partner by sacrificing own best choice it would certainly give them a higher satisfaction. If both reaches a solution (Football, Movie) it yields zero satisfaction to both, as now they are separated, ending up in different locations. Also, if both compromise for each other, considering only to make the other person better off even though for that their own utility reduces, the result is the same. Both compromising for each other leaves them at a situation where the wife waits outside the football stadium, looking out for the husband in the crowd, while the husband awaits beside the ticket counter in the theater wishing his wife to come and buy the ticket soon.(Remember the 0’ Henry classic “The Gift of The Magi”? True love made Della sell her precious hair that the queen of Sheba would be proud to possess, for buying a platinum fob chain for the watch of her husband Jim, while Jim sold his ancestral watch to buy an ornamental comb for her. Compromise from both ends left the duo incapable to enjoy their Christmas presents, thus being in a no payoffobtaining position. However, even though no monetary payoff was associated, they were happy at the end of the day knowing how much they cared for each other & the true extent of their love. Even though they could not use their Christmas presents that evening, the compromise of one made the other feel happy, that yields a positive utility to both, and giving the story a happy ending. This might look like a contradiction to what we said for the (Movie, Football) decision combination, by choosing which both players get a null payoff, but we will come to this point later.) So we find that the social optimum could only be reached at any one’s expense of his preferred choice. This made us curious about our first query. If we allow a couple in a similar scenario to decide between the two options, should they really behave like the theory suggests? If through simultaneous choices of the pair, any one N.E is actually reached, which one would it be? Or should they never compromise and be strict to their own choices only? And what about the case where both compromises? To what extent do their choices differ because of ego, leading to (Football, Movie) or true Compromising for each other leading to (Movie, Football)?

II. The Basic Experiment & Choices Initially, we conducted our experiment to check whether real-life solutions yield the same results as the theory predicts in case of a cooperative simultaneous one-shot game. For that, we have constructed the general Battle of Sexes (2*2) game in a more realistic way. For our experiment, we chose 15 couples, the members of each pair (We called it a Group) being familiar with the other. One member of a group is assigned as person1 while the other as person2 using a random lottery. We had

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given each of them an endowment of Rs.100, with which they can buy any one of two available tickets 1 or 2.1Now, the payoffs associated with the choices of the pair are constructed by monetary transformation of the utility attached with each player’s action in the original game discussed above. If both players in a group choose ticket 1 to buy, person1 gets Rs.400 while the other gets Rs.200 only and if both decide to choose ticket 2, the payoffs just get reversed. If the choices differ ((Ticket 1, Ticket 2) or (Ticket 2, Ticket 1)), both end up with zero amount of money. So, just like the original game, here person 1 would love to buy ticket 1 whereas the other player in the group would relish the possession of ticket 2, provided they choose the same ticket.2We let all the players to decide simultaneously and finally depending on their decisions, associated payoffs are calculated.

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Both players in a group must spend the entire endowment to buy either ticket1 or ticket2. Decision of a player is a binary choice here, choosing either of the two tickets available. 2

For simplicity, you might think of ticket1 as the football match ticket and ticket2 as the movie ticket, as it was in the original game discussed above. According to the traditional theory, we know (1,1) & (2,2) would be the optimal ticket combinations to choose, i.e, one player from a group compromises and both end up choosing the same ticket. But, what we saw was out of those 15 pairs, only 2pairs choose ticket combination (1, 1) whereas one pair was such where the person1 compromised for the other and the choices were (2, 2). So, only 20% of the total sample sticks to what theory predicts. Remarkably, the remaining 12 pairs equally shared their combination of ticket choices between (1, 2) & (2, 1). So, 6 out of 15 pairs (40%) choose (1, 2) while the remaining half a dozen pair (40% of the total sample size) compromised for each other and chooses (2, 1)! The ticket combination (1, 2) is chosen due to the egoistic behaviour of both subjects in a group. They both stick together to their own preferences thinking that the other will compromise. Each one of them was trying to maximize own possible payoff, at the expense of the other thus leading to a disaster for both by getting no money at all. But the other half dozen samples yield really astonishing results! Question that arises here is, even though they had prior knowledge of all the possible payoffs, what made them feel to compromise for each other, leaving with a null monetary payoff?

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6 5 4 3

Decision Combination

2 1 0 (1,1)

(1,2)

(2,1)

(2,2)

Benchmark Treatment: Decision Combinations for 15 Pairs Playing the Original BoS Game One possible explanation is both person1 &2 thought that the other one is going to stick with his best choice. So both of them compromised for each other thereby leading to a loss for both. This is exactly what happened in the story of the “Magi “as we discussed earlier: neither Jim nor Della thought the other would sacrifice his/her most precious possession for making the other one happy.

8 7.8 7.6 7.4 7.2 7 6.8 6.6 6.4

Ticket 1 Ticket 2

Person1

Person2

Benchmark Treatment: Cumulative Choices of Person1 & Person2

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Thus it led to a situation where both compromised for each other ending up at the evening with a comb set and a platinum fob chain, with no use of them. (This is just equal to the choice of ticket (2, 1) where both players are left with zero amount of money.) From the 2nd chart, we can see switching from own best to the other’s is quite common a case here.8 out of 15 persons assigned as person1 choose to stick with their best choice of ticket 1, while the other 7 switched. Almost the same results were reflected by the players assigned as person 2’s. Now, we asked ourselves a question based on these results: Do couples really compromise for each other because of their prediction on the partner’s behaviour of sticking around with own best choice? If so, it’s simply the maximization of payoff that’s really they are concerned about. The lack of communication might lead to a double-Compromising situation where both were unaware what the other is going to do, thus choosing the other’s best. Another possible explanation is they might want to compromise for each other to make sure their inherent faith on each other strengthens. Even though we initially had assumed this to be a single-shot game, remember the duo knew each other very well and they are very close in relationship. One might think, choosing his best action will lead to a misunderstanding between the two, the other thinking of him as a greedy person and not of compromising nature and this might affect the relationship in future. This simply means even though we tried to play a single-shot game, players being well known to each other might think of possible future consequences, thus deviating from their best choices, and choosing that option which will improvise their mutual understanding and personal relationship. What is of interest is that even though both players knew choosing either (1, 1) or (2, 2) would yield the maximum payoff for them, most of them either have chosen to stick around with their best choices, thus leading to an egoistic outcome of (1,2) and get nothing, or to compromise both and lead to a situation of over-Compromise, having no monetary payoff once again. So, the traditional theory is not being supported by the first experiment we conducted. Decisions are deviating from the social optimum and experimental outcomes, in general, shows most of the groups left with a payoff combination of RS.(0,0). One basic difference that we observe here is the general 2*2 BoS game, which we assumed to be a single-shot simultaneous game, is in practical not so. Rather, being familiar to each other let the duo decide in a manner that will strengthen their trust for each other and affect their future interactions. This is one vital observation totally neglected by the conventional theory. Even though being a single-shot game, players are assumed not to play it ever after, since they are very close to each other made them interact in various circumstances in near future. The players too had it in mind and while deciding for which action to choose, they also keep in mind this decision might have an impact in future interactions and decides accordingly.1The traditional theory never thought of this possibility of future interactions in different circumstances having an effect on the couple’s decision pattern. In a similar approach, we conducted this experiment once more but now with 15 different pairs where the group members were anonymous to each other. Being aware of this, the players played the simultaneous one-shot game, choosing between ticket1 and ticket2.

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Person1's choice 14 12 10 8 Person1's choice

6 4 2 0 1

2

Person1’s Choices in Anonymous Partner BoS Game Now we observe individuals are behaving more egoistically than before. 12 out of 15 persons assigned as person1 now stayed with own preference. It clearly proved being familiar does matter to an extent and players were compromising not because they think the other will stick to his choice, but to strengthen the relationship with the other player in his group, since both knew they would again have to interact in near future. When anonymity comes, being unknown to each other, neither player had the incentive to compromise and that’s what actually happened, as the result suggested too. Even though when both players compromised they got a null payoff, the fact that the other player is compromising gave each player an ethical satisfaction, which helps in strengthening the mutual understanding between them and faith for each other. So, we can not simply exclude this effect while constructing the payoff matrix for a (2*2) BoS game. It is the Decision of Compromise (we called it the Compromise Effect) of the other player that yields a positive utility for a person, even after ending up far away from being together in that particular Saturday evening. 1

In the Battle of Sexes, where the duo is assumed to be a husband and his wife, interacts daily over various issues. So, a single Saturday night ticket choice problem is not the end of their interactions in real life. They probably have to interact again over some issue in the very next hour.

III. The Game of the Magi: Compromise Effect & Reciprocity As being mentioned above, player m’s decision to compromise has an impact on player n’s payoff, provided both of them are very close in relationship (m, n=1, 2). The payoff matrix that we have used till now needs a slight change in payoffs associated and we have reconstructed it as follows, incorporating the compromise effect in it.

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Person2

Ticket1

Ticket2

Ticket1

(400,200)

(0,0)

Ticket2

(300,300)

(200,400)

Person1

The only change in the payoff matrix is in the lower left corner where for choosing the ticket combination (2, 1) the two players in the group will each get Rs.300 respectively. Here, we have incorporated the “compromise effect” in the basic game and changed the payoffs accordingly. If person1 willingly compromises for the other and vice-versa, it might be the case where both players end up at situations separated from each other (in case of the BoS game), or unable to utilize what they achieve for the other, since the partner already have sacrificed the thing what the achievement was for to use. Still, knowing about such compromising nature of the other player that his partner can even give up his best preference for the sake of herself and vice-versa, might give them a positive satisfaction. Since both players in a group knew each other, that possibly is going to affect their future interactions too, just like Jim and Della. After coming to know how much they care for each other, the bond between the duo is likely going to strengthen. This is why we have incorporated a positive payoff of Rs.300 each for the compromising choice of actions of both. Also, now we have instructed the players to play the game sequentially, i.e, first the person1 in a group decides his choice, then his choice is shown to person2 and depending on that choice, person2 gets his chance to choose. This is a sequential one-shot game, with compromise effect incorporated. As we can see, now, the general trend of decision combinations has drastically changed from the previous result, with almost 50% of the pairs now choosing (2, 1) and compromising for each other. Also, from the pie chart, we clearly see 9 out of 15 first movers are now compromising for the other player, even though, being the first mover, they had the chance of choosing their best possible ticket! So, there is some inherent trust in person1’s mind that if he chooses ticket2, the other player is not

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going to turn him down by choosing his best. Rather, he will reciprocate this behaviour choosing ticket1, giving each of them an equal payoff of Rs.300. Also, it is that compromising choice he decided and person2, seeing this, would most likely react in a similar manner, thus strengthening the trust between them. The experiment result supported this theory. 7 out of 9 followers (Almost 80%) reciprocated in a compromising way when person1 chose to compromise. Person1 also had it in mind if he chose ticket1, person2 being able to see his decision, will take him as a non-compromising person and might reciprocate such selfish kind of behaviour, by himself being egoistic and choosing ticket 2. And guess what, this indeed happened! In 2 out of those 6 cases where person1 chose ticket1, person2 decided to reciprocate such egoism by choosing ticket 2, giving none of them any payoff! It is this inherent trust and at the same time, the threat of a reciprocal egoism, made person1 select the compromising strategy of choosing ticket2. At the same time, person2 reciprocated in a similar fashion & chose ticket1 to get an equal payoff of Rs.300 each. One important thing to notice here is once we have incorporated the compromise effect in the payoff structure, each player being aware of this, reacts in a much more compromising way. As every player knew, by choosing the other’s best preference, he/she can behave in a cooperative pattern. This will ensure making the trust between the two stronger. This leads to a solution in reality that diverges from the social equilibrium, reaching neither (1, 1) nor (2, 2). In case of Battle of Sexes game, making the game sequential with perfect information leads to social optimum, as the theory suggests, is violated here. Rather, presence of this compromise effect let the duo behave in a much more cooperative way, each compromising for the other.

7 6 5 4

Decision Combination

3 2 1 0

(1,1)

(1,2)

(2,1)

(2,2)

Sequential Game with Compromise Effect: Decision Combinations of All 15 Pairs Another thing that we have just said needs a bit elaboration. The decision pattern of the follower shows whether those choices are driven by egoism or compromising behaviour. See, in 2 cases, where the first mover chose ticket1, the follower decided to choose ticket2, knowing that would give both of them a null payoff, whereas choosing ticket1 in that case would give him a minimum of Rs.200! So, their

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decisions are driven purely by reciprocal egoism. The followers even decided to forgo the Rs.200 payoff just to ensure the first mover gets nothing at all! The leader, being aware of this, decided to compromise to make sure the follower reciprocates in a similar way. So, compromise effect and reciprocal egoism (by person2) let person1 behave in a compromising way, whereas compromise effect and the fear of triggers’ strategy let person2 reciprocate such cooperative behaviour by person1, thus deviating from the theory-predicted equilibrium outcomes, leading to a solution that ensures escalating the mutual trust among them. We sincerely thank Prof. Gautam Gupta for helping us conduct the experiment and all participants for their kind support and voluntary involvement. Person1's Choice

1 2

Sequential Game with Compromise Effect: Choices of Person1 in All Groups

IV. The Game of the Magi Revisited: Simultaneous Single-Shot Choice In the next treatment, we have played the same game we played above with a difference of playing the game simultaneously. Here, none of the 2 members in a group was aware of the choice made by the other person in his group.

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Decision Combinations

1 2 3 4

Ticket Ticket Ticket Ticket

(1, (2, (1, (2,

1) 1) 2) 2)

In this simultaneous game, what we see is 8 out of 15 pairs were compromising for each other, choosing ticket combination (2, 1). So, even though none of them was aware of the other’s decision at the time of taking his decision, over 50% of the population trusted each other and decided not to behave egoistically but to compromise for each other. One other notable fact is that none of the pairs chose decision combination (1, 2). Therefore, not a single pair decided to act selfishly thinking only of themselves. Rather, they have chosen to trust each other in general and receive a payment of Rs.300 each.

8 7 6 5 4

Decision Combinations

3 2 1 0 (1,1)

(1,2)

(2,1)

(2,2)

Simultaneous Game with Compromise Effect: Decision Choices of 15 Pairs

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V. Does History Matter? In our final treatment, we kept the basic game same as before (Sequential game, single-shot with compromise effect incorporated) just with the difference of including 3 practice periods before the final round is played. After 3 trial periods, along with the decisions of both players in a group shown after each trial, the pairs were asked to choose between the two tickets 1 and 2. In this final treatment, again person1 from each group moved first deciding his choice and person2 in each group saw the decision taken by person1 in his group and decided accordingly. We have given the results here only for the first trial round and the final paying round, whereas the complete result for all the rounds are given in Appendix B. From the round1 results, we observe most of the pairs (Over 50%) still are choosing strategy combination (2, 1), therefore deciding to compromise for each other. Well, this was expected from what we have already seen. Inclusion of compromise effect let both chose in a coordinating way. They replicated this strategy combination for the next 2 trial periods too. But, in the final paying period, we saw a deviation in the choices by them. For the first 6 pairs, we informed this was the last treatment they were going to play and after this paying period, the experiment will be over. In the final paying round, person1’s of every group still decided to compromise for each other, based on the previous 3 trial period knowledge, but the other player, knowing already that was the last round of the treatment and of the entire experiment too, deviated from compromising strategy and chose to behave greedily, deciding to buy ticket 2. For the next 9 pairs, we had not informed previously whether that was going to be the last round or not and they reacted in the same manner as before, person1 trusting the other player in his group an person2 reciprocating to the former choice of person1 by choosing ticket1. To avoid any kind of backward induction, we only let the players know that was the last treatment after they had completely played the previous treatment.

8 7 6 5 4 3 2 1 0

Decision Com binations

(1,1) (1,2) (2,1) (2,2)

Sequential (History) Game: Decision Pattern of 15 Pairs in Trial Round1

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Decision Pattern in Round 1

11 12 21 22

Sequential (History) Game: Decision Pattern of 15 Pairs in Trial Round1

Decision Combinations

8 7 6 5 4

Decision Combinations

3 2 1 0

11

12

21

22

Sequential (History) Game: Decision Pattern of All 15 Pairs in Final Paying Round This proves something we tried to tell throughout this paper. In reality, the married couple we talked about in the original BoS game interacts daily over various issues.

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This continues till their relationship longs. But, before it’s over, none of them had any prior knowledge about when it’s going to be over. Even though it might seem choosing over a Football match or a movie is a one-time dilemma, and once that Saturday gets over, it’s all over. But what seems to be is not what exactly happening here. Unaware of the fact how long their relationship will continue, both members in a group (here the husband and wife) had the future consequences of a single decision in mind while deciding an action. They believe future interactions are interdependent of present decisions and deciding in a compromising way in period t can make interactions over the next period easy and profitable to both. Let us tell a story to make you believe the point. Think about the 1979 classic “Kramer vs. Kramer”, winner of 5 academy awards including best picture that year. The story was based on a just divorced man who must learn to care for his son on his own, and then must fight in court to keep custody of him. But what if both the husband and wife behaved in a compromising way before they get divorced? If over periods, both kept compromising for each other, would this problem really occur? Consequent egoism of both led them to a situation where compromise effect no longer exists, neither exists any kind of trust between the duo. What we try to say is past interactions certainly do have an impact over present decision making problems. Compromise effect let the inherent trust on each other grow over periods and people being aware of this, choose their decisions accordingly. As seen in our experiment, once people had the prior knowledge what the last treatment of the game is going to be, tried to maximize their profit in the final period. Thus, person2, knowing he had the upper hand in the final paying round being the last mover, decided to choose ticket 2, his own best choice. In case person1 chooses to play his personal best by choosing ticket1, person2 might have chosen ticket2 giving none of them any monetary payoff at all. Therefore, person1 is behaving in the best possible way by choosing ticket2, compromising for person2. But, person2 at the same time, being aware of the fact he is the final mover, decided to deviate from the compromising strategy and chose the action that maximized his own payoff, giving him Rs.400 leaving the other in his group with Rs.200 only. However, when in the next case, we had not informed the players when the experiment is going to end, all group members in general (6 out of 9) compromised for each other and chose (2, 1). When played for infinite periods, being feared by the trigger’s strategy, none of them deviates from their compromising choices, whereas in case of prior knowledge of when the final period is going to be played, players tend to deviate in the last round from the previous choices.

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Decision Combination

4 3 4

2 1 0

2 0 11

0 12

21

22

Decision Combination Decision Combination

Sequential (History) Game: Decision Pattern of First 6 Pairs (Aware) in Final Paying Round Decision Combination

6 4 2 0

6 2 11

0 12

Decision Combination 1

21

22

Decision Combination

Sequential (History) Game: Decision Pattern of Remaining 9 Pairs (Unaware) in Final Paying Round

Appendix: A 15

Instruction sheet Respondent No. N

Dear Friend,, Thank you very much for your help through your participation in our survey. We now explain the purpose of our survey briefly. Everyone cares about their own income as the more they earn, the more they can buy. But, income of other people also matters to them. However, individuals might not always be driven by the purpose of increasing their personal gain. They may compromise in certain situations for their loved ones and even accept lesser earnings. This survey is conducted to address the importance of such compromising nature of the people. In this survey, you are paired with a person who you are familiar with. Each one of you is given 100 rupees at the start of the game. Both of you will have to make a choice between either one of the 2 tickets 1 or 2. Both tickets are priced at Rs.100 each. So, you have to spend your entire endowment to buy any of the 2 tickets. If the choices made by both of you are same then both of you get a positive return greater than 100 rupees. Else, you end up with nil. We provide the following example for explaining the game and monetary payoffs associated with the choices of both players.  Example: - In a group, there are 2 persons 1 & 2. If both of them chooses ticket 1 then: 

Person 1 gets 400 rupees & Person 2 gets 200 rupees.

However, if both choose ticket 2 then  Person 1 gets 200 rupees & person 2 gets 400 rupees. •

If the choices differ (i.e. Person 1 chooses ticket 1 & person 2 chooses ticket 2 / vice-versa) then both end up getting 0(zero) rupees each.

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Thus, the payoff structure is:

Person 1’s choice Ticket Ticket Ticket Ticket

1 1 2 2

Person 2’s choice Ticket Ticket Ticket Ticket

Payoff of Person 1

1 2 1 2

400 0 0 200

Payoff of Person 2 200 0 0 400

In the next half hour you are going to be asked to make a choice between the 2 tickets, 1 & 2. It is essential that you are true to the choices you make. Please don’t choose an option because you feel that it is somehow expected of you. Your opinion & belief should be based entirely on your choice. The information gathered here will remain strictly confidential & will solely be used for research purpose. Kindly do not talk with each other during the survey.

Thank You

Case 2: In this case, you and your partner shall make your choices of the 2 tickets at the same time, as like the first game.

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•

The payoffs now have slightly changed. The complete explanation of the game and payments associated are given below:

There are 2 persons 1 & 2. If both of them choose ticket 1 then: Person 1 gets 400 rupees & person 2 gets 200 rupees.  However, if both choose ticket 2 then Person 1 gets 200 rupees & person 2 gets 400 rupees. If Person 1 chooses ticket 1 and person 2 chooses ticket 2, both of them get Rs.0 respectively. But, if Person 1 chooses ticket 2 and Person 2 chooses ticket 1, both of them get Rs.300 respectively.

Person 1’s choice

Person 2’s choice

Payoff Person

Payoff Person 2

1 Ticket1 Ticket1 Ticket2 Ticket2

Ticket1 Ticket2 Ticket1 Ticket2

Thank

400 0 300 200

200 0 300 400

You

Case 3:

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•

Once again you & your partner are required to make selection amongst 2 tickets 1 & 2. But, in this case, you and your partner will take decisions in a consecutive manner. So, person 1 in a group makes her choice first, and after seeing it, person 2 in that group makes her choice. Here, person 2 in a group will be aware of the first move made by person 1 & will have to take his/her decision accordingly.

•

The payoffs are just the same as used in treatment 1. The complete explanation of the choices and payments associated are given below:

Person 1’s choice

Person 2’s choice

Payoff of Person 1

Payoff of Person 2

Ticket1 Ticket1 Ticket2 Ticket2

Ticket1 Ticket2 Ticket1 Ticket2

400 0 300 200

200 0 300 400

Thank

You

Case 4: Here the basic structure of the game remains the same as the previous treatment with similar outcomes as follows:

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Person 1’s choice

Person 2’s choice

Payoff of Person 1

Payoff of Person 2

Ticket1

Ticket1

400

200

Ticket1

Ticket2

0

Ticket2

Ticket1

300

Ticket2

Ticket2

200

0 300 400

However, the history of the game will be known to you, that is, you & your partner will get a chance to make your choices amongst ticket 1 & 2 for the final game after playing for 3 trial periods each, where the choices of both the players will be shown after each trial period is played.

Thank

You

Appendix: B Experiment Results:-

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Benchmark Treatment(Simultaneous BoS) Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Group 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8

Decision 2 1 2 1 1 1 1 1 1 2 1 2 1 2 1

Profit 0 0 0 0 400 200 400 200 0 0 0 0 0 0 0

Subject 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Group 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15

Decision 2 1 2 2 2 2 1 2 1 2 1 2 1 1 2

Profit 0 0 0 200 400 0 0 0 0 0 0 0 0 0 0

Profit 400 200 300 300 400 200 300 300 200 400 400 200 400 200 300

Subject 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Group 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15

Decision 1 2 1 2 1 2 2 2 1 2 1 2 2 2 1

Profit 300 300 300 300 300 200 400 300 300 300 300 200 400 300 300

Simultaneous Compromise Effect (Treatment 1)

Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Group 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8

Decision 1 1 2 1 1 1 2 1 2 2 1 1 1 1 2

Sequential Compromise Effect Game (Treatment 2) Subject 1 2 3 4 5 6 7

Group 1 1 2 2 3 3 4

Type 1 2 1 2 1 2 1

Type1: Person1

Decision 2

Type2: Person2 OthersDecision 1

2 1 2 1 1

Profit 300 300 300 300 300 300 400

21

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15

2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

1 1 1 2 2 2 2 1 2 1 2 2 1 1 1 1 1 2 1 2 1 2 1

Sequential History Game (Treatment 3)

200 400 200 200 400 200 400 0 0 0 0 300 300 400 200 400 200 300 300 300 300 300 300

Type1: Person1 Type2: Person2

Round 1:Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Group 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11

Type 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

Decision 2

OthersDecision 1

2 1 2 1 1 1 1 1 2 2 2 2 2 1 1 2 2 1 1 1

Profit 300 300 300 300 300 300 400 200 400 200 200 400 200 400 300 300 0 0 300 300 400 200

22

23 24 25 26 27 28 29 30 Round 2:Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

12 12 13 13 14 14 15 15

1 2 1 2 1 2 1 2

1

Group 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15

Type 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

Decision 1

Group 1 1 2 2 3

Type 1 2 1 2 1

Decision 1

1 2 1 2 1 2 1

OthersDecision 2

2 1 1 1 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 1 1 1 2 2 2 2 2 1

400 200 300 300 300 300 300 300

Profit 0 0 300 300 400 200 400 200 300 300 300 300 300 300 300 300 300 300 300 300 400 200 400 200 200 400 200 400 300 300

Round 3:Subject 1 2 3 4 5

OthersDecision 2

2 1 1

Profit 0 0 300 300 400

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6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15

2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

1 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 1 1 1 2 2 2 2 2 1

200 400 200 300 300 300 300 300 300 300 300 300 300 300 300 400 200 400 200 200 400 200 400 300 300

Round 4 (Payment Round):Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Group 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12

Type 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

Decision 2

OthersDecision 1

2 1 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 1 2 2 2

Profit 0 0 300 300 400 200 400 200 300 300 300 300 300 300 300 300 300 300 300 300 400 200 400

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24 25 26 27 28 29 30

12 13 13 14 14 15 15

2 1 2 1 2 1 2

2 2 2 2 2 2 2

200 200 400 200 400 300 300

Appendix: C ZTREE Programs Used for Experiment:Benchmark Treatment: Background (Subjects=6, Groups=3) Globals Subjects Summary

Contracts Session New Program (Subjects Table): //PiBC //Payoff of a player if he plays B while the other plays C

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Pi11=0; Pi12=0; Pi21=0; Pi22=0; Endowment=100; Endowment Display Stage (New stage) Your endowment is (New Item) Variable:- Endowment Layout:- 1 Ok, I understand (New button) Decision Stage (New stage) You Have Rs.100 As Your Endowment (New Item) With This You Can Buy Either Ticket 1 or Ticket 2. To Buy Ticket 1, Enter 1 To Buy Ticket 2, Enter 2 Your Decision is----Variable:- Decision Layout:- 1 Input Max:-2, Min:-1 Done (New Button) Profit Display Stage (New Stage) New Program (Subjects Table): OthersDecision=find(same(Group) & not(same(Subject)),Decision); Profit=if(Decision==1,if(OthersDecisio n==1,Pi11,Pi12),if(OthersDecision==1 ,Pi21,Pi22)); Your Choice is to buy Ticket ---- (New Item) Variable:- Decision Layout:- 1

Layout:- 1 Your Profit is:- (New Item) Variable:- Profit Layout:- 1 Continue (New Button)

Parameter Table Program: Program for subject a (a= odd number of subject) //this player prefers ticket 1 Pi11=400; Pi22=200; Pi12=0; Pi21=0; Program for subject a (a= even number of subject) //this player prefers ticket 2 Pi11=200; Pi22=400; Pi12=0; Pi21=0;

Your Partner’s choice is to buy Ticket----- (New Item) Variable:- OthersDecision

Treatment 1: Simultaneous Compromise Effect Game Background (Subjects=6, Groups=3) Globals Subjects Summary Contracts Session New Program (Subjects Table): //PiBC //Payoff of a player if he plays B while the other plays C Pi11=0; Pi12=0; Pi21=0;

Pi22=0; Endowment=100; Endowment Display Stage (New stage) Your endowment is (New Item) Variable:- Endowment Layout:- 1 Ok, I understand (New button) Decision Stage (New stage) You Have Rs.100 As Your Endowment (New Item) With This You Can Buy Either Ticket 1 or Ticket 2. To Buy Ticket 1, Enter 1 To Buy Ticket 2, Enter 2

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Your Decision is----Variable:- Decision Layout:- 1 Input Max:-2, Min:-1 Done (New Button) Profit Display Stage (New Stage) New Program (Subjects Table): OthersDecision=find(same(Group) & not(same(Subject)),Decision); Profit=if(Decision==1,if(OthersDecisio n==1,Pi11,Pi12),if(OthersDecision==1 ,Pi21,Pi22)); Your Choice is to buy Ticket ---- (New Item) Variable:- Decision Layout:- 1 Your Partner’s choice is to buy Ticket----- (New Item) Variable:- OthersDecision Layout:- 1 Your Profit is:- (New Item) Variable:- Profit

Pi21=300; Program for subject a (a= even number of subject) //this player prefers ticket 2 Pi11=200; Pi22=400; Pi12=300; Pi21=0;

Layout:- 1 Continue (New Button)

Parameter Table Program: Program for subject a (a= odd number of subject) //this player prefers ticket 1 Pi11=400; Pi22=200; Pi12=0;

Treatment 2: Sequential Compromise Effect Game Background (Subjects=6, Groups=3) Globals Subjects Summary Contracts Session New Program (Globals Table): Person1=1; Person2=2; //PiBC //Payoff of a player if he plays B while the other plays C Pi11=0; Pi12=0; Pi21=0;

Pi22=0; Endowment=100; Type=0; Endowment Display Stage (New stage) Your endowment is (New Item) Variable:- Endowment Layout:- 1 Ok, I understand (New button) Person1 Decision Stage (New stage) Participate=if(Type==Person1,1,0); You Have Rs.100 As Your Endowment (New Item) With This You Can Buy Either Ticket 1 or Ticket 2. To Buy Ticket 1, Enter 1

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To Buy Ticket 2, Enter 2 Your Decision is----Variable:- Decision Layout:- 1 Input Max:-2, Min:-1 Done (New Button) Person1 Decision display stage(New stage) Participate=if(Type==Peson2,1,0); Decision1=find(same(Group) & Type==Person1,Decision); Person1’s choice is to buy ticket:--(New item) Variable- Decision1 Layout-1 Proceed (New button) Person2 decision stage(New stage) Participate=if(Type==Person2,1,0); You Have Rs.100 As Your Endowment (New Item) With This You Can Buy Either Ticket 1 or Ticket 2. To Buy Ticket 1, Enter 1 To Buy Ticket 2, Enter 2 Your Decision is----Variable:- OthersDecision Layout:- 1 Input Max:-2, Min:-1 Done (New Button) Profit Display 1 Stage (New Stage) New Program (Subjects Table): Participate=if(Type==Person1,1,0); OthersDecision1=find(same(Group) & Type==Person2,OthersDecision);

Profit1=if(Decision1==1,if(OthersDecis ion1==1,Pi11,Pi12),if(OthersDecision1 ==1,Pi21,Pi22)); Your payoff is ---- (New Item) Variable:- Profit1 Layout:- 1 Continue(New button) Profit display 2 stage (New stage) Participate=if(Type==Person2,1,0); Decision1=find(same(Group) & Type==Person1,Decision); Profit2=if(OthersDecision1==1,if(Decis ion1==1,Pi11,Pi12),if(Decision1==1,Pi 21,Pi22)); Your payoff is (New Item) Variable:- Profit2 Layout:- 1 Continue (New Button)

Parameter Table Program: Program for subject a (a= odd number of subject) Type=Person1; Pi11=400; Pi22=200; Pi12=0; Pi21=300; Program for subject a (a= even number of subject) Type=Person2; Pi11=200; Pi22=400; Pi12=300; Pi21=0;

Sequential History Game (3 trial Periods) Background (Subjects=6, Groups=3) Globals Subjects Summary Contracts Session New Program (Globals Table): Person1=1; Person2=2; //PiBC //Payoff of a player if he plays B while the other plays C Pi11=0; Pi12=0;

Pi21=0; Pi22=0; Endowment=100; Type=0; Endowment Display Stage (New stage) Your endowment is (New Item) Variable:- Endowment Layout:- 1 Ok, I understand (New button) Person1 Decision Stage (New stage) Participate=if(Type==Person1,1,0); You Have Rs.100 As Your Endowment (New Item) With This You Can Buy Either Ticket 1 or Ticket 2.

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To Buy Ticket 1, Enter 1 To Buy Ticket 2, Enter 2 Your Decision is----Variable:- Decision Layout:- 1 Input Max:-2, Min:-1 Done (New Button) Person1 Decision display stage(New stage) Participate=if(Type==Peson2,1,0); Decision1=find(same(Group) & Type==Person1,Decision); Person1’s choice is to buy ticket:--(New item) Variable- Decision1 Layout-1 Proceed (New button) Person2 decision stage(New stage) Participate=if(Type==Person2,1,0); You Have Rs.100 As Your Endowment (New Item) With This You Can Buy Either Ticket 1 or Ticket 2. To Buy Ticket 1, Enter 1 To Buy Ticket 2, Enter 2 Your Decision is----Variable:- OthersDecision Layout:- 1 Input Max:-2, Min:-1 Done (New Button) Profit Display 1 Stage (New Stage) New Program (Subjects Table): Participate=if(Type==Person1,1,0); OthersDecision1=find(same(Group) & Type==Person2,OthersDecision); Profit1=if(Decision1==1,if(OthersDecis ion1==1,Pi11,Pi12),if(OthersDecision1 ==1,Pi21,Pi22)); Your payoff is ---- (New Item) Variable:- Profit1 Layout:- 1 Continue(New button) Profit display 2 stage (New stage) Participate=if(Type==Person2,1,0); Decision1=find(same(Group) & Type==Person1,Decision); Profit2=if(OthersDecision1==1,if(Decis ion1==1,Pi11,Pi12),if(Decision1==1,Pi 21,Pi22)); Your payoff is (New Item) Variable:- Profit2

Layout:- 1 Continue (New Button) History Show stage (New stage) Period (New item) Variable- Period Layout-1 Person1’s choice (New item) Variable- Decision1 Layout- 1 Person2’s choice(New item) Variable- OthersDecision1 Layout- 1

Parameter Table Program: Program for subject a (a= odd number of subject) Type=Person1; Pi11=400; Pi22=200; Pi12=0; Pi21=300; Program for subject a (a= even number of subject) Type=Person2; Pi11=200; Pi22=400; Pi12=300; Pi21=0;

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Appendix: D Acknowledgement & References Prof. Gautam Gupta, Dept. of Economics, Jadavpur University, Kolkata Prof. Santanu Mitra, Jnan Chandra Ghosh Polytechnic, Kolkata Sanmitra Ghosh, Jadavpur University, Kolkata Arijit Chakraborty & Arpita Barua, Jadavpur University, Kolkata All participants & Dept. of Economics, Jadavpur University, Kolkata

Gupta. Gautam & Mitra. Santanu: The Logic of Community Participation: Experimental Evidence from West Bengal, Economic and Political Weekly, May 16, 2009 Vol. XLIV No 20 Urs. Fischbacher: Zurich

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