Thursday, February 01, 2007

Game Theory and Group Discussions: The (possible) case for cooperation in GDs

Hi Folks,I think it is possible (just for academic interest) to model what one should do in a GD so as to maximize chances of getting selected. By building a model, listing rules and assumptions, and specifying variables, one can use game theory to predict probable out comes.Now this is just a germ of an idea, and I request forum members to help build this model.You can suggest different variables, factors etc which can be used to play the game.

Basics: Game theory - Wikipedia, the free encyclopedia

Game Theory and Group Discussions:To get into several MBA institutes in India, a candidate has to go through a charade called a group discussion (GD). It will involve a discussion on an arbitrary topic by a group of competing candidates (8-15) for a limited number of seats, in a limited amount of time.

The objective of the game is for each candidate to score points, sometimes as the expense of other candidates, so as to maximise their own points.There are several such competing groups all over India, and the top ranking individuals most amongst them get to be on the merit list.

Almost everyone wants to be on the merit list (not ALL want to be).All players in all groups start with zero points.

Possible Rules:
1. You get marks if you are heard speaking by the moderator.
2. You get marks if the point heard above has relevant content.
3. You get negative marks if the content is irrelevant.
4. #2 & #3 are linearly multiplied for (say) 5 second stretches.
5. If you are able to hold attention for 30 seconds, you get bonus marks. (for both relevant and irrelevant)
6. If there is a fish-market situation (40% or more of group speaks simultaneously), then the whole group is penalised if order is not restored within 5 seconds.
6.5 If order is restored, then order-restorers get marks.
7. If you are overtly aggressive/offensive (shouting) you get negative marks. You might have to risk aggression to be heard by the speaker.
8. If you do not speak, you get negative marks.
9. If you start the discussion, you get marks.
10. If you start it badly (content and structure), you get negative marks.
11. Positive Marks if you start it well.
12. The chances of a fish-market increase with the increase in number of participants.
13. The chances of a fish-market increase if the topic given is NOT knowledge dependent (i.e. abstract, case-study)
14. A player gets + marks for cutting another speaker successfully, no harm if unsuccessful.
15. If a player can prevent another from cutting him in the middle of the discussion, he gains + points.
16. If 2 or more talkers talk simultaneously, then the one who dominates at the end of 5 seconds gets + marks, but if they are still speaking simultaneously at the end of 10 seconds, both get penalised - marks.
17. If one gives points that help structure the GD, you get bonus + points. You get additional + points if group actually follows the structure you gave.
18. You get + marks for giving time-related summations of the GD.
19. You get + points if you sum up the topic at the end.
20. Every one in the group gets + marks if the GD has a good impression on moderators, - otherwise.

Please suggest other such rules. The quantum of the marks/points can be weighed in later.

A major complication that is necessary for the game is to define the participants (i.e. aggressive/passive/knowledgeable/dumb etc). The personalities can always decide what the best course for a GD should be, or is likely to be.

One can bring in externalities as Oversmart candidates, who are just at GD to have fun, and don't care to maximise their own points, and malicious candidates, who are there to ruin the GD for others.

Thoughts/suggestions please

1 comment:

Maverick said...

Nice post.

Like the very well-known Prisoners' Dilemma problem, elaborating on which would lengthen the post, the situation in a GD can probably be classified into various aspects, all, or most of which need to be analysed.

1. Listening vs Speaking
2. Leading vs Agreeing
3. Cooperating vs Stealing the Show

The above cases certainly aren't rocket science.

Lets see what the assumptions would have to be like:

1. All participants are aware of the this "arrangement", and are aware of what "needs to be done". If, however there are only a few of them who are aware of the plan, the y can form a cartel, and the GD may be likened to an oligopolistic market, where these members can derive substantial, above-market gains.

2. The judges are not aware that a plan is in place. Otherwise, as can be guessed easily, the whole group can be penalised. There can be a whistle-blower, who, in exchange for protection, might secretively divulge the "inside" information, and spill the beans over the whole plan.

3. The participants would abide by the plan, come what may. Now this needs really smart people to be pulled off. The participants would not wilt under any sort of "pressure" or fear of being rejected if they do not act in their own interest outside the plan.

What are the likelihoods of each of the above assumptions holding true?

1. It is extremely likely that the members of the group would be aware of who the fellow participants are going to be. Hence, if a person has this idea in mind, it can be divulged to the others. However, it would take a long shot to convince all members that the plan is for the common good of all. This can lead to some "smarties" forming a cartel, and deciding to give each other a "fair" chance to speak, and listen while the other member of this cartel is speaking. If this goes unnoticed, it can lead to these people deriving above-normal gains.

2. The whistle-blower..Ahhh...This fear would always remain in the minds of the people, and shall be a major determinant of the payoffs of this game. All eyes would be roving around at all members, each trying to judge who can be a potential whistleblower. And if the judges know of this, and the members are unawares of this cross-arrangement, can spell doom for that group, maybe even including that person. This very fear of collective doom, however, can restrict all the persons from acting as whistleblowers. Hence, everyone would probably partner in the crime, so to say, and hope for the best payoff.

3. Due to fear of point 2 above occurring, and also due to the easily-predictable psychology of a participant in this whole affair, it is very likely that all members may not abide by it. This needs some more explanation.

As this is a multi-party game, payoffs are difficult to construct. However an humble attempt is in order:

1. The whole group wins - This situation would be known to the whole group, from discussion fora like Pagalguy, that if the group performs extremely well, and behaves well, there would be a synergy effect and the whole group would sail through without anyone risking elimination, ceteris paribus, i.e. all other things constant.

2. The whole group loses - This case might arise when the GD is not/perceived to be not going too well a person, or persons, and the subject here decides to break off from the plan. As the plan would be at the back of everyone's mind, each person would be keeping an eye out for such an evetuality, where a person is seeing to be violating the terms of the plan, and is perceived to be in a position to take unfair advantage at the cost of the others. This case can also arise if there are too many dumbasses in the group, who are there in the GD just for the heck of it, and wont bother if someone else too stands to lose due to their behaviour.

3. Individual payoffs can be tricky here, as group behaviour has been assumed. However, as the discussion nears its stipulated time, chances of defection would increase, as the time available for all members to react to a dazzling move by someone would be very small. In this case, a person can derive above-normal gains, much to the chagrin of the other conspirators.


Now, which of the above case is most likely. IMHO, it is extremely hard for any of the above cases to, if they occur, be attributable to the plan. Thats because it is unlikely for the plan to materialise itself. Since this is a short-term game, unlike an oligopoly a person can actually derive above-normal gains, and get off with it. There is no long-term as in the case of firms in an oligopoly. And most of us know that each person is there to sail through, irrespective of whether someone else goes through or not. This shall also be aggravated by the pressure of clearing this round, and finally landing up a seat in the B school. Hence, each person shall tend to cheat, and act according to his/her own strategy, which now, would take the shape most contrary to the plan, as the plan now appears to be a recipe for disaster. The very fear that someone might defect would be enough for everyone to not abide by the plan.

I know this has been a long post, but I still feel a lot needs to be added to it, to cover all cases in their entirety.