The Student’s Dilemma – A Coaching Centre’s Blessing

By Somya Barpanda

What is it that makes all coaching institutes click? Be it in any nook or cranny, it is hard NOT to find a centre offering you the golden chance to make it to your dream destination for higher education; Medical, Engineering, MBA etc. No doubt these new meccas of modern teaching do (to some extent) add to the competitiveness of candidates by equipping them with strategies to crack entrance exams. However, is it the success records of their past selections, their omnipresent advertisements which draw hoards of aspirants to opt for coaching? Or is there something more subtle to a student’s decision of getting admitted in an Aakash or a FIITJEE or T.I.M.E?

Let’s attempt analysing an average student’s decision-making process that goes behind choosing between ‘coaching’ and ‘no coaching’ (or self-study). We assume there are 2 students, of equal ability/calibre, who are to appear for a highly competitive entrance exam which offers just 1 seat.

The costs of getting enrolled for coaching are the fees and the time lost in travelling and during the lectures; time which could have been used in self-study. Both face equal costs. What matters to both is their ‘selection’ for the prized seat. So, we assign the chances of getting selected- ‘maybe selected’, ‘not selected’ and ‘selected’ as their payoffs i.e. their benefits/utilities. Each has an order of preference: ‘selected’> ‘maybe selected’> ‘not selected’- both prefer getting the seat over anything else. Also, let’s say that going for coaching yields a ‘relative advantage’ ONLY i.e.:

• If student-1 gets coached, and student-2 doesn’t, then the former gets selected and vice versa.
• But if both go for coaching, then none gets any edge over the other and they have equal chances of making it through and the payoff for both is ‘may be selected’
• If both don’t go for coaching and study on their own, then again the payoff for both is ‘may be selected’

Each student has two choices- ‘coaching’ or ‘no coaching’ and none knows what choice his respective competitor might make. Now, let’s formalise their decision boxes (the game matrix):

Here, the upper left box represents that when student-1 chooses ‘coaching’ and student-2 also chooses ‘coaching’, then both have equal chances of getting selected and the payoffs for both are ‘may be selected’. Other boxes follow the same pattern of interpretation.

What will both decide? The outcome will be the case when both choose ‘coaching’ (the upper left box). This is the Nash equilibrium – a point from which none will want to deviate. Here’s how we arrive at this conclusion:

(Note: Check vertically to keep track of student 1’s choices and horizontally for student-2)

• The lower right box is not an equilibrium/outcome. Here, given student-2 chooses ‘no coaching’; student-1 will want to change his decision to ‘coaching’ which corresponds to a higher payoff of sure ‘selection’ (see only Column 2 and focus on student 1’s pay offs only). Similarly, given student 1 chooses ‘no coaching’; student-2 too will want to deviate to ‘coaching’ as that yields him ‘selected’.
• In lower left box, again student-1 will wish to change his decision to ‘coaching’ as ‘may be selected’ is a better outcome for him than ‘not selected’ but student-2 won’t want to change his decision
• In upper right box, student-1 won’t want to change his decision, but student-2 would like to change his decision to ‘coaching’ which gives a better payoff of ‘may be selected’ against him ‘not getting selected’
• In upper left box, none will wish to change his position. Given student 2 chooses ‘coaching’, student 1 will want to choose ‘coaching’ and get the better payoff of ‘may be selected’ over ‘not selected’. We can argue similarly for student 2.

So, both decide to join the coaching institute as each is under the fear that his competitor might join it in case he himself chooses not to join thus making him lose out on his chances to get the single seat. Notice that both will be better off if both choose not to join (bottom right box) as they’ll save on the fee and self-study time lost in travelling and during the boring lectures and still get the same pay off of ‘may be selected’ which they’re getting now also albeit at a higher cost. If they could collude i.e. arrive at a deal of them not going for coaching no matter what, then both will gain. But there’ll always be a risk of the other party’s breach of contract. Plus, here we took only 2 students for simplicity; when the entire national population of aspirants chooses between ‘coaching’ and ‘no coaching’, it’s almost impossible to collude and make everyone comply with a no-coaching policy. This model’s similar to the famous ‘Prisoner’s Dilemma’ model where cooperation on part of everyone could leave every one better off. But as said before, cooperation on the scale of the whole nation’s set of aspirants is far-fetched. So, the students’ dilemma is a blessing for the coaching institutes rendering their B-Plan a sure-shot money spinner.