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What if "Maggus" don't have a choice ?

There are two possible reasons for stopping by this post; you happened to be among those hard-working study-serious college-goer who lament not being perceived as fun by his/her peers. Or you have a soft spot for these people, striving to pay off the debt from when he single-handedly completed your group project. There could be a hundred other reasons, so let's jump into the matter.

Let's construct a scenario with simplified assumptions. Suppose there are 5 students in your project team. Each of you has decided whether you want to work or not. If you decide to work, you must put in an effort of value "e". The project will be possible if at least 3 of the students participate. A successful project rewards everyone in the team "r", which is greater in value than "e". So what do you think will happen.
Let's assume that each of you is rational (which secretly implies you will maximise your personal gain whenever possible). Will all five contribute ?? Will no one work?? Is there another situation??
  • Will all of the five work?
Let's assume they do. But each of them realised that they put in more effort than required. And this information is available to all of them. In fact, two of them can slack and still get the reward "r". This is a better scenario for them since r > r - e. So the next time they work, all five may slack.
  • When no one works.
In this case, no or works, and there is no reward. In fact, there is no incentive for anyone to start working even since he/she can't single-handedly complete the project. So wasting that effort e needs to make sense.
  • Wait, what if just 3 of them worked?
And lo, here we have three (let's call them maggus) who decided to pull off the task. The whole group gets the reward. But will the non-working members start working? Well, no. They have a reward r and have no incentive to spend that effort e because that will reduce their gain to r - e. 
Can the maggus stop working? Well, no. they have a reward r - e.  If they stop working, the project will fail, reducing their net gains to 0. This is a Nash equilibrium. A point where no player can take an action that maximises his personal gain.

In fact, this is of serious consequence to public goods, notably called the free-riders problem. But what remains extremely important to conclude from this example, is there are some maggus who know they are stuck in a group that can't let them be otherwise. Just like I can't stop writing "in fact"s.

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