Lovers' Dilemma - Part 1
Being
an engineer is a unique gift, a power that lets you relate everything that
happens around you with what you learnt. When I want to cut a piece of paper in
circular shape, I think how accurately I can linearize my cuts so that final
product looks like a circle. When the wires of my headphones get entangled, I
think there must be some algorithm to untangle them in minimum time. A simple
game of cards which used to be mindless fun has now turned into an exercise of
calculating probabilities. Apart from this ‘going-to-the-root’ thing, it
fascinates me to see how this technical knowledge presents interesting
analogies that fit in everyday life. The Lovers’ dilemma is product of one such
attempt at applying concepts from game theory to non-technical problems in
life.
Game theory cannot be explained better without discussing Prisoners’ Dilemma (I do not intend to compare lovers and prisoners, however interesting it may sound) which is the easiest example for understanding the basic ideas of game theory.
Suppose two goons Ranga and Billa are caught at a crime site. They are going to be interrogated separately and depending on their performance they’ll be given a punishment. The scenario is modelled as a game below.
Denying and confessing the crime are the two strategies or actions that Ranga and Billa can make. The four possible outcomes of their actions decide the number of years they’ll have to spend behind bars. As a punishment is not desired by them, payoffs are negative, that is, lesser the punishment, more is the payoff. Ranga and Billa are, as Game theory calls them, rational players. The term ‘rational’ means both want to take an action that’ll increase their individual payoff (get minimum years in jail). They have no attachment to each other. One does not think of good or bad of the other. He only wants to get outcome that is optimum for him.
If one of them confesses, the one who is honest enough to confess gets free and the other one gets 4 years in jail because of confirmed evidence. If both of them deny committing the crime, they get a minimal punishment of 1 year each in jail. If both of them confess, the judge considers their honesty and serves them to a sentence of 2 years each. What will happen?
Let’s slide into Ranga’s shoes and see. Ranga thinks, “If Billa denies, I am better off by confessing because I’ll be free. What if Billa confesses? Again, I should confess because 2 years in jail is always better than serving 4 years in jail. Well then, I guess whatever Billa may do, confessing is the only action that’s going to do good to me. Done, I’m gonna confess.”
Billa also considers Ranga’s probable actions and decides that confessing is the best way. So on the fateful day, in their separate interrogations, both confess and both get 2 years in jail. This outcome is called Nash Equilibrium, a state from which no player has an incentive to deviate from. As outsiders, we can see that this verdict is not an optimum one. Both of them could have denied the crime and been off with 1 year in jail. But their rationality and lack of incentive to consider the action of denying landed them in a self-enforcing but non-optimal state.
Alas, if only Ranga and Billa had known game theory… But now that we do, why don’t we apply it to something interesting, maybe to some couples in love facing ups and downs?
Food for thought till the next post.
Game theory cannot be explained better without discussing Prisoners’ Dilemma (I do not intend to compare lovers and prisoners, however interesting it may sound) which is the easiest example for understanding the basic ideas of game theory.
Suppose two goons Ranga and Billa are caught at a crime site. They are going to be interrogated separately and depending on their performance they’ll be given a punishment. The scenario is modelled as a game below.
Denying and confessing the crime are the two strategies or actions that Ranga and Billa can make. The four possible outcomes of their actions decide the number of years they’ll have to spend behind bars. As a punishment is not desired by them, payoffs are negative, that is, lesser the punishment, more is the payoff. Ranga and Billa are, as Game theory calls them, rational players. The term ‘rational’ means both want to take an action that’ll increase their individual payoff (get minimum years in jail). They have no attachment to each other. One does not think of good or bad of the other. He only wants to get outcome that is optimum for him.
If one of them confesses, the one who is honest enough to confess gets free and the other one gets 4 years in jail because of confirmed evidence. If both of them deny committing the crime, they get a minimal punishment of 1 year each in jail. If both of them confess, the judge considers their honesty and serves them to a sentence of 2 years each. What will happen?
Let’s slide into Ranga’s shoes and see. Ranga thinks, “If Billa denies, I am better off by confessing because I’ll be free. What if Billa confesses? Again, I should confess because 2 years in jail is always better than serving 4 years in jail. Well then, I guess whatever Billa may do, confessing is the only action that’s going to do good to me. Done, I’m gonna confess.”
Billa also considers Ranga’s probable actions and decides that confessing is the best way. So on the fateful day, in their separate interrogations, both confess and both get 2 years in jail. This outcome is called Nash Equilibrium, a state from which no player has an incentive to deviate from. As outsiders, we can see that this verdict is not an optimum one. Both of them could have denied the crime and been off with 1 year in jail. But their rationality and lack of incentive to consider the action of denying landed them in a self-enforcing but non-optimal state.
Alas, if only Ranga and Billa had known game theory… But now that we do, why don’t we apply it to something interesting, maybe to some couples in love facing ups and downs?
Food for thought till the next post.
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