By Roop Kunwar Singh
So you think economics is meant only for the policy makers of the world? That equilibrium, payoffs, utility- all this technical jargon hardly matter in your day to day life? Well think again because every day, innumerable times, we tend to use a wide range of concepts of economics in our mundane life without even realizing it. One such concept is the Game Theory.
The Game theory is one of the four branches of the Economic Theory. It is defined as the study of mathematical models of conflict and cooperation between intelligent rational decision-makers (as put down by Roger B. Mayerson). As brought out in the definition, the game theory at its most elementary level deals with the behavior of subjects when in a decision making situation assuming the subjects to be rational human beings.
A game here refers to a formal mock-up of an interactive situation. It involves four main elements- Players of the game, Information available to each player, Actions available to each player and Pay off for each outcome. A Game classified into co-operative or non-cooperative game. A Co-operative game is one in which players have the liberty to interact with each other and take consensual decisions, whereas in case of a non-cooperative game, this facility is not available to the players. They are to take independent (but interdependent) actions and this situation is referred to as ‘Strategic Interdependence’. It is identification of the most balanced action in such situation where the game theory comes in.
Let us take the most widely used illustration of a non-cooperative game- The Prisoner’s dilemma. Let us suppose that two men have been caught trespassing a store and are suspected of having committed a robbery. As if now, the police only have enough evidence to charge them for trespassing and to indict any more, they will have to draw out a confession from them. So they put them in two different cells and ask them if they committed the robbery.
Now, both the criminals have two actions to choose from- either to confess or not to confess, without having any knowledge of the each other’s course. Let us further suppose that the sentence for committing robbery is 12 months in jail whereas that of trespassing is just 2 months. If both of them confess to the crime, then their sentence will be reduced to 8 months whereas if only one of them confesses, then he will be set free without any punishment while the other will have to serve the full sentence. So, the payoffs for their interdependent actions can be represented as follows:
Now, given this situation, let us see how an intelligent and rational human being will decide whether to confess or not confess. Consider Player 1. If we assume that player 2 is going to confess, then it leaves player 1 with two alternatives- either a sentence of 8 months or that of 12 months. Thus, he should confess. Similarly, if we assume that player 2 is not going to confess, again it would be better for player 1 to confess as it would free him from any sentence rather than going to jail for 2 months. Thus, in this situation, Confessing is a strictly dominating action. It is Likewise for player 2.
Thus, the most stable and safe options for both of them is to confess i.e. the payoffs in the top left box. Now a student of economics would point out that our preferences are monotonic (more utility-more satisfaction) and the payoffs in the bottom right box are visibly superior to that of our result. Well, this is what is referred to as ‘The Fallacy of Composition’ i.e. something that is true for all the constituents of the group but not true for the group as a whole. Although, both of them not confessing is the best option for them but since they are unaware of each other’s actions, it is a prudent and more rational path to confess.
This was the most basic illustration of the application of game theory. Here, we had only two alternatives for each player and also a strictly dominating action. But what if the number of players and actions is increased or if there is no strictly dominating action? If you are curious, refer to this engaging and illuminating compilation by William Spaniel – http://gametheory101.com/The_Basics.html
The Game Theory has found its footings outside economics as well. In subjects like psychology and even biology, it is being used extensively. But more than anywhere, it is our everyday life where the game theory has found its application. And most importantly, if we dig deeper, it somehow addresses the biggest dilemma of humans-Trust. Whether we trust our counterpart or not? Take the above illustration. It is clear that the best payoff for both of them would be if they both don’t confess. But can the first prisoner trust the other over here and vice-versa? Well, this is one question I believe even economics will find difficult to answer.
