Wisdom Tree

Game Theory

By Kritika Anuragi & Vandana Miglani

In our day-to-day lives, we come across several situations in which we are subjected to a conflict of interests; we then use the analysis of everyone’s perception before playing our cards so as to achieve the most favourable outcomes. This is the very basic concept of a subject called Game Theory. Wikipedia defines game theory as “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.” It gives us a mathematical taxonomy of social life and predicts what people are most likely to do and believe others will do in cases where everyone’s actions affect everyone else’s and the outcome is based on the actions of all the involved stakeholders. Game theory has applications in mathematics, applied sciences, economics, and even biology. The outcomes of a wide spectrum of real-life events such as wars, elections, the stock market, poker, salary negotiations and even relationships can be predicted by the use of game theory. Predicting the answers of an MCQ test is the simplest application of game theory.

Princeton’s John Nash received a Nobel prize in economics for his work on Game Theory. Game theory is flawless and fails only in cases where the user fails to apply it efficiently. In the current scenario where game theory is becoming a global phenomenon and has multidimensional applications, it becomes increasingly meaningful to learn game theory. The most common example used to introduce game theory to beginners is the Prisoner’s dilemma. However, the Lover’s dilemma is more relatable and makes it easier to understand the heavy terminology in a simplified manner.

Our rational mind forces us to think that ‘romantic bliss’ is the most favourable outcome for both the parties. But, according to John Nash, the dominant strategy (i.e. one that leads to minimal loss – no matter what the other person does) is to stay silent (lest one person confesses their love and gets rejected), and is most likely to be chosen by both the stakeholders; even though the “best possible outcome” is actually for both parties to take the plunge and say how they feel. Hence, game theory doesn’t necessarily yield the ‘best’ possible outcome, just the most logical one, and its success is chiefly dependent on the proficiency of the user.

In order to clearly understand the concepts of this subject, let’s delve further into its depths. Put forward by Nash, ‘Nash Equilibrium’ is a popularly used concept in Game Theory. Every game consists of the following 3 components – a set of players, actions/choices available to them and their payoffs or outcomes. A pure strategy, Nash Equilibria is a set of actions such that none of the players can obtain a higher payoff if they choose to deviate unilaterally from their profile. To understand this further let us consider the matrix illustrated. In this game, there are 2 actions available to each player – A or B, having the following conditions – a) If both choose A, they each get 2. b) If both choose B, they each get 1. c) If they choose different actions, they both get 0. Also, in this game, player 1 chooses a row and player 2 chooses a column and the cells indicate the payoffs for the moves undertaken by them. Now, cell (B, B) is a Nash Equilibrium as any unilateral deviation (either in a row i.e. horizontally or column i.e. vertically) would result in a lower payoff for the deviating player. Similarly (A, A) is also a Nash Equilibrium. In some cases, the equilibria may correspond to outcomes which may be inefficient or unfeasible (as there are in some cases, outcomes which are more preferred by players) and hence, the concept was further extended to Bayes-Nash Equilibrium.

Game theory is indeed a fascinating subject and aside from its obvious uses in the field of economics and political science, it is also used in predicting the outcomes of a social interaction in the social sciences. If this brief description captured your interest then we would suggest you to follow up on this article and learn from online channels – ‘Game Theory Online’ and ‘The Game Theorists’ to master the art of analysing the intellectual prowess of competitors to ace in every walk of life.