Game Theory

 

Game Theory is the task of modeling the strategic interactions between parties also known as players who are rational and make interdependent decisions. Due to the interdependence,  the players are forced to make the optimal choices by calculating the other player’s best choices and strategies to make one of their own.

 

Before starting, let’s make ourselves familiar with certain keywords commonly used in the game theory:-

 

  1. Game
    In this context, a game is basically any set of circumstances that has a result based on the player’s decision.

  2. Player
    A strategic decision maker who is dependant on its counterparts to decide which selection to make to determine the outcome of the game.

  3. Strategy
    Strategy is a complete set of steps that a player will follow given the format of the game.

  4. Payoff
    A quantifiable payout that a player receives after achieving an outcome.

  5. Information Set
    When the information provided in the game has a sequential component to it, it is termed as information set.

  6. Equilibrium
    It is a point in the game where the players have made their decision and an outcome has been reached

 

Assumptions

 

  1. As in any concept of economics, there is the assumption of rationality, i.e., the players will make the best possible decisions for the maximization of their payoff

  2. While the game is being studied, it is assumed that the payouts listed in the various scenarios include the sum of all the payoffs related to that outcome so that there are no what-if situations in the future.

  3. Even though the number of players in each game and the number of scenarios in each game could be infinite, for the sake of simplicity, we will be taking the case of two players with two available choices each.

 

Solving a game with an example


 

Example


 

 

In the given scenario we can see that there are two players and each player has a choice to either chose the strategy A or the strategy B. The payoffs are given in the order of first player 1 followed by player 2. Now to solve the game we will use the reverse approach in which we’ll see what will be the last decision by player two, then the second last decision by player one, and so on

 

In this case, we can see that in the case player one chooses strategy A then player two gets two options, 1 to either choose A and 2 to choose B. Since the decision made by the player is going to be perfect bounded by rationality, choosing the strategy A would give him an advantage over choosing B making his payoff to be 3 instead of two.

 

Just like this, in the case if player 1 chooses strategy B, player 2 will choose the strategy A as the payoff in this case would be 2 instead of 1 in strategy B.

 

This leaves player 1 with two choices, if the player takes the strategy A, they know that player 2 will choose strategy A giving a payoff of 1. On the other hand, if the player 1 chooses the strategy B, player two will choose strategy A giving the player 1 a payoff of 4. Hence the player 1 will choose strategy B which will cause player 2 to choose strategy A giving a total outcome of (4, 2).