Game Theory

Game Theory

In Game Theory analysis, we try to find out the optimal choice for a player (Oligopolist) given the choices by other player (competitor or rival). Such interdependent decision making is the hallmark of Oligopoly markets/competitions. We follow these steps in solving the problem.

Player is an oligopolist in game theory. Payoff is an outcome of a certain action by a player. Payoff matrix is a table showing all possible actions that can be taken by each player with their payoffs. Dominant Strategy is the optimal strategy for player regardless of what the other player does.

1) Find dominant strategy for each player separately. If each player has a dominant strategy in the game, each would select the dominant strategy and game will have dominant strategy equilibrium.

2) If only one player has a dominant strategy, then the player would assume that player with dominant strategy will adopt the dominant strategy. That is rule of the game. If dominant strategy exists for player A, player A would select dominant strategy. The other player, player B which does not have a dominant strategy, would assuming that his rival selects the dominant of his own, will select the optimal choice that exist for him, given the choice taken by player A.

Example 1: Payoff Matrix for an Advertising Game (in 000s PKR)

| | |Firm B |

| | |Advertise |Don’t Advertise |

|Firm A |Advertise |(4,3) |(5,1) |

| |Don’ Advertise |(2,5) |(3,2) |

To solve...