The TwoPersonGame.xlsx Model

Two Player Non-constant Sum Game

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Two firms, Blue and Gold, must each choose an advertising policy.

Each firm's profit depends not only upon its own advertising choice, but also the other firm's choice.

Each firm's profit is increased by its own advertising, but decreased by advertising by the other.

The net effects are shown by two matrices, one for Blue, and one for Gold.

Notice that if both firms do "No ads", they will each have a profit of 4.

But is that a stable equilibrium? Will either be tempted to change its choice?

This model finds a stable equilibrium, where neither is motivated to unilaterally change its choice.

Each firm has a decision variable, Weight(i) for each possible choice.

= 0 means never take this action. = 1 means always take this action.

Mixed strategies are allowed, i.e., 0 < Weight(i) < 1.

Keywords:

Complementarity Constraints | Game Theory | Two person game | Bi-matrix game | Mixed strategy | Non-constant sum game |