Game theory can be applied to the science of managerial economics. For instance, how does a business person win the simultaneous-move, one-shot business game. In these games, players make decisions at the same time or, at the very least, they don’t know their rival’s decision prior to making their own. In addition, the game is played only once.
Assume that two players, you and me, are trying to determine whether or not to increase our sales by expanding our business to a second location in a neighboring town. The illustration shows the payoff options associated with our possible decision combinations.
My decisions are represented on the left side of the table. The top row represents my choice to expand, and the bottom row is my choice to not expand. Your decisions appear across the top of the payoff table — the left column represents your choice to expand and the right column is your choice to not expand.
Each cell in the payoff table presents the results of the actions you and I take. In this example, I assume the payoffs are the business’s monthly profit.
Thus, if I decide to expand and you decide to expand, the resulting payoffs are contained in the upper-left cell of the payoff table. The cell indicates that my monthly profit is $2,400 and your monthly profit is $3,500. If, instead, I decide to not expand while you decide to expand, my profit is $1,400, while your profit is $5,000.
A dominant action is an action whose payoff is always highest, regardless of the action chosen by your opponent. Your dominant action is to expand. To understand why, note the following:
If I decide to expand, you read across the top row, and your possible payoffs are $3,500 if you also expand or $3,000 if you don’t expand. You should expand because it leads to a better payoff.
If I decide to not expand, you read across the bottom row, and your possible payoffs are $5,000 if you expand or $2,500 if you don’t expand. Again, you should expand.
No matter what I choose, you always get a better payoff — higher profit — if you expand. To expand is a dominant action for you because its payoff is always better than not expanding.
A similar situation exists for me:
If you decide to expand, I read down the left column, and my possible payoffs are $2,400 if I also expand or $1,400 if I don’t expand. I should expand because it leads to a better payoff.
If you decide to not expand, I read down the right column, and my possible payoffs are $4,000 if I expand or $2,000 if I don’t expand. Again, I should expand.
To expand is a dominant action for me because no matter what you choose, I get a better payoff — higher profit — by deciding to expand instead of not expanding.
You should never choose an action that is dominated.
So, how does our game turn out? Because the dominant action for both of us is to expand, we both choose that action. I receive $2,400 in monthly profit, and you receive $3,500 in monthly profit. Our combined profit is $5,900.
Interestingly, this payoff is not the best combined payoff for us. If I expand and you don’t expand, our combined payoff would be $7,000 — $4,000 for me and $3,000 for you. This higher combined payoff provides an incentive for us to merge.