Managerial economics can help you figure out how much of a threat an new competitor can be. For instance, you’ve heard a rumor that if you decide to expand your business into a rival’s territory, the rival has threatened to expand into your territory. Before making your decision on whether or not to expand, you need to determine whether the threat is credible.
A credible commitment requires the commitment’s benefit to exceed its cost. In that case, the commitment is credible because the firm has an incentive to follow through. In the situation of whether or not your rival expands into your territory after you expand into its, the commitment — threat — is credible if the benefit outweighs the cost.
Your rival says it will expand only if you expand first. You’re concerned about your rival’s threat to expand, because if both firms expand, your profit is only $10,000. You need to use backward induction to test whether or not your rival’s commitment is credible.
In the decision tree, your decision appears at the far left, because you choose first. You have two possible choices — expand or don’t expand. After you decide, your rival responds. To determine whether your rival’s threat to expand is credible, you take the following steps:
Because you’re trying to decide whether to expand, focus on the upper branch of the decision tree that corresponds to expand.
If you expand, your rival can expand or not expand.
If your rival chooses to expand, his profit is $25,000. If your rival chooses not to expand, his profit is $40,000. As a result, your rival chooses not to expand for the higher profit.
Your rival’s commitment isn’t credible.
If your rival chooses to expand after you expand, its profit is $15,000 less — only $25,000 instead of $40,000 — than if it didn’t expand. Your rival is better off (makes a higher profit) by not expanding even if you choose to expand.
You should expand, recognizing that your rival’s commitment isn’t credible.
This example reinforces how fun game theory is. If you look again at the illustration, you quickly see you just had $80,000 worth of fun because the way you play the game determines whether you win or lose.