Chapter 14: Increasing Revenue with Advanced Pricing Strategies

Chapter 12: Game Theory: Fun Only if You Win

In the previous example, if the B & O and Pennsylvania railroads cooperate, they each earn $15 million annual profit. If the B & O Railroad has an infinite time horizon, the present value of $15 million annual profit at a 5 percent interest rate is

or $315 million.

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Playing Well

How you play the game determines whether you win or lose, so you want to play the game well. Playing any game well requires you to consider how your rival responds to your decisions. But as the next section on preempting rivals illustrates, you can also change your rival’s behavior if you play well.

Preempting rivals

You’ve developed a highly-regarded bike shop in the local community. A larger neighboring community has a bike shop owned by a rival. Your rival’s bike shop is larger and you fear that the rival may be considering entering your market. You need a strategy that enables you to preempt your rival. This is an obvious game theory situation where you must take into account your rival’s actions.

Assume the possible scenarios are represented by the decision trees in Figure 12-6 with the payoff being annual profit. The upper panel describes the current situation. If your rival expands, you can either expand or not expand. Using backward induction, your rival takes the following steps:

1. If your rival doesn’t expand, the status quo continues.

The status quo is represented by the lower branch on the decision tree. If your rival doesn’t expand, you won’t do anything — there are no branches for your decision — and the profits are $100,000 for your rival and $80,000 for you.

2. If your rival expands, you don’t expand.

If your rival expands, you don’t expand because if you expand your profits are $20,000 versus if you don’t expand, your profits are $25,000.