You are the founder and CEO of a new chain of health clubs called Paleo Gyms and Prehistoric Fitness Clubs. The concept behind this new fitness craze is to only perform exercises that our ancient ancestors might have done: moving boulders, climbing trees, throwing sticks, etc.—all while wearing heavy animal pelts.

Your business is growing rapidly, and you have identified San Diego as the next city where you should consider opening a Paleo Gym and Prehistoric Fitness Club. To launch a new gym, however, you will need to spend $700k on the cost of the facility plus equipment (designer rocks, artisanal logs, and such).

You will also need to spend some money on promoting the new center both in the month preceding the launch (pre‐launch spend) and in the month when it opens (opening spend). For each of these time periods, you can set your advertising spend at a lower rate of $250k for the month, or at a higher rate of $550k. Your advertising spend does not need to be consistent across months; you may set your pre-launch spend at the lower rate and then increase to the higher rate for the opening spend, or vice versa.

Unfortunately, you have a rival in this emerging market: the Chiseled from Stone Age Luxury Spas and Training Centers. Once Chiseled from Stone sees your pre‐launch advertising for a new Paleo Gym in San Diego, you suspect that there is a good chance they will follow suit by opening one of their clubs in that market as well. You estimate that if your pre‐launch spend is low ($250k), then there is a 60% chance that Chiseled from Stone will enter the San Diego market as well. If, however, your pre‐launch spend is high, you believe that Chiseled from Stone might be somewhat wary of going up against your strong advertising campaign and, therefore, the likelihood of them opening a new center in San Diego will only be 40%. If your rival doesn’t enter the market, you won’t need any opening spend advertising at all. If they do enter, you will then need to decide to run a high or low opening spend campaign.

If Chiseled from Stone does open a center in San Diego, they will also face a choice about whether to support their new gym with either an aggressive (high $) or non‐aggressive (low $) advertising campaign. Looking back at their past gym openings, you figure there is a 50% chance that Chiseled from Stone will support their new gym with an aggressive ad campaign, no matter what your own advertising looks like. Unfortunately, you won’t know what type of advertising campaign your rival will run until after you have had to decide on the level of your own opening spend.

Naturally, you want to maximize your company’s profits but, in terms of revenue expectations for your new gym, there are a number of possible scenarios that may occur, depending on whether your rival also enters the market, and upon both of your firms’ advertising in the month when your gym opens.

The revenue projections (not counting your costs to launch and advertise) for your gym are as follows:

$2.5m if you enter the San Diego market but your rival does not

$2m if your opening spend is high and your rival engages in a non‐aggressive advertising campaign

$1.5m if your opening spend is high and your rival engages in an aggressive advertising campaign

$1.5m if your opening spend is low and your rival engages in a non‐aggressive advertising campaign

$1m if your opening spend is low and your rival engages in an aggressive advertising campaign

$0 if you choose not to launch a new gym in San Diego

What is your expected profitability (revenues minus costs) for opening a new Paleo Gym and Prehistoric Fitness Club in San Diego assuming that you follow the best, profit‐maximizing course of action?