Pokemon Go - How much are you willing to pay to catch them all?

It didn't take long for the entrepreneurial to find opportunities to profit from Pokemon Go. The New Zealand Herald reported on Saturday that:

New ads are popping up on Craigslist nearly every day from people who say they will log on to your "Pokemon Go" account and effectively run up your score while you are stuck at work or sitting in class.

On a recent July afternoon, two 24-year-old Pokemon "trainers," Lewis Gutierrez and Jordan Clark, walked through Brooklyn's Prospect Park with their eyes glued to their phones, tapping and swiping away to catch virtual Pokemon for clients paying about $20 per hour for the service.

Of course, this is nothing new. As the article notes, there are plenty of similar offers on online forums from people willing to level up your World of Warcraft characters, or to sell you high level characters.

Would you be willing to pay $20 per hour for someone else to visit Pokestops, catch pokemon, etc. for you? A rational (or quasi-rational) decision maker weighs up the costs and benefits of their decisions. The cost here is $20 (per hour of gameplay). How large is the benefit, and does it outweigh the cost?

First, we need to recognise that there are two benefits to Pokemon Go: (1) the act of playing itself leads to some satisfaction or happiness (not to mention the benefits of physical activity from all the walking around); and (2) the sense of achievement from having a high-level trainer (which might be kudos from your friends, a type of conspicuous consumption). If you play the game yourself, you receive both benefits, but if you pay someone to play for you, you only receive the second benefit.

Now, if we think about the opportunity cost of playing Pokemon Go, we might compare that $20 with your hourly wage (since for each hour playing Pokemon Go, you forego one hour of working). So if your wage is above $20 per hour, then it is lower cost to have someone else play for you. So provided the benefit from an hour of Pokemon Go leveling-up is worth more to you than $20, it makes sense to pay someone else to do it. However, despite these tips for playing at work, or employers who might encourage you to play the game at work, most people wouldn't take time off working in order to play Pokemon Go.

For most people, the choices are: (1) play Pokemon Go and forego the other leisure activity (but receive both benefits); (2) do the other leisure activity and forego Pokemon Go; or (3) do the other leisure activity and pay someone else $20 to play Pokemon Go for you (but receive only the second benefit).

Think about the costs and benefits of the three options. For Option (1), the benefits are the 'activity benefit' of playing (call it B1) plus the 'conspicuous consumption benefit' (call it B2); the opportunity cost is the benefit of the other leisure activity foregone (call it B3). For Option (2), the benefits are B3 while the opportunity costs are B1 and B2. For Option (3), the benefits are B2 and B3 while the opportunity costs are B1 and B2 and $20.

It turns out that, regardless of whether you prefer Option (1) or Option (2), in order for Option (3) to be preferred, then the conspicuous consumption benefit (B2) must be greater than $20, and perhaps much more if playing Pokemon Go is your preferred leisure activity. [*]

So, people who pay others to play Pokemon Go for them are just valuing the conspicuous consumption benefit at more than $20. Make of that what you will.

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[*] Pointless algebra time!

The net benefit of Option (1) is B1+B2-B3.

The net benefit of Option (2) is B3-B1-B2.

The net benefit of Option (3) is B3-B1-$20.

Let's first assume that you value the other leisure activity and playing Pokemon Go yourself equally (so B1+B2 = B3). You would be indifferent between Options (1) and (2), because the costs and benefits are equal (and net benefits of both are zero). Would Option (3) be better? The net benefit of Option (3) is B3-B1-$20, which in this case simplifies to B2-$20 (since B3-B1 = B2). So, you would choose Option (3) only if your conspicuous consumption benefit (B2) is greater than the $20 per hour you are paying someone else to play for you. This is also the case if you prefer Option (2) over Option (1), since the difference in net benefits between Option (2) and Option (3) is the difference between B2 and $20.

What about if you prefer Option (1) over Option (2)? In this case, B1+B2>B3. So, B1+B2 = B3+D (where D is the difference in value between the two options).

If Option (3) is preferred over Option (1), then B3-B1-20 > B1+B2-B3. This simplifies to:
B3 - B1 - 20 > (B3 + D) - B3
B3 - B1 > 20 + D
B2 - D > 20 + D
B2 > 20 + 2D

So to prefer Option (3), the conspicuous consumption benefit has to be more than $20 (plus twice the difference in value between playing Pokemon Go yourself and the alternative activity). Note that, holding B2 and B3 constant, the higher B1 is the less likely it is that B2 will be large enough to choose to pay someone else to play Pokemon Go for you.