Prisoner's Dilemma: A Hockey Player's Perspective on Visors

As a Canadian, no blog would be complete without a mention of our favorite national pass-time--the great sport of hockey!  I was watching a game recently where a player sustained a bad injury close to his eye as he was hit with top end of a hockey stick.  Luckily, the stick was an inch away from creating a debilitating eye injury.  This did bring a question to my mind though on why all hockey players don't have visors on their helmet?  According to Wikipedia, only 60% of NHL players have visors.  I did a little bit of digging and found that there are a number of reasons why a player would not want to wear a visor, among them the issue of visibility stood out.  Hockey players not only complain that visors reduce their peripheral vision, but that the visors also attact ice debris and water specs (during hard stops) that create distractions. 

This issue can be structured as a Prisoner's Dilemma.  Let's say we have 2 hockey players: Brule and Fisher.  These individuals play center for the Oiler's and Senator's respectively.  Both players value scoring goals over safety and believe that they perform better without a visor on.  For each the payoffs are as follows:

• 4 - Opponent wears visor and I don't: In this case I have an advantage since I will have better visibility
• 3 - We both wear visors: In this case we both have an equal handicap and we gain the safety provided by a visor
• 2 - Neither of us wears a visor: In this case neither of us has a handicap, but we are more likely to get injured
• 1 - I wear a visor but my opponent does not: In this case I am at a disadvantage to my competitor

Laying this out in a game table we have:

The dominant strategy for both Brule is to select No Visor.  This is also the dominant strategy for Fisher.  As a result both players end up at "No Visor".  If the players can both agree to wear a visor, they can increase their payouts from 2,2 to 3,3.  Of course, this is a rather unlikely scenario.  A more realistic way for the players to get a higher payout is if the NHL placed a mandate requiring all hockey players to wear a visor (with the exception of goalies who wear cages!)

For more information on visors and associated statistics, please see:
http://en.wikipedia.org/Hockey_helmet