Saturday, 9 March 2013

Free drink anyone

I was in a restaurant the other day, waiting for someone, and could not but help overhear a conversation between a restaurant manager and an elderly lady organizing a dinner party. They were discussing the arrangements for the party, and had just got onto the topic of drinks.
   The manager reminded her that drinks were not included in the package. 'Would she like to prepay for some wine and put it on the table?'
   She said 'no because not everyone drinks wine'.
   'OK, so, would she like to pre-book some wine under the proviso that it only has to be paid for if it gets drunk?'
   Displaying the characteristics of a true game theorist she replied 'well if you tell them they can drink it they are clearly going to drink it aren't they! No, I'm not doing that'.
  The next gambit of the manager was 'you could start a tab at the bar under the proviso that the tab will be split amongst all the guests at the end of the party'.
  To my horror she thought this was not such a bad idea. But, thankfully, she said she would have to think about it.
  How can a game theorist make sense of this exchange? The objective of the manager is to make profit - and that means selling as many drinks as possible. The dinner guests will drink according to the price of a drink. Suppose the 'face value' price of a drink is £2. If the drinks are 'free' - because they have been pre-booked and paid for - then the guests will drink the most. If the drinks have to be bought individually at £2 each they will drink the least. The interesting case is where the tab will be shared. Suppose there are 20 guests. Then the effective price of a drink is £2/20 = 10 pence. Which is as good as 'free'. So, from the manager's perspective splitting the tab is as good as the drinks being pre-booked.  The guests are going to drink a lot more than if they had to pay for it individually.
   From the guests perspective the tab is the worst outcome. They still have to pay for drinks but the incentive structure means they will drink a lot. Specifically, each drink costs every guest 10 pence each. So, if a guest has another drink that costs him 10 pence, but also costs the other guests £1.90. There is a negative externality. Indeed, the drinks tab is a common resource which will be over-exploited by the guests. The guests would be better off if they had to pay for their drinks individually. For example, suppose that at a cost of £2 each guest would have 3 drinks and at a price of 10 pence have 6 drinks. The total cost per guest is £6 if drinks are paid for individually and £12 if drinks are on the tab.
   From the perspective of the elderly lady organizing the party, there are mixed incentives. Clearly, if she doesn't pay for drinks then she's better off. Her main concern will thus likely be how much the guests enjoy the evening. While it may seem good that the guests drink and enjoy themselves, this is a misconception. The tab will almost certainly be antagonistic because of the negative externality problem it creates.    

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