Is Santa a Mixed Strategy?

Why tell your kids the Santa myth? Perhaps Santa Claus is a way for a parent to pursue a mixed strategy. The critical characteristics of Santa Claus - that he's always watching and will only give you gifts if you are good - are the same as the typical parents.

The parents strategies in a child-rearing game are a mix of carrots and sticks. So too are "Santa's strategies". And the parent plays both roles. Why is that so?

The difference is in the sticks. Parents' stick strategies usually involve punishment, but not new toy starvation (of course, that could be more of a general proposition invoked by rote on every trip to the store). But parents' strategies do include the carrot of mass gift giving (e.g., birthdays, Valentine's day, Easter, road trips) without the stick of  new toy starvation.

My guess is that Santa Claus is a way for parents to mix strategies. Disciplining kids often makes the parent feel bad. Having them toe the line to a mythological Santa Claus for 10% of the year may just increase the utility of the parents. And this goes a long way towards explaining why the Santa Claus myth holds more sway over parents than the Christian justification for Christmas, or even over the holidays of other faiths.

This discussion was motivated by the post "Santa Claus and Capitalism" at The Calico Cat.