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Wednesday 16 Aug 2017 | 23:33 | SYDNEY
Wednesday 16 Aug 2017 | 23:33 | SYDNEY

Reader riposte: Brady Bunch game theory



16 June 2011 07:56

Jeremy Bray responds to Sam Roggeveen:

I'm afraid I have to take issue with your post gaming out Peter Brady's best strategy for dealing with the 'broken vase' situation.

One of the very few things that I remember from my third-year game-theory classes is that, after switching from a single-round game to a repeated game, participants have to begin taking into account the enduring effects of their behaviour on other participants. This changes the expected payoffs significantly and in most cases will discourage 'cheating' on other participants.

Unless Peter applies a very heavy discount rate to whatever happens from the next day onwards, that 'Brady sibling ostracisation' mentioned in passing by 'modehero' will weigh sufficiently heavily on his thinking to incline him towards confessing. As will the knowledge that his siblings, seeing him about to 'get away with it', will have a strong incentive to blow the whistle on the whole charade.

Of course, you could say that, given that very little or none of the experience of each episode of a sitcom carries over to the next one, Peter actually is in a one-time game, and might be better off taking the risk by staying mum. But then if we broaden our perspective we see that television programming is a repeated game, with networks seeking to retain viewers in the 'family viewing' timeslot by presenting stories that gel with the worldviews of the audience, and facing the punishment of being ignored if (when?) they lose credibility. I suspect that millions of parents wouldn't appreciate their children seeing another child appear to be rewarded for psychopathic behaviour, and network executives wouldn't appreciate the consequences of this for the programme's ratings.

Thus, Peter Brady was destined to confess: on so many levels, it was the only rational thing for him to do.

I'll let you get back to important work on foreign policy now  :-)

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