In case you missed it, Alvin Roth, recent co-winner of the 2012 Nobel Prize in Economics, was interviewed this Wednesday past on BFM:
What's the relevance here? One of the problems with designing public policies is that most of the outcomes in the areas of interest that are being targeted aren't within functioning markets where prices provide signals and coordinate the allocation of resources. While economic theory can and does provide some guidance, just trying to reproduce a functioning market within milieus that don't support them has, shall we say, met with mixed results.
That's where game theory comes in - it's a way to look at the responses of participants to particular situations and stimuli. Or as Mankiw would probably put it, people respond to incentives. Game theory is thus a way to model and look at non-price incentives, although that's probably too narrow a definition (I'm looking at it purely in policy terms).
In policy design, what I think is that policies for non-market based environments (for example reducing government red tape or getting teachers more involved with their students where there is little to no monetary incentive), should have game theoretic foundations. Too often I think, policies are based on the gut feeling of the policy makers involved, or whichever consultant or management fad happens to be the flavour of the day (*cough* Blue Ocean Strategy *cough*).
I'm not knocking the good intentions of the people involved, or their expertise, but I think game theory has a lot to offer if we're only willing to leverage on its capabilities.