Modeling Britain's New Government

Who says formal theory has no relevance to real life? Apparently Liberal Democrats have been using game theory to model potential negotiations over the formation of a government for at least several months. After the election, but before Cameron and Clegg came to terms, Tony Price tried to model those negotiations:

Game theory says you need to understand your "outside options": what the alternative to a deal with this group is. How well you do depends on how good you can make all the outside options. Here's a go at the decision tree Clegg faces. ...

The logic of my version is:

- A deal with Labour now is unlikely to deliver PR, which is what would make it worthwhile from LD's point of view
- A deal with Tories will not deliver PR
- A Tory minority government risks giving Tories a majority in 9 months and missing the historic moment
- Clegg will be very tempted to do a deal with the Tories with inbuilt failure so that LD's can return to a PR negotiation with other parties in 9 months
- Present that deal as stesman-like: "The economic crisis demands it, and I will not make the country suffer for PR ... but once the economy is on the mend, I will insist on my PR reward"

Price came up with the game tree below.



Not bad, as it has turned out.

UPDATE: Apparently the embed of the game tree isn't working perfectly. It is here.

(ht: @TimHarford)