I feel that having Compositional game theory accepted for publication marks the end of the first chapter for me, and marks open games as a proper research topic. I want to record how open games came to be, told through the story of this paper, which took almost 3 years from writing to acceptance. (That’s roughly the same amount of time as the Higher Order Decisions/Games duo, although they definitely felt longer. Their story can wait for another blog post.)
Towards compositional game theory
- PhD thesis, Queen Mary University of London
- Links: My preferred version, Official version
I wrote this not just as a thesis, but (against all advice) as a resource for other people to learn about open games. In spite of some problems, it will probably remain my preferred reference on open games for years to come. It contains plenty of its own introduction, so I won’t introduce it again here.
Compositional game theory reading list
The best starting point, for a reader who knows a little about both game theory and category theory, is the paper Compositional game theory.
Additional background and motivation is provided by the blog post A first look at open games and the preprint Compositionality and string diagrams for game theory.
By far the most complete exposition is my PhD thesis Towards compositional game theory. It is fully self-contained for readers who know category theory but not game theory.
If you don’t have background in category theory, my current recommendation is Seven sketches in compositionality by Brendan Fong and David Spivak.
Patch for ‘Coherence for lenses and open games’
- Coherence for lenses and open games, arXiv v2
I have been working on referee reports from version 1 (which was rejected for good reasons). I have uploaded an intermediate state of corrections, for the benefit of the reviewers of my extended abstract for STRING’17. This put me in the awkward position of uploading a paper that I know probably still contains some errors, although it’s less wrong than the previous version.
A generalisation of Nash’s theorem with higher-order functionals
- In Proceedings of the Royal Society A, 2013
- Links: published article, arXiv
This is my first paper, written in the first few months of my Ph.D. and published quickly. Four and a half years later it is still technically my best paper by the usual (wrong) metrics. Obviously now I wouldn’t dare to do something as outrageous as submitting a paper to such a highly-ranked journal.
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