Even I think open games are hard to understand, and I invented them.
(Perhaps this is just me though. Grothendieck wrote “The very idea of scheme is of infantile simplicity — so simple, so humble, that no one before me thought of stooping so low.” [Grothendieck, Récoltes et Samailles, translated by Colin McLarty] So simple, in fact, that it took me years before I understood the definition of a scheme.)
Here I will give the best starting-out intuition I can give for open games, based on a few years of giving research talks consisting of three-quarters introduction. I’ll make no attempt to explain how they work — for that, section 2 of my thesis is still the best thing.
Continue reading “A first look at open games”
As might be expected, the rules of the game are an important concept in game theory. But the way that game theory treats its all-important rules is very un-subtle: it is firmly built into the epistemic foundations that the rules are common knowledge, which makes it extremely difficult to talk about breaking the rules. If any player breaks the rules, or even if any player suspects another player of breaking the rules (up to any level of epistemic reasoning), you are simply outside the scope of your model. Of course the possibility of breaking any individual rule, and the consequences for doing so, can be manually built into your game, but then it is unclear whether it can reasonably be called a ‘rule’ any more.
Continue reading “Breaking the rules”
I have a small article in Inspired Research, the biannual magazine of the cs.ox department. Read it on page 16 here.
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.
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.
Continue reading “A generalisation of Nash’s theorem with higher-order functionals”
This is the first in a series about social aspects of blockchains. I began writing an article that launched straight into an application, but it was too confusing without first laying some general groundwork on ‘blockchains with institutions’, the subject of this article. As a teaser, the article I had begun was discussing a design for a democracy that is significantly harder to overthrow than existing designs, by making democratic institutions inseparable from a nation’s currency.
I strongly feel that the surprising discovery of Turing-complete blockchain computation by Vitalik Buterin in 2013 is a huge and completely unforeseen game-changer in social philosophy, and that there is far too little awareness of its implications among philosophers, economists and other social theorists.
Continue reading “Blockchains with institutions”
This post is copied (with some small modifications and additional comments) from section 0.4 of my Ph.D. thesis, Towards compositional game theory. It is loosely based on a talk I gave at Logic for Social Behaviour 2016 in Zürich.
The term compositionality is commonplace in computer science, but is not well-known in other subjects. Compositionality is the principle that a system should be designed by composing together smaller subsystems, and reasoning about the system should be done recursively on its structure. When I thought more deeply, however, I realised that there is more to this principle than first meets the eye, and even a computer scientist may not be aware of its nuances.
Continue reading “On compositionality”