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Selection functions, bar recursion and backward induction

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If you have a question about this talk, please contact Dan Ghica.

I’ll talk about my recent work with Paulo Oliva from Queen Mary reported in the paper “Selection functions, bar recursion and backward induction”. Here is the abstract of the paper: Bar recursion arises in constructive mathematics, logic, proof theory and higher-type computability theory. We explain bar recursion in terms of sequential games, and show how it can be naturally understood as a generalisation of the principle of backward induction that arises in game theory. In summary, bar recursion calculates optimal plays and optimal strategies, which, for particular games of interest, amount to equilibria. We consider finite games and continuous countably infinite games, and relate the two. The above development is followed by a conceptual explanation of how the finite version of the main form of bar recursion considered here arises from a strong monad of selections functions that can be defined in any cartesian closed category. Finite bar recursion turns out to be a well-known morphism available in any strong monad, specialised to the selection monad. Obviously I won’t have time to talk about all that (and the monad stuff was already done in previous lab lunches).

This talk is part of the Lab Lunch series.

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