For those of you that are interested, there is a formal logic that can be used to reason about such problems, called Dynamic Epistemic Logic: https://eprints.so

For those of you that are interested, there is a formal logic that can be used to reason about such problems, called Dynamic Epistemic Logic: https://eprints.soton.ac.uk/261816/1/EUMAS2.pdf https://eprints.soton.ac.uk/261816/1/EUMAS2.pdf A book chapter on the topic is available here: http://www.vub.ac.be/CLWF/SS/DELhandbookarticle.pdf http://www.vub.ac.be/CLWF/SS/DELhandbookarticle.pdf Course slides and other information can be found here: https://sites.google.com/site/thealexandrubaltagsite/teaching/dynamic-epistemic-logic-2017-2018 https://sites.google.com/site/thealexandrubaltagsite/teachin... It is a fascinating topic. Equipped with DEL, you can approach similar problems dealing with knowledge, belief, private and public announcements systematically.