I like this framing, especially as it gracefully handles the way that communication isn’t like Guess Who—you have priors that don’t look like “uniform over the following N possibilities”, your payoffs for actually finding the answer might be nonconstant depend on what the answer is, some resource limitation might make the maxi-p(win) strategy different from the optional discriminator—but once you start thinking about how you’d win a game with those rules, strategies for smarter search suggest themselves.
I like this framing, especially as it gracefully handles the way that communication isn’t like Guess Who—you have priors that don’t look like “uniform over the following N possibilities”, your payoffs for actually finding the answer might be nonconstant depend on what the answer is, some resource limitation might make the maxi-p(win) strategy different from the optional discriminator—but once you start thinking about how you’d win a game with those rules, strategies for smarter search suggest themselves.