Consensus protocols in multiplayer video games
Section IX of the following paper proposes a variant of your idea:

OpenConflict: preventing real time map hacks in online games.  Elie Bursztein, Mike Hamburg, Jocelyn Lagarenne, and Dan Boneh.  IEEE Security &amp; Privacy 2011.

The difference is that they propose that detection can be done by the central server, after the fact, by analyzing all of a client's status messages for consistency.  Your scheme differs only by having other clients do the same analysis.  (Their proposal also has some extra hashing and signatures and cryptography, which can probably be ignored for your purposes.)

Their scheme is basically a more sophisticated version of what you propose: rather than requiring everything to be broadcast, it only has to be uploaded to the server at the end of the game.  This has two advantages: (a) it significantly reduces network traffic, because they upload to the server rather than broadcasting to everyone; (b) by using commitments and hashes, they don't have to broadcast the full status messages to all other players on-the-fly; instead, it's enough to batch up all of those messages and upload them at the end (all that they need to broadcast at each step is just a commitment/signed hash, which will be much smaller and thus much more efficient to broadcast).  I wouldn't be surprised if they were already familiar with your proposal, but considered it too trivial and too inefficient, and so wrote only about a more sophisticated version that is less obvious and more efficient.

I recommend you take a look at the following book:

Exploiting Online Games: Cheating Massively Distributed Systems.  Greg Hoglund and Gary McGraw.  Addison-Wesley.