I have read in a few places that $\mathbf{PH}$ can be interpreted in terms of the complexity of determining the winner in two-player games. I would like to know a) the original reference for this result and/or b) a concise explanation of it that requires little to no background in complexity theory (e.g., less than [Goldreich's book](http://books.google.com/books?id=EuguvA-w5OEC)).



Where does the game-theoretic characterization of PH come from?
The answer to part (a) of your question is this reference:



> 
> A. Meyer and L. Stockmeyer. The equivalence problem for regular expressions with squaring requires exponential space. In *Proceedings of the 13th IEEE Symposium on Switching and Automata Theory*, pages 125-129, 1972. [[pdf]](http://people.csail.mit.edu/meyer/rsq.pdf)
> 
> 
> 


What an amazing paper this was! Two later papers that discuss refinements of the result include these:



> 
> C. Wrathall. Complete sets and the polynomial-time hierarchy. *Theoretical Computer Science* 3:23-33, 1977.
> 
> 
> A. Chandra, D. Kozen, and L. Stockmeyer. Alternation. *Journal of the ACM* 28(1):114-133, 1981.
> 
> 
> 


