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PDQ Paper Battle

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My brother posed a problem to me:
Create a strategy/tactics battle game with only a handful of memorizable rules, such that all one needs to play are a writing utensil and empty paper 8.5X11 or less. [Not a BG proper, but it would be easily transferable to such.]

IOW, I want a game of strategy with the simplicity of, but less abstraction than, chess.

I have more or less abandoned the complication of simulated "wargaming" and 'game theory' like "Lanchester's Squares Law of Attrition" and other more complicated algorithms.

What I expect the result to be is an amalgam of Paper-Rock-Scissors, Tic-Tac-Toe, and the "Prisoner's Dilemma" somehow played out with 'units' in turns.

I was hoping that you could help me with my research:

*If you know any novel tidbits, or shortcuts, involving Game Theory, plz URL [Little things, like the Prisoner's Dilemma. No graduate theses plz, as Game Theory is an entire branch of mathematics]

*Background mathematics behind: Risk, Warhammer/tabletop, RPG game battle system

*Rules of thumb when it comes to sizing up sides of a battle, attrition, etc

No need to be Google for me, but if you have come across any of those had to find gems in your web travels, plz URL me

Thanks in Advance, MB

PDQ Paper Battle

The obligatory is an excellent resource.

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