(If you haven’t read Part II of my Game Theory essays, you may be missing out.)
Ok, lets look at some Known and Unknown Games.
Rock-Paper-Scissors (henceforth RPS) is a known game. Ultimate judge of your opponent’s psycology, or trivial exercise in picking the best random move? It’s the latter, and sadly, this is the case for many games that can be reduced to RPS.
(If you don’t Know RPS, Suppose: if your opponent picks randomly, you have a 1/3 chance of tying, 1/3 of winning, and 1/3 of losing. All of your choices are equivalent. Congradulations, you now Know RPS.)
Consider the situation of Truncated Paper-Rock-Scissors (henceforth RPS-). In RPS-, there are two players, player A, and player B. Player A is prohibited from using rock. Player B is aware of this limitation.
Who is more likely to win? How more likely? What strategies might A employ? What about B? (Note: ‘Choose randomly’ is an acceptable strategy, however because R, P, and S now have actual functional differences, it drifts back towards an exercise in psychology.)
If a series of games are played, where A must win one game to win the series and B must win two, who is more likely to win, assuming A and B both choose from their rational choices*? (*hint: this is different than choosing randomly.) Assume that neither player wants the game to go on forever.
Eventually, extensive analysis of RPS- will turn it into an empty game. I just came up with it last night though, and I (believe that I) Know RPS-, yet I still find it interesting. So there might be salvation for equilibria*-less games. Gamist design depends on it.
(*A big word economists like to use, and subject of a future essay.)