Complete and Incomplete Information
How much does the player know about the game they're playing?
A game (or economic situation) of complete information, according to Wikipedia must have the quality that
the utility functions (including risk aversion), payoffs, strategies and "types" of players are thus common knowledge.
To simplify: Every player, at all times, is aware of all the accessible pertinent information they need to play the game optimally.
Chess is often cited as the canonical complete information game. All pieces are always visible to both players at all times, and the rules of the game are also always known to both players at all times. It is also clear what the objective of each player is, put the opponent’s king in checkmate.
Just by looking at the board state, the only differentiating factor between players (in theory) should be skill and experience with chess.
The only information that isn’t available to each player is what the other player is thinking and what their next move is going to be.
In contrast, let’s talk about games of incomplete information. This quote from Game Theory, Alive by Anna R. Karlin and Yuval Peres explains:
Sometimes a player does not know exactly what game he is playing, e.g., how many players there are, which moves are available to the players, and what the payoffs at terminal nodes are.
This is a stuffy academic way of saying that the player does not have direct access to all useful information about the game state.
For example, in a game of poker, each player doesn’t know which cards his opponents received, and therefore doesn’t know the payoffs
Which makes sense right? You can’t see your opponents’ hands (or the order of the deck), so you aren’t aware of the true value of anyone’s hands. You have to use other information you have access to such as revealed cards, chip balances and players’ bets.
Games of incomplete information carry with them a requirement to operate under risk and uncertainty. Even an optimally tuned AI would need to gamble to some extent.
Why does this matter? The biggest things to consider are:
Information Load: In chess, it is possible to “think many moves ahead” as the only unknown factor is what your opponent will do next. This can overwhelm some players with information but can also test players’ ability to filter through that information.
Luck: If there is incomplete information, players are often required to play the odds and gamble well. However, the revelation of extreme good or bad luck can make victories and defeats seem arbitrary and random, but it can also make for some spectacular probabilistic drama. Ever heard of D&D?
Pacing: Because new information is revealed to the player over the course of a game like poker, the players are drip-fed new information over time which changes their strategy. In chess, the player can only ever truly be surprised by an unexpected blunder or novel strategy. Or a cheating scandal!
Think about the PvP games you enjoy, do you like complete information? Or do you like some things to be hidden from you?