Strategies and Solutions#
In our textbook, Dr. Nordstrom provides the following:
- Strategy
A strategy for a player is a complete way to play the game regardless of what the other player does.
As we develop strategies for the players, we must consider what the players know at the point in the game where they make decisions. In chess, the players know the exact board state. While the opponent’s strategy may not be clear to us, we can still all the moves she has made.
In baseball or softball, the pitcher is getting signs from the dugout or the catcher. The pitcher knows what pitch will be thrown, but the batter does not. The batter must deal with the fastball or curve or slider without knowing exactly which one will be thrown.
Information#
From the Nordstrom text, we learn the definition for the information sets of games like checkers and chess.
- Perfect Information
If players have perfect information, each player knows what all of his or her own options are, what all of his or her opponent’s options are, and both players know what the outcome of each option is. Additionally, players know that both players have all of this information.
Poker is an example of a game with imperfect information. When Joanna has to make a decision to raise, call or fold, she knows her cards but not her opponent’s cards.
Solutions#
Note from above that a strategy indicates how the player will play the game in its entirity from the first decision made until the last. The reason will be clear as we consider the next definition.
- Solution
A solution for a game consists of a strategy for each player and the outcome of the game when each player plays his or her strategy.
The value of the game is the outcome of the game and must be described for both players.
- Finite
A finite game means the game must end after a finite number of moves or turns. In other words, the game cannot go on forever.