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Summary
Game theory is a branch of economics that studies rational decision making. It often looks at game-like situations, but it is not a general theory of games or game design.
A decision tree is a diagram that maps out all of the possible decisions and outcomes that a player can take in a game. A completed decision tree is equivalent to the formal space of possibility of a game. A game must have the following characteristics to be reducible to a decision tree:
Time in the game takes place in turns or other discrete units.
Players make a finite number of clear decisions that have knowable outcomes.
The game is finite (it can't go on forever).
Even if a game meets these criteria, most games are too complex to be diagrammed as a decision tree. Decision trees are most useful for mapping aspects of games, or as conceptual tools for thinking about the formal structure of a game.
A game theory game is limited to rational players who simultaneously reveal a strategy to arrive at an outcome, which can be defined in a strict measure of utility. Usually, game theory limits itself to games with only two players.
A rational player doesn't exist in the real world. A rational player is a completely logical player that plays only to maximize winnings, regardless of emotions, ethics, and social attachments.
A game theory strategy is a complete plan for playing a game. A strategy explicitly and comprehensively covers every possible situation that a player might encounter in the course of playing a game, including every possible strategy that an opponent might select.
In a game theory game, rational players make a simultaneous decision about what strategy to take. They know the complete rules of the game and the possible outcomes of their decisions, but they do not know the strategy that the other player will take.
The results of a game theory game are measured in utility, which is a numerical representation of the players' desire for a certain outcome. Attractive outcomes are assigned higher positive numbers, and less attractive outcomes are assigned lower numbers. Negative numbers represent an unpleasant utility.
A payoff matrix is a grid of cells used to diagram the possible outcomes of a game theory problem.
In a zero-sum game, the winnings of the victor are equal to the losses of the loser. Games such as Chess with a single winner and a single loser are zero-sum games.
Every two-player, zero-sum game theory game has a solution, a proper way to play the game that will maximize winnings for the player every time. When there is a single best solution to a game for both players, the solution is known as a saddle point.
Saddle points in any game can lead to degenerate strategies, also called exploits. A degenerate strategy is a way to play a game that leads to victory every time. Generally, degenerate strategies are to be avoided in games because they diminish uncertainty and meaningful play.
Some game theory solutions consist of mixed strategies, where players select among different strategies with a weighted percentage.
