Games as Game Theory Systems - Ch 19

Game theory: mathematical study of decision making, how people make decisions in specific circumstances
Game theory is important for game designers because,
1- it analyzes situation that resembles games
2- focuses on relationships between decisions and outcomes

Decision trees: a branching tree-style diagram that outlines all of the possible moves a player can make in a game
what games can be decision trees?
-time takes place in turns or in other discrete units
-players make a finite number of moves
-game is infinite
-decision trees are different for two, three or four players
-a decision tree is a diagram of the formal space of possibilities of a game

Game theory games: consists of

- rational players who     : they know everything about a game situation, they play to win

- simultaneously reveal a : both rational players simultaneously choose their strategies

- strategy     : comprehensive,

- to arrive at an outcome

- that can be defined in a strict measure of utility: a mathematical measure of player satisfaction

- played with two players

payoff matrix: matrix created by mapping decision tree into a grid, one axis represents one player’s decision, cells represent outcomes of the decision
-payoff = utility

Two important concepts of game theory:
1- zero sum games: the utilities of  two players for each game outcome are inverse of each other; for every gain of player one, the other player loses

2- saddle point: property of payoff matrix; each player is trying to maximize his own gains while minimizing the gains of other player. Minimax theorem in mathematics.

-very important for game design, once one finds it, there is no reason to play

-degenerates strategy (exploits), ensures victory every time