Competitive Decision Making - Game Theory
Overview
Competitive decision making is decision making in the presence of other agents whose decisions also affect the outcome.
The standard example of this is the situation of two players playing a game, such as chess. The mathematical theory that
studies these types of situations is game theory, although, it is meant to apply to any competitive decision making situation.
Definitions and Assumptions
- Payoff
- are the costs and rewards of the game being played. In game theory, payoffs are represented as numbers,
however, the only relevant fact of each payoff is the ordering of payoffs, not the size of each payoff, per se.
In a formal setting, the requirement boils down to having a set of well defined
preferences
over the final outcomes of the game.
- Rationality
- it is generally assumed that all players are
rational
- Information
- Perfect Information - a game where the choices and all outcomes are known ahead of time
- Incomplete Information - a game where not all information is available.
Types of Games
Strategy Types
- Pure Strategy
- a pure strategy is a fixed strategy where every choice is specified for a each turn of the game through a set of rigid rules.
That is, given a particular state of the game, the move that a pure strategy will make is completely know, or algorithmically determined
to a fixed choice.
- Mixed Strategy
- a mixed strategy is a strategy that randomizes its choices over a set of pure strategies.
Topics