1. Introduction
Game theory is used for decision-making process under some conflicting situations where there are two or more competitors (players) involved.
Game theory provides solution of games, assuming that each of the players wants to maximize their gains and minimize their losses.
Basic terms
player : Each competitor or participant (may be individual or organization) is called a player.
Two-person game : If the number of players is two, then it is called two-person game
n-person games : If the number of players is n, then it is called n-person game.
Zero-sum game : If the sum of gains of player-1 and losses of player-2 is equal, so the sum of gains and losses equals to zero, then it is known as zero-sum game.
Non-zero sum game : If the sum of gains and losses is not equal to zero, then it is either negative or positive, then it is called non-zero sum game.
Strategy : A player selects an action from list of of all predetermined actions druing the game is called strategy
There are mostly two types of strategies
Pure strategy : If the players play the same strategy for each move during the game, then it is called pure strategy game.
Mixed strategy : If a player play different strategy with some particular probability distribution for each move during the game, then it is called mixed strategy game.
Payoff : The outcome of the game is called payoff.
Payoff Matrix : Table or matrix that shows the outcomes or payoffs in terms of gains or losses of different strategies.
Maximin principle : For player A, Select the minimum element from each row and write them in Row Minimum column.
Now Select the maximum element from Row Minimum column and enclose it in rectangle [ ]. It is called Row MaxiMin.
Minimax principle : For player B, Select the maximum element from each column and write them in Column Maximum row.
Now Select the minimum element from Column Maximum row and enclose it in circle ( ). It is called Column MiniMax.
Optimal strategy : The course of action which maximizes the profit of a player or minimizes his loss is called an optimal strategy.
Value of the Game : It refers to the expected outcome of the game, when players follow their optimal strategy. It is generally denoted by V.
Assumptions of Game Theory
- There are finite number of competitors (players)
- Each player tries to maximize his gains and minimize his losses
- Each player has finite number of possible courses of action
- The choices of action are assumed to be made simultaneously, so that no player knows his competitors move until decided
- The outcome of game is predetermined and fixed
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
|
