In a game theory, assume each of the players is economically rational-
- Assess outcomes
- Choose actions to get the preferred outcomes from the given actions of other players
Different situation that encourage a player to maximize his utility through the responses from other players to act perfectly is called a game.
It is possible actions that are taken by the players while playing.
If any player act on probability one, then the action in that particular situation is termed as pure strategy.
When no action is taken with probability, the actions of those situations are considered as mixed strategy.
Payoff Matrix or Reward Matrix:
It is an array of i-th and j-th entry in different situation of the game. This shows the outcome. If positive entry gets highlighted, it shows gain whereas if negative entry gets highlighted, it shows loss for the row-player.
Two sorts of games are not equivalent. In this context, matric games are considered as normal form games or strategic form games whereas extensive form games are the trees games.
It is the criterion that any player chooses to maximize the outcome of the strategy with latest payoff by minimizing opponent’s countermoves.
It is the criterion that any player chooses to overcome the strategy of the opponent with latest payoff because of maximizing opponent’s countermoves.
When a payoff matrix get its entry with maximum of row minima and minimum of column maxima, this entry is known as saddle point of the particular game. Here, this type of game is strictly determined.
Value of the Game:
Suppose a game gets its saddle point. This saddle point value is referred as the value of the particular game. If this value sets to zero, then these types of gamesare considered as fair.
In a zero-sum game, the interests of each player are diametrically opposed. This means that when one player wins, other losses. If two persons play this type of game, then it is known as two-person zero-sum game.
In this chapter, we will consider only the matrix games
Suppose in any of this game, the total payoff is divided among the players. If this divided payoff value is invariant, it means the game does not depend on the mix of different strategies. This type of game can simple is called as constant-sum game.