Game Theory

The Game Theory is the study of the strategic interaction or behaviour of two or more participant or ‘players’ that are conscious that their actions do affect each other. Strategic Decisions are those in which a person, when deciding what actions to take, should take in to consideration the possibility of others to respond to the action.

For example, when two publishing companies in a city choose price for their magazines, knowing that their sales are determined mutually, they are players in the game with the other. They are in a game on who buy their magazines and not with the readers with the reason of, the readers ignores his or her effect on the publishing company.

A game is a situation or a state where the players or the participants’ take depends not only on their choices but also on the decisions of their rivals. This is also called Strategic Interactions where the participant’s optimal decisions depend on what the other players do in the game.

There are four elements to describe a game and these are: the players, actions, information, strategies, the rules where each player’s decision can highly effect on the other player/s, there will be outcome of every move and this can bring you to success or failure and lastly, the payoffs of each possible outcome such as: the price or the money each player collect for a specific outcome of an action.

The players are the participants or individuals that create and take actions. Each participants make a decision to maximize his or her utility. While the action or the move is created and done by the player whenever she is called to move or act upon the situation. The Information in a game is designed with the use of concepts of information set or the rules in the game. The elements of an information set are the different values that player thinks are possible. Information can be common knowledge if it is known to all players, if each participants are aware of this information, if each player knows that all the players know that everyone is aware of it. In a game of complete information, all players know the rules of the game. The strategy is a rule that tells the player what action to do for every situation or instances of the game that comes hand in hand with the information set to create in every conceivable situation.

Below are two example of games:

1.    Matching Pennies

In this game, every player has the chance to select one side of a coin and if the coin match, Participant A wins and collects the price (this may vary depending on the deal, this can be money, service or a physical thing) from Participant B. While on the other hand, if the coins don’t match, Participant B wins and gets the price from Participant A.

2.    The Boeing- Airbus Game

Boeing and Airbus have to choose between to invest in the development of a Super Jumbo for long distance travel and if both of them develop successfully the latest plane then their profits will go down by 50 million a year. And if only the other develop the Super Jumbo, it will make an addition of 80 million a year in profits while there will be a drop of 30 million a year for the other company. If no company develops the place then there will be no changes.

3.    Prisoner’s Dilemma

There are two suspects that are arrested and charge of a crime. The police officer lack sufficient evident to convict the suspects unless the suspect confess. The police hold then in separate cells and explain the corresponding consequence from the actions they could take. If neither of them confesses, then they will both be convicted of a minor offence and will be sentences to jail for a month. If both confess themselves then they will both be sentenced to jail for six months. And if one confesses then the confessor will be released immediately and the other will be sentenced to jail for nine months.

The strategic form of the game can be in the form of following the payoff matrix.