Perfect Information:

A player is said to have perfect information in a game if his information each contains a single element.The game is perfect if each player has perfect information in the game.
Today I will discuss about another two interesting game.One of the game is 2-2 Nim and onother one is very popular card game.Both the games are two person games.

2-2 Nim:

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In this game you need four match-sticks.Then set out them in two piles,each with two sticks.Player-I and player two will take alternative turns.Each turn of the game,each player will select a pile with at least one stick and remove at least one stick from the pile.Player can choose more sticks but only from the same pile.The game will be ended when both the piles will be emptied.And the player removing the last stick will lose the game and he will pay $1 unit to his opponent.

Game Tree:

The game tree of this game is presented below:

From the game tree we conclude that player-I has three strategies and player-II has six strategies.Ther are,
I-1:Take 1 stick from (II,II) and 1 stick from (II,-).
I-2:Take 1 stick from (II,II) and 2 sticks from (II,-).
I-3:Take 2 sticks from (II,+I).
II-1:Take 2 sticks from (II,-) and take 1 stick from the smaller pile of (II,I).
II-2: Take 2 sticks from (II,-) and take 1 stick from the larger pile of (II,I).
II-3: Take 2 sticks from (II,-) and take 2 sticks from the larger pile of (II,I).
II-4: Take 1 stick from (II,-) and take 1 stick from the smaller pile of (II,I).
II-5: Take 1 stick from (II,-) and take 1 stick from the smaller pile of (II,I).
II-6: Take 1 stick from (II,-) and take 1 stick from the smaller pile of (II,I).
We observe that each information set construct with a single element and so the game is one of the perfect information.we also observe from the game tree that player-II can always win the game.

Payoff Matrix:

The payoff matrix of this game is:

Two Person Gamebling Card Game:

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For playing this game you need three cards.They are King,Ten and Deuce(Two).Player-I will choose one card from three cards and places it for face down on the table.Now player-II will call “High” or “Low”.If he is right(King=High,Deuce=Low) he will win $3 from player-I.But if the card is Ten that means he is wrong then he has to pay $2 to the player-I.If he called “Low” and the card is “Ten” then he will win $2 from player-I.Again if the card is “Ten” he called “High”,then it is player-I’s turn to choose between “King” and “Deuce”.Then he will lays his card for face down on the table.Player-II then calls “High” or “Low”,and he wins $1 if he is right.If he is wrong then he will loses and $3 to player-I.

Game Tree:

To construct the game tree,we will use the following observation;
K=”King”,D=”Deuce”,T=”Ten”,Hi=”High”,Lo=”Low”

We observe from the above game tree that player-I has four pure strategies and player-II has three pure strategies.They are:
I-1:Choose “K”.
I-2:Choose “T” and if again Choose “K”.
I-3:Choose “T” and if again Choose “D”.
I-4:Choose “D”.
II-1:Call “Hi” and if againg call “Hi”.
II-2: Call “Hi” and if againg call “Lo”.
II-3:Call “Lo”.

Payoff Matrix:

The payoff matrix of this game is:

Thanks for reading my article.this game is one of my favourite one.After reading my post I hope you will understand the game.If yo have any question you can comment and resteem my post.
Best Regards @linco