Create a two-player game:

Create a three-player game where each choice has a probability:

Create a three-player game where each player only has one action, meaning each of their actions is part of the same information set:

Consider a tree game:

Consider the array of all payoffs:

To determine if a tree game is zero sum, verify that the total payoff is always 0:

TreeGame objects include properties that give information about the game:

The "Properties" property gives a list of the properties available:

The "Object" property gives the object type of the game:

The "Summary" property gives a brief summary of information about the game:

The "NumberOfPlayers" property gives the number of players in the game:

The "NumberOfActions" property gives the number of actions in the game:

"MinMaxPayoffs" gives the lists of minimum and maximum payoffs for each player:

The "Tree" property gives a Tree representation of the game:

The "Plot" property plots the tree game in the same fashion as the default TreeGamePlot:

The "MatrixGame" property converts any TreeGame into a MatrixGame:

Create a two-player game where both players only have one information set each:

Plot the game:

Create a two-player game where one player is not time aware:

Plot the game:

Specify the color function used for the graph and tree of the tree game:

This changes the appearance of the tree:

Specify the color function used for the graph and tree of the tree game:

This changes the appearance of the tree:

It also changes the appearance of the graph:

A prize is concealed behind one of three curtains, and game show host Monty Hall asks you to guess where the prize is. After you guess, Monty opens one of the curtains that does not conceal a prize, leaving closed only your original choice and one other curtain. You are given the option of staying with your original choice or switching to the other closed curtain.

Generate the Monty Hall problem:

Plot the game:

The Escalation game is defined as follows. Two nations are in conflict. One nation has the choice to initiate or not initiate, and another nation has the choice to either acquiesce or escalate. Note a third player, "Nature", is often used to portray the randomness of the payoffs. This game is also called the Nuclear game, in reference to the atomic threats during the Cold War.

Generate the Escalation game:

Consider the tree:

The Revolution game is defined as follows. A colony has the choice to either rebel of concede to the status quo. The country can either grant independence or suppress the rebellion. If the colony concedes to the status quo, the country can either tax or not tax the colony. This game is usually studied in cases where the payoffs for the suppressed rebellion are unknown.

Generate the Revolution game:

Consider the tree:

The Naval Deployment game is an extension of the Battle of Bismarck game to an army that flees and another that is pursuing.

Generate the Naval Deployment game:

Show the graph:

Consider the Centipede game:

Generate a Centipede game with "double-or-nothing" increasing payoffs:

Show the graph:

The Beer-Quiche game is a signaling game defined as follows. Player B is considering dueling player A. B does not know whether A is a wimp or surly. B prefers a duel if A is a wimp. Player A wants to avoid a duel. First, B observes whether A chooses to have beer or quiche for breakfast. Both players know that wimps prefer quiche while surly people prefer beer. Note a third player, "Nature", is often used to portray the randomness of the type of A. Moreover, Player A is often called the "sender" of the signal, and player B is the "receiver".

Generate a Beer-Quiche game:

Show the graph:

Consider a two-by-two game of tic-tac-toe where two adjacent X's or O's are required to win (for example, in

, X wins, but is a tie):

Consider the array of all payoffs:

To determine if a tree game is zero sum, verify that the total payoff is always 0:

Consider the tree of all named openings from chess tournaments above 2200 ELO, 2005–2015:

Note the payoffs denote the proportion of games won in these tournaments for each player.

For example, the payoff for a given opening implies over all games with that opening, on average, White has won of them, Black has won of them, and there was a draw in of them.

Plot the tree game:

The Entry game is well known in economics and motivates the avoidance of monopolies. A potential entrant chooses whether to enter a market controlled by a monopolist. If the entrant enters, the monopolist can either begin a price war or share the market.

Create the corresponding game:

Show the tree:

This is equivalent to the Entry game:

Compute the sub-game perfect equilibrium:

Consider a small firm and a large firm choosing between a high price and a low price for the same product.

Create the corresponding game:

Show the tree:

Compute the sub-game perfect equilibria:

The legend of Li Guang and his 100 horsemen is a signaling game where a general is either strong or weak, and the hero, Li Guang, has to either retreat or prepare.

Generate the game:

Plot the battle: