Gambit: Software Tools for Game Theory | ||
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This section gives a quick overview of the graphical interface, using a simplified game of poker to illustrate the main features and concepts.
This chapter takes a high-level tour of the Gambit graphical interface using as an example the simple one-card poker game appearing in [Mye91]. This game is included in the Gambit distribution as poker.efg, and can be found in the efg subdirectory of the directory in which Gambit is installed. (For example, in the standard installation under Microsoft Windows, this would be c:/Program Files/Gambit/efg/poker.efg.) By convention, files ending in .efg store extensive form games, and files ending in .nfg store normal form games.
When launched, Gambit displays a window similar to this: [1]
There are three equivalent ways to open a saved game from any window in Gambit:
Select the Open menu item from the File menu;
Use the shortcut key combination Ctrl-O;
Click on the file folder icon on the toolbar.
The extensive form game tree is drawn with the root node at far left, with branches going from left to right, and successive nodes to the right of their predecessors. Each node is represented as a horizontal line. Every non-terminal node is a decision node and is represented by the color of the player who makes a decision at that node. Nodes are connected by branches, which are represented by two connected line segments, which can be thought of as the "fork" and the "tine". The fork is used in the graphics display to indicate graphically the probabilities of taking each branch. The tine is used as a location at which to display textual information about the branch.
The poker game begins with Chance selecting either a Red card or a Black card to deal to Player 1. This is represented in the tree by the grey node and subsequent branches labeled "Red" and "Black". The forks of the branches have superimposed black lines stretching halfway along the fork, indicating a probability of one-half that each card is chosen. After each of the two possible draws, Player 1, whose nodes are colored in red, has the option to either "Raise" or "Fold". If Player 1 folds, the game ends; if he raises, Player2, with nodes colored in blue, then has the option to either "Meet" or "Pass" in either case, the game ends after Player 2's choice. All terminal nodes are drawn in black in this picture.
In this game, outcomes are attached to each of the six terminal nodes, and payoffs to the two players are indicated to the right of the corresponding node, with Player 1's payoff listed first, then Player 2's. Outcomes are indicated to the right of nodes, but may be attached to nonterminal nodes, in which case their payoffs are interpreted as incremental payoffs. Outcomes may also be displayed by textual name rather than by their payoff vector.
Information sets are identified by a pair of numbers. The first number indicates the number of the player who has the choice at the information set. The second number provides an identifying number for the information set which is unique among that player's information sets. Whenever possible, information sets are also represented by vertical lines connecting the nodes that are members of the same information set. In this game, Player 1 observes which card he has drawn prior to making his choice to "Raise" or "Fold" ; therefore, the node following Chance's "Red" move is in a separate information set, numbered (1,1), from the node following Chance's "Black" move, which is in information set (1,2). Player 2, on the other hand, does not observe Player 1's card, and so Player 2 has one information set, numbered (2,1), with two member nodes connected by a vertical line.
The analytical features of Gambit are located on the Tools menu.
Dominance, which interfaces to routines for identifying and eliminating dominanted actions;
Equilibrium, which provedes access to algorithms provided by Gambit to compute Nash equilibria of the game;
Qre, which organizes Gambit's facilities for computing and manipulating quantal response equilibria;
Normal form, which contains items to create normal forms corresponding to the extensive form game.
[1] | All the screenshots contained in this manual were taken on a Linux system using the Sawfish window manager. If you use a different operating system or window manager, your windows may appear slightly differently. |
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About this manual | Finding Nash equilibria using the extensive form |