Strategic games#
Gambit has full support for constructing and manipulating arbitrary N-player strategic (also known as normal form) games.
For extensive games, Gambit automatically computes the corresponding reduced strategic game. To view the reduced strategic game corresponding to an extensive game, select or click the strategic game table icon on the toolbar.
The strategic games computed by Gambit as the reduced strategic game of an extensive game cannot be modified directly. Instead, edit the original extensive game; Gambit automatically recomputes the strategic game after any changes to the extensive game.
Strategic games may also be input directly. To create a new strategic game, select , or click the new strategic game icon on the toolbar.
Navigating a strategic game#
Gambit displays a strategic game in table form. All players are assigned to be either row players or column players, and the payoffs for each entry in the strategic game table correspond to the payoffs corresponding to the situation in which all the row players play the strategy specified on that row for them, and all the column players play the strategy specified on that column for them.
For games with two players, this presentation is by default configured to be similar to the standard presenation of strategic games as tables, in which one player is assigned to be the “row” player and the other the “column” player. However, Gambit permits a more flexible assignment, in which multiple players can be assigned to the rows and multiple players to the columns. This is of particular use for games with more than two players. In print, a three-player strategic game is usually presented as a collection of tables, with one player choosing the row, the second the column, and the third the table. Gambit presents such games by hierarchially listing the strategies of one or more players on both rows and columns.
The hierarchical presentation of the table is similar to that of a contingency table in a spreadsheet application. Here, Alice, shown in red, has her strategies listed on the rows of the table, and Bob, shown in blue, has his strategies listed on the columns of the table.
The assignment of players to row and column roles is fully customizable. To change the assignment of a player, drag the person icon appearing to the left of the player’s name on the player toolbar to either of the areas in the payoff table displaying the strategy labels.
For example, dragging the player icon from the left of Bob’s name in the list of players and dropping it on the right side of Alice’s strategy label column changes the display of the game as in Here, the strategies are shown in a hierarchical format, enumerating the outcomes of the game first by Alice’s (red) strategy choice, then by Bob’s (blue) strategy choice.
Alternatively, the game can be displayed by listing the outcomes with Bob’s strategy choice first, then Alice’s. Drag Bob’s player icon and drop it on the left side of Alice’s strategy choices, and the game display changes to organize the outcomes first by Bob’s action, then by Alice’s.
The same dragging operation can be used to assign players to the columns. Assigning multiple players to the columns gives the same hierarchical presentation of those players’ strategies. Dropping a player above another player’s strategy labels assigns him to a higher level of the column player hierarchy; dropping a player below another player’s strategy labels assigns him to a lower level of the column player hierarchy.
As the assignment of players in the row and column hierarchies changes, the ordering of the payoffs in each cell of the table also changes. In all cases, the color-coding of the entries identifies the player to whom each payoff corresponds. The ordering convention is chosen so that for a two player game in which one player is a row player and the other a column player, the row player’s payoff is shown first, followed by the column player, which is the most common convention in print.
Adding players and strategies#
To add an additional player to the game, use the menu item , or the corresponding toolbar icon . The newly created player has one strategy, by default labeled with the number 1.
Gambit supports arbitrary numbers of strategies for each player. To add a new strategy for a player, click the new strategy icon located to the left of that player’s name.
To edit the names of strategies, click on any cell in the strategic game table where the strategy label appears, and edit the label using the edit control.
Editing payoffs#
Payoffs for each player are specified individually for each contingency, or collection of strategies, in the game. To edit any payoff in the table, click that cell in the table and edit the payoff. Pressing the Escape key (Esc) cancels any editing of the payoff and restores the previous value.
To speed entry of many payoffs, as is typical when creating a new game, accepting a payoff entry via the Tab key automatically moves the edit control to the next cell to the right. If the payoff is the last payoff listed in a row of the table, the edit control wraps around to the first payoff in the next row; if the payoff is in the last row, the edit control wraps around to the first payoff in the first row. So a strategic game payoff table can be quickly entered by clicking on the first payoff in the upper-left cell of the table, inputting the payoff for the first (row) player, pressing the Tab key, inputting the payoff for the second (column) player, pressing the Tab key, and so forth, until all the payoff entries in the table have been filled.