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>Gambit: Software Tools for Game Theory</TH
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><A
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>&#60;&#60;&#60; Previous</A
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><DIV
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><H1
><A
NAME="GUI.REF"
>Graphical Interface Reference</A
></H1
><P
>This chapter covers the graphical interface in some detail.</P
><DIV
CLASS="SECT1"
><H1
CLASS="SECT1"
><A
NAME="GUI.CONV"
>Conventions used in the graphical interface</A
></H1
><P
>This section discusses features of the graphical interface which
are common between the extensive and normal forms.  For features which
are specific to the extensive form, see <A
HREF="gui.efg.html"
>the section called <I
>Extensive form games</I
></A
>, and for
features which are specific to the normal form, see <A
HREF="gui.nfg.html"
>the section called <I
>Normal form games</I
></A
>.  </P
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="GUI.CONV.STRUCTURE"
>Structure of game windows</A
></H2
><P
>Extensive and normal form windows in the graphical interface share a
common structure:
<P
></P
><UL
><LI
><P
>A game window, which displays the game tree of the extensive form
or the payoff table of the normal form;</P
></LI
><LI
><P
>A profile table, displayed when the <B
CLASS="GUIMENUITEM"
>Profiles</B
>
menu item is checked on the <B
CLASS="GUIMENU"
>View</B
> menu, which organizes
all strategy profiles currently in memory;</P
></LI
><LI
><P
>A navigation window, which displays information about the currently
selected object in the game, and can be used to navigate through the
game display;</P
></LI
><LI
><P
>An outcomes window, which lists all the outcomes currently defined in
the game, and their associated payoffs to all players;</P
></LI
><LI
><P
>A supports window, which organizes all the supports which have been
computed by dominance elimination or defined by the user</P
></LI
></UL
>
The last three windows are organized into a notebook, which is displayed
whenever any of the <B
CLASS="GUIMENUITEM"
>Navigation</B
>,
<B
CLASS="GUIMENUITEM"
>Outcomes</B
>, or <B
CLASS="GUIMENUITEM"
>Supports</B
>
menu items are checked on the <B
CLASS="GUIMENU"
>View</B
> menu.</P
><P
>Details about the game window will be left for the subsequent separate
sections addressing extensive and normal forms; the rest of this section
will look at each of the auxiliary windows in turn.</P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="GUI.CONV.PROFILES"
>Working with strategy profiles</A
></H2
><P
>The profile table organizes all mixed or behavior strategy profiles,
as appropriate, that have been computed by algorithms or entered by
the user.  Display of the profile table is togged by the checkable
menu item <B
CLASS="GUIMENUITEM"
>Profiles</B
> on the <B
CLASS="GUIMENU"
>View</B
>
menu.  The profile table is also automatically displayed when an
algorithm returns solutions.  A draggable sash along the top of the
profile table permits resizing of the profiles window to taste.</P
><P
>Each row in the table corresponds to one strategy profile.
When a profile is selected, its row is highlighted; the selected profile
is used by the game window to display strategy or action probabilities,
values, or other information.  Information about the current profile 
also appears in the <TT
CLASS="GUILABEL"
><B
>Navigate</B
></TT
> window.
Selecting a profile is done by left-clicking on the row corresponding to
the profile.</P
><P
>A variety of data dependent on the generating algorithm are available
for most mixed or behavior profiles. Not every category is relevant
for every profile.  If a certain data member is either not relevant or
not available, it will be displayed as <TT
CLASS="GUILABEL"
><B
>----</B
></TT
>.</P
><P
>Clicking with the right mouse button within the profile table 
accesses a popup menu with the following items:
<P
></P
><UL
><LI
><P
><B
CLASS="GUIMENUITEM"
>New</B
> creates a new profile and opens
a dialog to edit its properties.  All profiles created with the
<B
CLASS="GUIMENUITEM"
>New</B
> command are tagged with a creator
field of <TT
CLASS="GUILABEL"
><B
>User</B
></TT
>.</P
></LI
><LI
><P
><B
CLASS="GUIMENUITEM"
>Duplicate</B
> creates a copy of the currently
selected profile.</P
></LI
><LI
><P
><B
CLASS="GUIMENUITEM"
>Delete</B
> deletes the currently selected profile
from the list of profiles.</P
></LI
><LI
><P
><B
CLASS="GUIMENUITEM"
>Properties</B
> displays a dialog to view
and edit properties of the profile, including the probabilities assigned
to actions or strategies.  Profiles which are edited using this dialog
have their creator field reset to <TT
CLASS="GUILABEL"
><B
>User</B
></TT
>.</P
></LI
></UL
>
The <TT
CLASS="GUILABEL"
><B
>Properties</B
></TT
> dialog also appears when a profile's
entry in the table is double-clicked.</P
><P
>When both the extensive and normal form representations of a game are
displayed, the profile lists in the two windows are coordinated.
Corresponding profiles are listed in the same order in the two windows,
and operations such as changing the currently-selected profile, or
deleting a profile, change the profile list accordingly in both windows.
The mapping from normal form mixed strategies to extensive form behavior
strategies is done using Kuhn's Theorem; as such, the results are
unpredictable if the extensive form game is not of perfect recall.</P
><P
>When a game is edited and payoffs are changed, the equilibrium
fields such as <TT
CLASS="GUILABEL"
><B
>Nash</B
></TT
> will be reset.
In some cases, these will be updated to yes or no answers; in others
for which no definitive test is available, the fields will reset to
<TT
CLASS="GUILABEL"
><B
>DK</B
></TT
> (for "don't know").
When a game is edited to change the number
of information sets, actions, or strategies, all profiles are deleted.</P
><DIV
CLASS="NOTE"
><P
></P
><TABLE
CLASS="NOTE"
WIDTH="100%"
BORDER="0"
><TR
><TD
WIDTH="25"
ALIGN="CENTER"
VALIGN="TOP"
><IMG
SRC="./stylesheet-images/note.gif"
HSPACE="5"
ALT="Note"></TD
><TH
ALIGN="LEFT"
VALIGN="CENTER"
><B
>Changes from previous versions</B
></TH
></TR
><TR
><TD
>&nbsp;</TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
>In versions prior to 0.97, this was referred to as the
<TT
CLASS="GUILABEL"
><B
>Solutions</B
></TT
> window, and appeared as a separate frame.
The nomenclature has been changed to reflect the usefulness of investigating
the properties of profiles which might not satisfy any particular solution
concepts.  Additionally, in prior versions, solutions had to be manually
mapped from a normal form back to its corresponding extensive form, and
the two solution lists were separate.</P
></TD
></TR
></TABLE
></DIV
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="GUI.CONV.SUPPORTS"
>Working with supports</A
></H2
><P
>A support is a subset of the actions (for extensive forms) or strategies
(for normal forms) of a game.  Supports are most commonly generated as the
result of computing the dominated actions or strategies in a game, but
may also be manually edited for specific purposes.</P
><P
>The supports currently defined on a game are accessible via the
<B
CLASS="GUIMENUITEM"
>Supports</B
> menu item on the <B
CLASS="GUIMENU"
>View</B
>
menu.  The support panel is in the same notebook window as the outcome
and navigation panels.</P
><P
>The main body of the support panel shows, in tree form, the actions or
strategies in the currently selected support.  In extensive form games,
the window is organized hierarchically by player, then information set;
in normal form games, by player.  Strategies or actions not present in
the current support are shown in light grey.</P
><P
>At the top of the support panel is a drop-down list of all supports
currently defined.  The first support is always the "full support",
which cannot be edited.  Selecting a support from this list makes the
support the new current support, and changes the display of the game
accordingly.  The arrow buttons next to the drop-down change the current
support to the previous or next support in the list, respectively.</P
><P
>The <B
CLASS="GUIMENUITEM"
>Dominance</B
> item on the <B
CLASS="GUIMENU"
>Tools</B
>
is used to identify actions or strategies which are dominated.  For each
iteration of elimination of dominated strategies this algorithm performs,
the corresponding support is added to the list of supports.  Therefore,
using the arrow keys to scroll through the supports after finding dominated
actions or strategies is a useful way of seeing which actions or strategies
were removed at each iteration.</P
><P
>Supports may be constructed and edited by hand as well.  Right-clicking
in the support panel displays a menu with the following options:
<P
></P
><UL
><LI
><P
><B
CLASS="GUIMENUITEM"
>Duplicate support</B
> creates a new support with
the same actions or strategies as the current support.  The new support
becomes the current support.</P
></LI
><LI
><P
><B
CLASS="GUIMENUITEM"
>Delete support</B
> deletes the current support from
the support list.  Note that the "full support" cannot be
deleted.</P
></LI
></UL
>
The actions or strategies in any support other than the 
"full support" may be edited by left-clicking on the entry
in the tree for the action or strategy, and pressing the space bar.</P
><P
>The algorithms in the <B
CLASS="GUIMENUITEM"
>Equilibrium</B
> dialog on
the <B
CLASS="GUIMENU"
>Tools</B
> menu compute Nash equilibria on the
currently selected support.  This is useful, since cutting down on the
number of actions or strategies the algorithm must consider can help
substantially in efficiency.  So long as the current support differs
from the full support only in the (possibly iterative) removal of
strictly dominated actions or strategies, algorithms will be able to
find all Nash equilibria.  So long as the current support differs from
the full support only in the (possibly iterative) removal of weakly
dominated actions or strategies, algorithms will find only Nash
equilibria (but can possibly miss equilibria involving weakly
dominated actions or strategies).  For any other support, algorithms
may return profiles which are not Nash equilibria on the whole game,
but which are Nash equilibria on the game defined by restricting the
original game to actions or strategies found in the current support.
Note that such profiles will be indicated in the profiles window with an
<TT
CLASS="GUILABEL"
><B
>N</B
></TT
> in the <TT
CLASS="GUILABEL"
><B
>Nash</B
></TT
> column.</P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="GUI.CONV.OUTCOMES"
>Working with outcomes</A
></H2
><P
>Gambit has a flexible interpretation of outcomes, particularly in
extensive form games.  Gambit permits outcomes to appear in more than
one place in a tree or normal form.  Additionally, outcomes may appear
at nonterminal nodes in a game tree, in which case payoffs are interpreted
as the incremental payoffs of reaching that point in the tree.</P
><P
>Each game has a predefined "null" outcome.  The payoff to all
players at a null outcome is defined to be zero.  New extensive form games
are created with only the null outcome; when creating a normal form game,
the New Game dialog box offers by default to create one outcome per
contingency in the normal form game.</P
><P
>Outcomes are manipulated using a grid interface accessible by the
<B
CLASS="GUIMENUITEM"
>Outcomes</B
> item on the <B
CLASS="GUIMENU"
>View</B
>
menu.  The outcomes grid functions similar to a spreadsheet.
<DIV
CLASS="NOTE"
><P
></P
><TABLE
CLASS="NOTE"
WIDTH="100%"
BORDER="0"
><TR
><TD
WIDTH="25"
ALIGN="CENTER"
VALIGN="TOP"
><IMG
SRC="./stylesheet-images/note.gif"
HSPACE="5"
ALT="Note"></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
>There is some variance in the grid behavior between the GTK and Windows
versions of Gambit, due to variance in the wxWindows implementation.  
Hopefully this will standardize in future versions.</P
></TD
></TR
></TABLE
></DIV
></P
><P
>A new outcome is automatically created whenever the <B
CLASS="KEYCAP"
>Enter</B
>
key is pressed while on the last row of the outcomes table.  Alternately,
a new outcome can be created by right-clicking in the grid, which generates
a context menu for the outcomes window, and select 
<B
CLASS="GUIMENUITEM"
>New</B
>.
<DIV
CLASS="NOTE"
><P
></P
><TABLE
CLASS="NOTE"
WIDTH="100%"
BORDER="0"
><TR
><TD
WIDTH="25"
ALIGN="CENTER"
VALIGN="TOP"
><IMG
SRC="./stylesheet-images/note.gif"
HSPACE="5"
ALT="Note"></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
>For GTK users: A quirk in GTK causes a <B
CLASS="KEYCAP"
>CTRL</B
>-<B
CLASS="KEYCAP"
>N</B
> shortcut to appear on this menu item.  The shortcut does not create
an outcome, but rather a new game.</P
></TD
></TR
></TABLE
></DIV
></P
><P
>Editing outcome payoffs and labels is done in-place in the grid.  Note that
editing payoffs may cause computed profiles to cease being Nash equilibria
(or, perhaps, cause them to become Nash equilibria); these changes will
occur automatically in the Profiles window, if displayed.  Strategy,
action, and node values similarly will recompute after any payoff change.</P
><P
>Outcomes may be deleted using the <B
CLASS="GUIMENUITEM"
>Delete</B
> on
the context menu.  Deleting an outcome results in any nodes (in the
extensive form) or contingencies (in the normal form) with that outcome
having their outcome reset to the null outcome, with zero payoffs.</P
><P
>Outcomes are attached to nodes or contingencies in one of two ways.
In either case, first select the node or contingency where the outcome
will go.
<P
></P
><UL
><LI
><P
>Using the <B
CLASS="GUIMENU"
>Edit</B
> menu, select <B
CLASS="GUIMENUITEM"
>Node</B
>
or <B
CLASS="GUIMENUITEM"
>Contingency</B
>, as appropriate.  The presented
dialogs have a drop-down choice listing all outcomes and their payoffs;
select the desired outcome, and press OK to dismiss the dialog.</P
></LI
><LI
><P
>Using the outcomes window, select the outcome and right-click to get the
context menu.  Select <B
CLASS="GUIMENUITEM"
>Attach</B
>, and the outcome
will be attached to the selected node or contingency.</P
></LI
></UL
>
In a similar way, outcomes may be detached from nodes or contingencies,
either by selecting the null outcome when editing the node or contingency,
or by selecting <B
CLASS="GUIMENUITEM"
>Detach</B
> from the context menu
in the outcomes window.</P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="GUI.CONV.STANDARD"
>Standard Nash equilibrium algorithms</A
></H2
><P
>In most cases, the first task a user will ask Gambit to do after entering
a game is to compute some Nash equilibria.
In general, it is not possible to "black box" the
process of computing a Nash equilibrium, or a refinement thereof.
The algorithm best suited to a particular task depends upon both
the properties of the game, such as whether it is zero-sum, or how
many players it has, the number of equilibria the user wants to find,
and what refinements, if any, the equilibria should satisfy.
However, both theory and experience can inform choices for algorithms
and parameter settings which work "well" in general.</P
><P
>For both extensive and normal forms, Gambit provides a set of
standard Nash equilibrium computation algorithm settings.  
These standard procedures are run from the Nash equilibrium dialog
(accessible with the
<B
CLASS="GUIMENUITEM"
>Equilibrium</B
> item on the 
<B
CLASS="GUIMENU"
>Tools</B
> menu).  Standard algorithms to compute one,
two, or all Nash equilibria are available for both extensive and normal
forms, as well as for selected refinements as appropriate.
Refinements currently supported by Gambit are sequential and
subgame perfect Nash equilibria on the extensive form, and
(trembling-hand) perfect equilibria on the normal form.
<A
NAME="AEN411"
HREF="#FTN.AEN411"
>[1]</A
></P
></DIV
></DIV
></DIV
><H3
CLASS="FOOTNOTES"
>Notes</H3
><TABLE
BORDER="0"
CLASS="FOOTNOTES"
WIDTH="100%"
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
WIDTH="5%"
><A
NAME="FTN.AEN411"
HREF="gui.ref.html#AEN411"
>[1]</A
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
WIDTH="95%"
><P
>An implementation of Yamamoto's algorithm
[<SPAN
CLASS="CITATION"
><A
HREF="bib.html#YAM93"
>Yam93</A
></SPAN
>]
for finding one proper
equilibrium in a normal form game is currently planned for release
0.97.1.x.</P
></TD
></TR
></TABLE
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