Game Description Language, or GDL, is a logic programming language designed by Michael Genesereth for general game playing in artificial intelligence, as part of the General Game Playing Project at Stanford University. GDL describes the state of a game as a series of facts, and the game mechanics as logical rules. GDL is hereby one of the alternative representations for game theoretic problems.
Purpose of GDL
Quoted in an article in New Scientist, Genesereth pointed out that although Deep Blue can play chess at a grandmaster level, it is incapable of playing checkers at all because it is a specialized game player. Both chess and checkers can be described in GDL. This enables general game players to be built that can play both of these games and any other game that can be described using GDL.
The following is the list of keywords in GDL, along with brief descriptions of their functions:
- This predicate is used to require that two terms be syntactically different.
- The predicate
does(?r,?m)means that player (or role)
?min the current game state.
- The predicate
goal(?r,?n)is used to define goal value
?n(usually a natural number between 0 and 100) for role
?rin the current state.
- This predicate refers to a true fact about the initial game state.
- The predicate
?mis a legal move for role
?rin the current state.
- This predicate refers to a true fact about the next game state.
- This predicate is used to add the name of a player.
- This predicate means that the current state is terminal.
- This predicate refers to a true fact about the current game state.
A game description in GDL provides complete rules for each of the following elements of a game.
Facts that define the roles in a game. The following example is from a GDL description of the two-player game Tic-tac-toe:
(role xplayer) (role oplayer)
Rules that entail all facts about the initial game state. An example is:
(init (cell 1 1 blank)) ... (init (cell 3 3 blank)) (init (control xplayer))
Rules that describe each move by the conditions on the current position under which it can be taken by a player. An example is:
(<= (legal ?player (mark ?m ?n)) (true (cell ?m ?n blank)) (true (control ?player)))
Game state update
Rules that describe all facts about the next state relative to the current state and the moves taken by the players. An example is:
(<= (next (cell ?m ?n x)) (does xplayer (mark ?m ?n))) (<= (next (cell ?m ?n o)) (does oplayer (mark ?m ?n)))
Rules that describe the conditions under which the current state is a terminal one. An example is:
(<= terminal (line x)) (<= terminal (line o)) (<= terminal not boardopen)
The goal values for each player in a terminal state. An example is:
(<= (goal xplayer 100) (line x)) (<= (goal oplayer 0) (line x))
With GDL, one can describe finite games with an arbitrary numbers of players. However, GDL cannot describe games which contain an element of chance (for example, rolling dice) or games where players have incomplete information about the current state of the game (for example, in many card games the opponents' cards are not visible). GDL-II, the Game Description Language for Incomplete Information Games, extends GDL by two keywords that allow for the description of elements of chance and incomplete information:
- The predicate
sees(?r,?p)means that role
?pin the next game state.
- This constant refers to a pre-defined player who chooses moves randomly.
The following is an example from a GDL-II description of the card game Texas hold 'em:
(<= (sees ?player ?card) (does random (deal_face_down ?player ?card))) (<= (sees ?r ?card) (role ?r) (does random (deal_river ?card)))
Michael Thielscher also created a further extension, GDL-III, a general game description language with imperfect information and introspection, that supports the specification of epistemic games — ones characterised by rules that depend on the knowledge of players.
Other formalisms and languages for game representation
In classical game theory, games can be formalised in extensive and normal forms. For cooperative game theory, games are represented using characteristic functions. Some subclasses of games allow special representations in smaller sizes also known as succinct games. Some of the newer developments of formalisms and languages for representation of some subclasses of games or representations adjusted to the needs of interdisciplinary research are summarized as the following table. Some of these alternative representations also encode time related aspects:
|Name||Year||Means||Type of games||Time|
|Congestion game||1973||functions||subset of n-person games, simultaneous moves||No|
|Sequential form||1994||matrices||2-person games of imperfect information||No|
|Timed games||1994||functions||2-person games||Yes|
|Gala||1997||logic||n-person games of imperfect information||No|
|Graphical games||2001||graphs, functions||n-person games, simultaneous moves||No|
|Local effect games||2003||functions||subset of n-person games, simultaneous moves||No|
|Game Petri-nets||2006||Petri net||deterministic n-person games, simultaneous moves||No|
|Continuous games||2007||functions||subset of 2-person games of imperfect information||Yes|
|PNSI||2008||Petri net||n-person games of imperfect information||Yes|
|Action graph games||2012||graphs, functions||n-person games, simultaneous moves||No|
This section needs expansion. You can help by adding to it. (July 2019)
A 2016 paper "describes a multilevel algorithm compiling a general game description in GDL into an optimized reasoner in a low level language".
A 2017 paper uses GDL to model the process of mediating a resolution to a dispute between two parties, and presented an algorithm that uses available information efficiently to do so.
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