See also: Game theory § Alternative game representations
Consider a game of three players, I,II and III, facing, respectively, the strategies {T,B}, {L,R}, and {l,r}. Without further constraints, 3*23=24 utility values would be required to describe such a game.
L, l
L, r
R, l
R, r
T
4, 6, 2
5, 5, 5
8, 1, 7
1, 4, 9
B
8, 6, 6
7, 4, 7
9, 6, 5
0, 3, 0
For each strategy profile, the utility of the first player is listed first (red), and is followed by the utilities of the second player (green) and the third player (blue).
In algorithmic game theory, a succinct game or a succinctly representable game is a game which may be represented in a size much smaller than its normal form representation. Without placing constraints on player utilities, describing a game of players, each facing strategies, requires listing utility values. Even trivial algorithms are capable of finding a Nash equilibrium in a time polynomial in the length of such a large input. A succinct game is of polynomial type if in a game represented by a string of length n the number of players, as well as the number of strategies of each player, is bounded by a polynomial in n[1] (a formal definition, describing succinct games as a computational problem, is given by Papadimitriou & Roughgarden 2008[2]).
^Cite error: The named reference Papadimitriou2007 was invoked but never defined (see the help page).
^Cite error: The named reference Papadimitriou2008 was invoked but never defined (see the help page).
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