Succinct game

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 ${\displaystyle n}$ players, each facing ${\displaystyle s}$ strategies, requires listing ${\displaystyle ns^{n}}$ 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 (a formal definition, describing succinct games as a computational problem, is given by Papadimitriou & Roughgarden 2008).

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