This question was asked in an AI exam. How would you answer such question?
If the game is not sequential, there would be no game tree and no need for pruning. Alpha-beta is a technique applied to look-ahead search. Alpha-beta has demonstrated utility in algorithms that play combinatorial games.
(Even in iterated dilemmas, it doesn't really branch because it's simultaneous, more of a vine than a tree. Decisionmaking would be based on mathematical analysis of the payoff matrix and statistical analysis of competitor behavior over time.)
Symmetry indicates that a single role definition is shared among the players. Zero-sum indicates that the aggregated gain over all players for any possible disposition of game play is zero.
Alpha-beta is a search thrift strategy invented in 1956 by John McCarthy. It is used by an individual player to maximize the probability of favorable game disposition by selecting from move options based on the permutations of game play dependent on each possible selection.
These do not seem, prima facie, to be mutually exclusive. Alpha-beta may be an effective computing cost reduction strategy on symmetric zero-sum games. An example is chess game play automation. Furthermore, Reinfield (1983) quotes Knuth and Moore (1975): "The most widely used method for pruning trees of two-person zero-sum games like chess is the alpha-beta algorithm."
If the values of the chess game play dispositions of win, draw, and loss are assigned 1, 0, and -1 respectively, then chess is a zero-sum game. If a single random bit is used to determine which player moves first, chess is symmetric. The various machine players in the winner's circle from 1978 to 2017 that used alpha-beta to achieve their victory confirms.
An analysis of alpha-beta pruning, DE Knuth, RW Moore, Artificial intelligence, 1975
An improvement of the Scout tree-search algorithm, A Reinefeld, ICCA Journal, 1983