Finite games have a well-defined end. Dynamic games involve the taking of turns, as opposed to static games, where players choose independently and their choices are revealed simultaneously. The classic Prisoner s Dilemma situation is a static game. Zero-sum games mean that for one person to win, another has to lose. Complete information is exactly what it seems to be, complete knowledge of the situation.
Poker is a common example of a game with incomplete information.
There are good reasons that game theory puzzles are usually this particular type of game. Payoffs are easy to calculate in a zero-sum game, particularly one with only two players. Dynamic games are easier to follow than static games. If played as a dynamic game, the strategy is clear and produces a win for the second player every time. Most importantly, finite games of complete information are always solvable.