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A lot of times my sibling and I have played chess and have ended up with just two kings. We have never known what would happen next. Two kings on the board would somehow result in an infinite game, as each can move forever wheresoever they like Hence, in such situations, is the game cancelled, tied, or withdrawn?

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This is covered in FIDE's Laws of Chess 5.2b)

The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.

The term "insufficient mating material" describes this situation informally. However, the term "dead position" also applies to e.g. this kind of position:

[fen "8/6k1/8/p2p2p1/P2P2P1/8/1K6/8 w - - 0 1"]

Even with worst opposition, neither side can make any advances here, because the kings cannot cross the line set by the pawns. Therefore, this is an immediate draw by the same rule.

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    Are there ever disputes about whether a position is dead? If White's flag were to fall, but White claimed the position was one where no legal sequence of moves would result in Black achieving checkmate, would there be any procedure for adjudicating such a claim? I would expect that in most over-the-board positions it would be pretty obvious when a position is dead or when a helpmate would exist for Black, but what if it isn't clear?
    – supercat
    Jul 8, 2015 at 1:54
  • @supercat This sounds more like a new question. Anyway, in my 30+ years of active play and 10+ years of serving as arbiter, I never encountered/heard of a case in which this rule was actually applied. BTW, I don't like the word "adjudication" for resolving this situation, as it doesn't require deep analysis, only facts-checking. I expect players to realize they have reached a dead position by themselves, so there would be no need for checking this. And please note: In your example, White wouldn't need to make a "claim" before the flag fall. A dead position ends the game - without a claim!
    – Ray
    Jul 8, 2015 at 9:10
  • I don't agree that "insufficient mating material" is an 'informal' way of saying "dead position". "Insufficient mating material" (specifically KvK or KNvK or KBvKB where all bishops are on the same colour square) is just one case of "dead position". There is also "inevitable stalemate" and (as your diagram shows) "blocked position".
    – Laska
    Apr 5, 2018 at 4:25
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It is a draw (tie) because of "insufficient mating material". The game ends in this state.

The condition also arises when both sides are down to King+Bishop or King+Knight with no pawns on the board.

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    Note that King + Bishop and King + Knight are only insufficient mating material against a bare king. There are mating positions in which both sides have only a knight, or a bishop on different colors. If both sides have a only a bishop on squares of the same color, then it is an immediate draw as mate isn't possible.
    – RemcoGerlich
    Jun 10, 2015 at 13:13

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