In such a case, the minimum payoff might be one that would not have occurred anyway because the opponent might never find it optimal to implement a strategy that would make it come about. Game theory assumes that one has opponents who are adjusting their strategies according to what they believe everybody else is doing. The exact level of sophistication of the opponents should be part of one's strategy. To analyze such a game, one puts oneself in the other player's shoes, recognizing that the opponent, being clever, is doing the same. When this consideration of the other player's moves continues indefinitely, the result is an infinite regress.
Game theory provides the tools to analyze such problems.
Game theory can be used to analyze a wide range of strategic interaction environments including oligopolies, sports, and politics. Many product failures can be attributed to the failure to consider adequately the responses of competitors. Game theory forces one to consider the range of a rival's responses. The decision makers in the game. Choices available to a player.