How can players successfully employ a two-person zero-sum strategy?

A two-person zero-sum game is characterized by the principle that one player's gain is precisely equal to the other player's loss. This means that the total amount of utility available in the game remains constant; any benefit one player receives results in an equivalent detriment to the opponent. By ensuring their gains equate to the opponent's losses, players effectively leverage this characteristic to maintain a strategic edge.

The essence of employing a two-person zero-sum strategy lies in recognizing that the players are in direct competition, and each must plan their moves in a manner that maximizes their own outcomes while simultaneously minimizing the potential gains of their opponent. This understanding is critical in zero-sum situations, where players are continuously assessing their strategies against one another's actions to navigate the competitive landscape successfully.

In contrast, while maximizing one's gains, using statistical probabilities, or monitoring the opponent's strategy can all play a role in strategic decision-making, these actions do not capture the fundamental nature of a zero-sum game as accurately as ensuring that one player's gains balance out the other's losses. This balancing act directly underscores the competitive dynamic inherent in two-person zero-sum games.