If the losses of player A are the game of the player B, then the game is known asans.Fair gameNon- a zero-sum gameZero-sum gameUnfair game

Break Down the Problem

1. Identify the type of game based on player losses and wins.
2. Understand the definitions of fair game, non-zero-sum game, zero-sum game, and unfair game.

Relevant Concepts

1. Zero-sum game: A situation in game theory where one player's gain is exactly balanced by the losses of other players.
2. Non-zero-sum game: A scenario where the total gain or loss can be greater than zero, meaning that players can benefit or suffer simultaneously.
3. Fair game: A game where each player has an equal chance of winning, leading to no player having an advantage over the other.
4. Unfair game: A game where one player has a distinct advantage over another.

Analysis and Detail

• If player A's losses correspond to player B's gains, this typically suggests a direct inverse relationship, characteristic of a zero-sum game.
• In a zero-sum game, any advantage gained by one player equals an equivalent disadvantage for another.

Verify and Summarize

Based on the definitions and analysis, if player A loses exactly what player B gains, then the situation perfectly fits the description of a zero-sum game.

Final Answer

The answer is: Zero-sum game.