zero sum game

A zero-sum game is a concept in game theory where one participant's gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). In other words, the total net benefit (or payoff) to all players sums to zero. ### Key Characteristics: 1. Strict Competition One player's gain is another's loss. 2. No Mutual Benefit Cooperation does not improve outcomes. 3. Fixed Total Payoff The sum of all payoffs is always zero. ### Examples: - Chess One player wins (+1), the other loses (-1), net result = 0. - Poker (among players) The total money won equals the total money lost. - Sports competitions One team's victory means the opponent's defeat. ### Mathematical Representation: If two players (A and B) have payoffs ( P_A ) and ( P_B ), then: [ P_A + P_B = 0 ] This means ( P_A = -P_B ). ### Contrast with Non-Zero-Sum Games: In non-zero-sum games (e.g., trade negotiations, prisoner's dilemma), cooperation can lead to mutual gains or losses. ### Applications: - Economics (trade, auctions) - Military strategy - Poker and other competitive games - Business negotiations (in some cases) Would you like a deeper explanation of any aspect?