When One Player's Win Is Another's Loss (Zero-Sum)

Why this matters

Zero-sum games are the cinema of game theory — chess, poker, sports — and they are the exception, not the rule. Most strategic interactions you'll encounter are non-zero-sum: both sides can gain, both can lose, or one can gain while the other is indifferent. Mistaking a non-zero-sum interaction (a team, a merger, a negotiation) for a zero-sum one is one of the classic ways smart people sabotage themselves.

Demo

A game is zero-sum if, for every outcome, payoffs sum to zero (or any constant — 'constant-sum' generalises cleanly). In 2 players this reduces to $u_1 = -u_2$.