Does every gain to a winner have to come at a loser's expense?

Verdict. As a general rule the statement is false. It is true only of one class of strategic situations, the zero-sum (or constant-sum) games, where the players' interests are completely opposed. In many economic interactions, voluntary exchange above all, one side's gain does not have to come out of the other side's pocket, and both can end up better off.

When the statement holds: zero-sum and constant-sum games.

• In a game, each player's payoff, the gain or loss she ends with, depends on her own choice and on the choices of others.
• In a zero-sum game, if one side loses the other wins, and the net change in wealth is zero. Such games are games of total conflict, with a clear winner and a clear loser: one player's gain is exactly the other's loss.
• In a constant-sum game the total is a fixed amount rather than zero, as in gambling, where the sum staked stays the same and only its division among the players changes.
• Example, our own: two finalists in a state chess championship in Chennai play for a single trophy and a fixed purse of ₹50,000 split ₹35,000 to the winner and ₹15,000 to the runner-up. Whatever extra one player takes home, the other loses, because the purse cannot grow. Here the statement is true.

When it fails: games where both can gain or both can lose. Many real situations are neither zero-sum nor constant-sum:

• Both can win. People trade voluntarily only when each expects to gain from the exchange; if either side expected to lose, the exchange would not happen. One of the principles of economics is that trade can make everyone better off: competition is not always a matter of one side's win being the other's loss, and countries that trade gain from it. International trade lets all the trading countries benefit.
• Both can lose. In a war, both sides can suffer heavy losses and end up as losers.
• Cooperation can pay. Games need not be played in conflict; cooperation can benefit both parties, although each may still be tempted to cheat for a personal gain.

In such games the total payoff changes with what the players do, so a gain for one need not be a loss for the other.

Example: a sale of potatoes to a dhaba. Our own figures. A farmer near Agra values a sack of potatoes at ₹600 (the least he would accept). A dhaba owner on the highway values the same sack at ₹900 (the most she would pay). They agree on a price of ₹750.

• The farmer gains ₹750 − ₹600 = ₹150.
• The dhaba owner gains ₹900 − ₹750 = ₹150.
• Together the exchange creates ₹300 of gain that did not exist before (₹900 − ₹600). Neither party is harmed: each is better off than without the sale, so there is no loser at all.

Conclusion. The statement describes a zero-sum game correctly, where a fixed total means one player's gain is the other's loss. It is false as a general claim, because in non-zero-sum situations, such as voluntary trade, both sides can gain together, and in others, such as war, both can lose.