Représentations des Jeux

In a zero-sum game, one player's gain exactly equals another player's loss, keeping total resources constant. Non-zero-sum games differ because gains and losses are not perfectly balanced, allowing all players to benefit or lose together. Understanding cooperative vs non cooperative games helps clarify how different game structures enable different strategic outcomes.

A bidding war for a contract is a classic zero-sum game example. When one company wins the contract, the other loses out entirely, reflecting the fixed outcome where the winner's gain directly equals the loser's loss. The total value remains constant regardless of which company secures the bid.

Positive-sum games occur when all participants can receive gains, with the total outcome larger than any losses. For example, two firms collaborating on new technology both increase market shares and profit. Negative-sum games are opposite: total losses exceed individual gains, such as price wars where reduced margins hurt all competitors despite one capturing more market share.

By identifying whether a game is zero-sum or non-zero-sum, players can better predict potential benefits or losses and adjust their approach accordingly. In zero-sum games, competitive strategies dominate. In positive-sum games, cooperative approaches may yield mutual gains. This classification enables players to align their tactics with the actual payoff structure and available opportunities.

In a costly lawsuit between two companies, combined legal expenses and damages often exceed any benefits the winner receives. Both parties lose overall due to high transaction costs, making the total outcome negative. Even the victorious company may end up worse off financially than if the dispute had been resolved through negotiation or settlement.

A trade agreement is a positive-sum game because both countries can benefit from improved trade terms simultaneously. Each nation gains access to better goods, services, or markets, creating mutual advantage. The combined gains exceed any losses, leaving both countries better off than before the agreement, demonstrating how cooperation can expand total value.

In a private poker game, the total amount won by some players exactly equals the amount lost by others. No new value is created; money simply transfers between participants. The fixed pool of chips or money ensures that every winner's gain corresponds precisely to losers' losses, making it a perfect zero-sum scenario.