Why can individually advantageous choices leave both people worse off?

A strategic situation is one in which the result of a choice depends partly on what someone else chooses. Game theory represents such relationships through players, available actions and payoffs. The representation makes incentives explicit, but its conclusions depend on how the situation is modeled.

Consider an invented game with actions cooperate and defect. Mutual cooperation gives each player 3 points. A player who defects while the other cooperates gets 5, while the cooperator gets 0. Mutual defection gives each player 1. These numbers are preference scores supplied for the example.

Defecting gives a player more points whichever action the other chooses: 5 rather than 3 against cooperation, and 1 rather than 0 against defection. Mutual defection is therefore a Nash equilibrium: neither player can improve their own payoff by changing alone while the other stays put. Yet both would receive more at mutual cooperation.

Equilibrium does not mean the best joint outcome or a moral recommendation. Repeated interaction, agreements, different preferences or changed rules can alter the incentives. The lesson is a precise relationship within the stated game, not proof that cooperation is impossible or that one table predicts real social behavior.