Game theory: non-cooperative games

Game theory studies choices where each player's outcome depends on what others do. A strategy is a complete plan of action, and a Nash equilibrium is a set of strategies where no player can gain by changing alone, given what the others are doing. The prisoner's dilemma shows why equilibrium need not be good for everyone: each prisoner gains by confessing whatever the other does, so both confess, even though both staying silent would have been better for both. Worked example: with payoffs (silent, silent) = 3 each, (confess, silent) = 5 for the confessor and 0 for the silent one, and (confess, confess) = 1 each, confessing is the dominant strategy and (confess, confess) is the Nash equilibrium.