If they both deny it, then both children will be punished for three weeks. One child must rely on the idea of another child to avoid minor punishment. The connection between them is that game theory generally looks at how individuals or groups make choices that will affect other parties. The two children's first thought must have been their interests, but this would have led to the most extended punishment for both. The best option for them is for them to both admit and punish for a fortnight. Thus, this is the Nash equilibrium, also called the non-cooperative equilibrium. Prisoner's Dilemma Another example of a non-cooperative game is the well-known Prisoner's Dilemma game. The game involves two players, or defendants, who are kept in separate rooms and thus are unable to communicate. Players must decide, by themselves in isolation, whether to cooperate with the other player or to betray them and confess to law authorities. As shown in the diagram, both players will receive a higher payoff in the form of a lower jail sentence if they both remain silent. If both confess, they receive a lower payoff in the form of a higher jail sentence. If one player confesses and the other remain silent and cooperates, the confessor will receive a higher payoff, while the silent player will receive a lower payoff than if both players cooperated with each other. The Nash equilibrium therefore lies where players both betray each other, in the players protecting oneself from being punished more. The battle of the sexes game The game is about two players, boy and girl, deciding either going to a football game or going to an opera for their date, which respectively represent boy's and girl's preferred activity (i.e. boy prefers football game and girl prefers opera). This example is a two-person non-cooperative non-zerosum (TNNC) game with opposite payoffs or conflicting preferences. Because there are two Nash equilibria, this case is a pure coordination problem with no possibility of refinement or selection. Thus, the two players will try to maximise their own payoff or to sacrifice for the other and yet these strategy without coordination will lead to two outcomes with even worse payoffs for both if they have disagreement on what to do on their date. See also Mutual assured destruction Grim trigger Intra-household bargaining Proper equilibrium Tit for tat Trembling hand perfect equilibrium Trigger strategy War of