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In the Cournot Duopoly model of oligopoly, Nash Equilibrium occurs when each firm chooses the quantity to produce that maximizes its own profit, given the production level of the other firm. The equilibrium quantity and price are less than monopoly level.

In the Stag Hunt, the Nash Equilibrium can be either players hunting a stag (cooperate) or hunting a rabbit (defect). If each assumes the other will hunt for the stag, cooperation is the best response. However, trust issues might lead to independent rabbit hunting.

In the Battle of the Sexes, a Nash Equilibrium is reached when each player chooses an activity that their partner prefers, resulting in two pure Nash Equilibria. It's a coordination game where the best response depends on the other's action.

In Rock-Paper-Scissors, Nash Equilibrium is a mixed strategy where each player is equally likely to play rock, paper, or scissors. This equilibrium is indifferent to the opponent’s choice, as no pure strategy dominates the game.

In a Coordination Game, Nash Equilibria occur at points where all parties choose the same course of action, because any unilateral deviation doesn't lead to a better outcome. Multiple Nash Equilibria are possible if there are multiple points to coordinate on.

The Hawk-Dove Game models a scenario where two strategies exist: aggressive (Hawk) and peaceful (Dove). The Nash Equilibrium can be a mixed strategy where each player uses a probability mixture of playing Hawk or Dove to optimize their payoff.

In the Prisoners' Dilemma, Nash Equilibrium occurs where each prisoner chooses to betray the other, despite both being better off cooperating. This is because each prisoner's best response is to betray, regardless of the other's choice.

In a Public Goods Game, Nash Equilibrium typically results in underinvestment in the public good since each individual rationally decides to free ride on the contributions of others, even though they would all be better off if everyone contributed.

In Matching Pennies, the Nash Equilibrium is a mixed strategy where each player randomizes their choices with equal probability. No pure strategy equilibrium exists as players have opposite interests.