Nash equilibrium

Examples of Nash equilibrium in the following topics:

• Game Theory Applications to Oligopoly

  • This is known as a Nash equilibrium.
  • The Nash equilibrium is an important concept in game theory.
  • If a player knew the strategies of the other players (and those strategies could not change), and could not benefit by changing his or her strategy, then that set of strategies represents a Nash equilibrium.
  • If any player would benefit by changing his or her strategy, then that set of strategies is not a Nash equilibrium.

• Duopoly Example

  • The result of the firms' strategies is a Nash equilibrium--a pair or strategies where neither firm can increase profits by unilaterally changing the price.
  • However, not colluding and charging the marginal cost, which is the non-cooperative outcome, is the only Nash equilibrium of this model.

• The Prisoner's Dilemma and Oligopoly

  • This set of strategies is thus a Nash equilibrium in the game--no player would be better off by changing his or her strategy.
  • Analyze the prisoner's dilemma using the concepts of strategic dominance, Pareto optimality, and Nash equilibria

• Homogeneous versus Heterogeneous Solution Equilibria

  • The equilibrium constants for homogeneous and heterogeneous solutions need to be calculated differently.
  • The equilibrium constant K for a given reaction is defined as the ratio of the products of a reaction to the reactants, measured at equilibrium.
  • The reaction quotient measured at equilibrium is the equilibrium constant K.
  • A heterogeneous equilibrium is a system in which reactants and products are found in two or more phases.
  • The equilibrium constant K is simply [Br2], with the concentration of the pure liquid Br2 excluded.

• Equilibrium Constant Expression

  • The equilibrium constant is an expression that gives the ratio of reactants and products at equilibrium.
  • This constant is known as the equilibrium constant.
  • Their activity is 1, so they do not need to be written in the equilibrium constant.
  • The progress of an equilibrium reaction can be visualized.
  • The equilibrium constant,denoted by K, is the ratio of products to reactants at equilibrium.

• First Condition

  • The first condition of equilibrium is that the net force in all directions must be zero.
  • For an object to be in equilibrium, it must be experiencing no acceleration.
  • The condition $F_\text{net} = 0$ must be true for both static equilibrium, where the object's velocity is zero, and dynamic equilibrium, where the object is moving at a constant velocity.
  • Below, the motionless person is in static equilibrium.
  • This car is in dynamic equilibrium because it is moving at constant velocity.

• The Zeroth Law of Thermodynamics

  • The Zeroth Law of Thermodynamics states that systems in thermal equilibrium are at the same temperature.
  • If A and C are in thermal equilibrium, and A and B are in thermal equilibrium, then B and C are in thermal equilibrium.
  • Temperature is the quantity that is always the same for all systems in thermal equilibrium with one another.
  • The double arrow represents thermal equilibrium between systems.
  • If systems A and C are in equilibrium, and systems A and B are in equilibrium, then systems B and C are in equilibrium.

• A Brief Definition

  • The right-to-manage model, developed by the British school during the 1980s (Nickell), views the labor union and the firm bargaining over the wage rate according to a typical Nash Bargaining Maximin.

• Macroeconomic Equilibrium

  • In economics, the macroeconomic equilibrium is a state where aggregate supply equals aggregate demand.
  • In economics, equilibrium is a state where economic forces (supply and demand) are balanced.
  • Without any external influences, price and quantity will remain at the equilibrium value .
  • The result is the economic equilibrium for that good or service.
  • Similar to microeconomic equilibrium, the macroeconomic equilibrium is the point at which the aggregate supply intersects the aggregate demand.

• Reaction Quotients

  • If Q < Keq, the reaction will move to the right (in the forward direction) in order to reach equilibrium.
  • If Q > Keq, the reaction will move to the left (in the reverse direction) in order to reach equilibrium.
  • Eventually, the concentrations become constant; at this point, the reaction is at equilibrium.
  • The equilibrium constant, Keq, can be expressed as follows:
  • However, most reactions will generally reach equilibrium in a finite period of time.