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A Nash equilibrium, as opposed to a competitive equilibrium, tells you how an economy will settle when some component of competition has been removed, such as by government regulation.
Let me provide a very simple example. You and another person are bargaining for a pair of shoes, you have money they have shoes. Enough people doing this is a market and competition will set the price based on scarcity.
Now imagine two shoe producers, one with good low cost shoes and another not. Instead of competing, the other producer goes to the elected representative and asks for a "fair trade" law to protect the poor business from bankruptcy by limiting market access. A competitive equilibrium will not form, but a Nash equilibrium will. It would be a game played by politicians, consumers, and shoe makers. The goal of the game would be to make the most money given each person's own needs and the impact of removing competition.
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