How is Nash equilibrium achieved in a competitive market?

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The Nash equilibrium occurs when all participants in a market are pursuing the optimum strategy for their own interests, taking into account the strategies of the other participants and assuming that these remain unchanged.

It is therefore possible to achieve the Nash equilibrium in a competitive market where supply and demand are constant and the market is otherwise stable. In a perfectly competitive market, a large number of sellers offer identical products to a large number of consumers in a marketplace with no bars to entry. The perfectly competitive market may be a hypothetical situation constructed by economists, but it is evident that such a market would inevitably gravitate towards the Nash equilibrium, as do markets that approach or approximate perfect competitiveness.

If you have, for instance, ten companies all selling identical widgets to the public for $5 each, it is clear that the company which attempted to sell the widgets for $6 would fail, as no one would buy the overpriced widgets when cheaper alternatives were available. On the other hand, if Nash equilibrium has been achieved, the company which tried to gain a larger market share by lowering the price to $4 would also fail, since it would not be economically viable to sell the widgets at such a low price, and the company in question would fail to recoup its costs. Thus, every possible change in each company's policy would be a bad decision so long as the others all retain the same policies, and the market remains stable in other respects, and the competitive market remains in Nash equilibrium.

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