<P> The Nash equilibrium is widely used in economics as the main alternative to competitive equilibrium . It is used whenever there is a strategic element to the behavior of agents and the "price taking" assumption of competitive equilibrium is inappropriate . The first use of the Nash equilibrium was in the Cournot duopoly as developed by Antoine Augustin Cournot in his 1838 book . Both firms produce a homogenous product: given the total amount supplied by the two firms, the (single) industry price is determined using the demand curve . This determines the revenues of each firm (the industry price times the quantity supplied by the firm). The profit of each firm is then this revenue minus the cost of producing the output . Clearly, there is a strategic interdependence between the two firms . If one firm varies its output, this will in turn affect the market price and so the revenue and profits of the other firm . We can define the payoff function which gives the profit of each firm as a function of the two outputs chosen by the firms . Cournot assumed that each firm chooses its own output to maximize its profits given the output of the other firm . The Nash equilibrium occurs when both firms are producing the outputs which maximize their own profit given the output of the other firm . </P> <P> In terms of the equilibrium properties, we can see that P2 is satisfied: in a Nash equilibrium, neither firm has an incentive to deviate from the Nash equilibrium given the output of the other firm . P1 is satisfied since the payoff function ensures that the market price is consistent with the outputs supplied and that each firms profits equal revenue minus cost at this output . </P> <P> Is the equilibrium stable as required by P3? Cournot himself argued that it was stable using the stability concept implied by best response dynamics . The reaction function for each firm gives the output which maximizes profits (best response) in terms of output for a firm in terms of a given output of the other firm . In the standard Cournot model this is downward sloping: if the other firm produces a higher output, your best response involves producing less . Best response dynamics involves firms starting from some arbitrary position and then adjusting output to their best - response to the previous output of the other firm . So long as the reaction functions have a slope of less than - 1, this will converge to the Nash equilibrium . However, this stability story is open to much criticism . As Dixon argues: "The crucial weakness is that, at each step, the firms behave myopically: they choose their output to maximize their current profits given the output of the other firm, but ignore the fact that the process specifies that the other firm will adjust its output ...". There are other concepts of stability that have been put forward for the Nash equilibrium, evolutionary stability for example . </P> <P> Most economists e.g., Paul Samuelson caution against attaching a normative meaning (value judgement) to the equilibrium price . For example, food markets may be in equilibrium at the same time that people are starving (because they cannot afford to pay the high equilibrium price). Indeed, this occurred during the Great Famine in Ireland in 1845--52, where food was exported though people were starving, due to the greater profits in selling to the English--the equilibrium price of the Irish - British market for potatoes was above the price that Irish farmers could afford, and thus (among other reasons) they starved . </P>

The equilibrium price in the market is determined by