11.8
ベルトラン寡占のナッシュ均衡
A Nash equilibrium occurs when no firm has an incentive to change its strategy given its competitor’s choice.
Consider two firms, TrueTech and BestCo, producing identical products.
Their market demand function is P = 300 − Q and P = 300−(��1+��2), where Q1 and Q2 are the quantities produced by TrueTech and BestCo, respectively.
Both firms have the same marginal cost, which is MC1 = MC2 = $30.
BestCo sets its price first, fearing undercutting by TrueTech. Both firms eventually set prices equal to their marginal cost at $30 to avoid losing market share.
Using the demand equation P = 300 − Q, substituting the price of thirty dollars yields 30 = 300−Q and Q = 270 units total units supplied to the market by both firms.
The reaction function indicates a firm's optimal price based on its competitor's price.
The positive slope for both firms arises because when a competing firm raises its price, the other firm can benefit from offering a higher price as well.
The intersection of TrueTech's and BestCo's reaction functions marks the Nash equilibrium, where neither firm has an incentive to adjust its price.
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