The Nash equilibrium in a Bertrand game of price setting where all firms have different marginal cost is:

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In a Bertrand game with different marginal cost, the Nash equilibrium is for each firm to set price equal to its own marginal cost. This results in a zero-profit equilibrium, where no firm can increase its profits by deviating from this strategy as any deviation would lead to a loss in market share. However, this outcome is inefficient as it does not maximize total welfare as some mutually beneficial transactions will be foregone due to higher prices set by firms. Therefore, the Nash equilibrium in this scenario is inefficient.

The Nash Equilibrium in a Bertrand Game of Price Setting