Insuring Customers of a Unionized Firm Against Loss of Network Benefits

We study how optimally to insure customers of a unionized firm, such as an auto maker, against the loss of network benefits that occurs when other consumers abandon the firm.  The union first announces a wage.  A random demand shock is then realized.  The firm then chooses its price and, finally, consumers decide whether or not to buy from the firm.  Common knowledge of payoffs is perturbed slightly in order to obtain a unique outcome.  In this outcome the union chooses an excessive wage, leading consumers to abandon the firm too often.  The first best can be costlessly attained by providing consumers with countercyclical insurance.