| Summary: | In many markets firms set posted prices which are potentially negotiable. We analyze the optimal marketing mix of pricing and bargaining when price takers buy at posted prices but bargainers attempt to negotiate discounts. The optimal bargaining strategy involves the firms offering bargainers randomly-sized discounts. Competing firms keep posted prices high to weaken the bargainers’ outside option, thus forgoing the chance to increase profits from price takers by undercutting their rival. A range of posted price equilibria are possible, and the higher price in the range inrceases when the proportion of bargainers goes up or the bargainers become less skilled. We consider how firms and competition authorities might encourage more consumers to bargain and determine the conditions under which each would choose to do so. Finally, we study the firms’ strategic decision about how much bargaining discretion sales staff should be allowed. Both firms allowing full bargaining flexibility is always an equilibrium - but not always the most profitable one. If there are enough bargainers, both firms committing to only matching the rival’s posted price is also an equilibrium: price matching moderates competition, thus raising profits.
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