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The authors examine a duopoly pricing game where some customers know of no firms, others know of only one firm, and some know of both firms. Firms have constant and identical marginal costs, sell homogenous goods and choose prices simultaneously. Customers observe the prices of the firms that are known to them. They show that there is no equilibrium in pure price strategies for this game. They find a mixed strategy equilibrium, and show that it has intuitively appealing comparative static properties.
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