Mixed Strategy Nash Equilibrium Predictions as a Means of Organizing Behavior in Posted-Offer Market Experiments

Introduction In posted-offer markets the competitive outcome for a market, defined by the intersection of market supply and market demand curves, is frequently not a Nash equilibrium for the market viewed as a stage game. Rather, one or more sellers often have incentives to deviate unilaterally from the competitive outcome. A simple example illustrates. Consider a market with two sellers, S1 and S2, and a single, fully revealing buyer. Sellers S1 and S2 can each offer two units for sale at a constant cost of c. The buyer will purchase up to three units at a maximum price of vh per unit, and will pay up to vl for a fourth unit, with vh>vl>c. In the competitive prediction for this market, four units trade at a price of vl, and earnings for each seller are 2(vl – c). But this competitive outcome is not a Nash equilibrium if vh – c >2(vl – c), since in this case either seller could increase earnings unilaterally by posting a price of vh and selling a single unit. Holt (1989) defines sellers as having market power in this instance when the competitive price is not a pure strategy Nash equilibrium. When market power arises, a Nash equilibrium in pure strategies typically does not exist. Notice above, for example, that the price vh cannot be supported as a pure strategy Nash equilibrium, since a posting of vh, by, say, seller S1 will induce seller S2 to post vh – ε, thereby guaranteeing S2 a sale of two units. Incentives to undercut remain for any price down to the point where earnings from selling two units as the low price seller are equal to earnings from selling a single unit at a price vh. Defining this lowest price as pmin, sellers will undercut each other until pmin = (vh + c)/2. A common price of pmin also cannot be supported as a pure strategy Nash equilibrium because only three units will trade at this price, and one of the sellers will fail to earn the security earnings available at the price vh. Any static