Business, 04.03.2020 04:26 BluSeaa

Each of two sellers has available one indivisible unit of a good. Seller 1 posts the price p1 and seller 2 posts the price p2. Each of two buyers would like to obtain one unit of the good; they simultaneously decide which seller to approach. If both buyers approach the same seller, each trades with probability 1 ; the disappointed buyer does not subsequently have the option to trade with the other seller. (This assumption models the risk faced by a buyer that a good is sold out when she patronizes a seller with a low price.) Each buyer’s
preferences are represented by the expected value of a payoff function that assigns the payoff 0 to not trading and the payoff 1 − p to purchasing one unit of the good

at the price p. (Neither buyer values more than one unit.) For any pair (p1, p2) of prices with 0 ≤ pi ≤ 1 for i = 1, 2, find the Nash equilibria (in pure and in mixed

strategies) of the strategic game that models this situation. (There are three main

cases: p2 2 p1 − 1, 2 p1 − 1 p2 1 (1 + p1), and p2 > 1 (1 + p1).)

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Each of two sellers has available one indivisible unit of a good. Seller 1 posts the price p1 and se...

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