Bertrand Competition For Inputs and Walrasian Outcomes Export

@article{stahl_88_bertrand_competition_for_inputs, abstract = {Market making by merchants, who obtain stock from suppliers and resell it to consumers, is modeled as a two-stage pricing game, with winner-take-all competition for the inputs (in contrast to \$.xed-capacity models). There is a unique subgame-perfect Nash equilibrium (SPNE) which is Walrasian for elastic demand and non- Walrasian for inelastic demand. Alternatively, when merchants jirst sell forward contracts to consumers and then compete for supplies, the unique SPNE is always Walrasian. Thus, we have an equilibrium model in which the Walrasian price arises not from the benevolent actions of a jictitious auctioneer but from optimal price-setting behavior of merchants.}, author = {Stahl, Dale O.}, citeulike-article-id = {2636895}, citeulike-linkout-0 = {http://www.jstor.org/stable/view/1814706}, comment = {== Bertrand competition for inputs takes the following form: (i) All firms, i, submit a bid B (ii) Firm with highest B wins and receives a supply of inputs governed by supply function S(B). Losers receive nothing. (iii) In a tie supply is either distributed equally, or randomly allocated to one firm. == Second stage: firms play Bertrand competition by submitting an ask-price bid. == With equal-sharing in the event of a tie in the bidding game, there exists an SPNE of the game only when the Walrasian price (the price for which the bid price and ask price yield an equal quantity of supply and demand) is greater than the sales-revenue maximising price. The equilibrium leads to the Walrasian outcome. == In the random-tie-breaking rule case, there is always an equilibrium in which monopoly profits are competed away in the first stage, and randomly chosen winner is a monopolist in the second stage. This outcome is only walrasian when the Walrasian price is greater than the sales- revenue maximising price. == If the stages are reversed so that the firms offer forward contracts then the unique eqm is: set an ask price equal to the Walrasian price, and then the bid price necessary to fulfil these forward contracts (also equal to the Walrasian price by definition. Thus the forward contracts case always gives rise to walrasian prices. In this game, all firms are always active in both stages, and submit tie bids in equilibrium.}, journal = {American Economic Review}, keywords = {after\_market, auctions, bertrand, demand, market, supply, walrasian\_equilibrium}, number = {1}, pages = {189--201}, posted-at = {2008-04-07 10:05:36}, priority = {0}, title = {Bertrand Competition For Inputs and Walrasian Outcomes}, url = {http://www.jstor.org/stable/view/1814706}, volume = {78}, year = {1988} }

TY - JOUR ID - stahl_88_bertrand_competition_for_inputs L3 - citeulike-article-id:2636895 N2 - Market making by merchants, who obtain stock from suppliers and resell it to consumers, is modeled as a two-stage pricing game, with winner-take-all competition for the inputs (in contrast to $.xed-capacity models). There is a unique subgame-perfect Nash equilibrium (SPNE) which is Walrasian for elastic demand and non- Walrasian for inelastic demand. Alternatively, when merchants jirst sell forward contracts to consumers and then compete for supplies, the unique SPNE is always Walrasian. Thus, we have an equilibrium model in which the Walrasian price arises not from the benevolent actions of a jictitious auctioneer but from optimal price-setting behavior of merchants. IS - 1 JF - American Economic Review EP - 201 TI - Bertrand Competition For Inputs and Walrasian Outcomes VL - 78 SP - 189 KW - after_market KW - auctions KW - bertrand KW - demand KW - market KW - supply KW - walrasian_equilibrium N1 - == Bertrand competition for inputs takes the following form: (i) All firms, i, submit a bid B (ii) Firm with highest B wins and receives a supply of inputs governed by supply function S(B). Losers receive nothing. (iii) In a tie supply is either distributed equally, or randomly allocated to one firm. == Second stage: firms play Bertrand competition by submitting an ask-price bid. == With equal-sharing in the event of a tie in the bidding game, there exists an SPNE of the game only when the Walrasian price (the price for which the bid price and ask price yield an equal quantity of supply and demand) is greater than the sales-revenue maximising price. The equilibrium leads to the Walrasian outcome. == In the random-tie-breaking rule case, there is always an equilibrium in which monopoly profits are competed away in the first stage, and randomly chosen winner is a monopolist in the second stage. This outcome is only walrasian when the Walrasian price is greater than the sales- revenue maximising price. == If the stages are reversed so that the firms offer forward contracts then the unique eqm is: set an ask price equal to the Walrasian price, and then the bid price necessary to fulfil these forward contracts (also equal to the Walrasian price by definition. Thus the forward contracts case always gives rise to walrasian prices. In this game, all firms are always active in both stages, and submit tie bids in equilibrium. AU - Stahl, Dale PY - 1988/// UR - http://www.jstor.org/stable/view/1814706 ER -