13.Screening - SCREENING GAMES The structure of a SCREENING...

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SCREENING GAMES The structure of a SCREENING GAME is similar to that of a signaling game, except that the order of moves is changed… The uninformed player (Player 1) moves first. HE OFFERS A “MENU” (contract) TO THE INFORMED PLAYER (Player 2). The game ends with the informed Player 2 choosing an option from the menu. Screening Game Example : A seller does not know a Buyer’s taste and ability to pay. The seller offers the menu of the following form… Buy at 5TL each, for purchases less than 25 units, Buy at 4TL each, for orders between 25 and 50 units, Buy at 3TL each, for orders greater then 50 units. The buyer picks one of these alternatives (or does not buy any amount). The game ends after the Buyer’s choice. Screening Game Example : Hyundai does not know its dealer’s talent. It offers the dealer two contracts: Contract A : I pay you 400.000TL if you to sell more than 100 cars, 200.000 if you sell 50-100 cars/year. Contract B : I pay you 50.000TL plus extra 1000 TL for each car you sell per year. The dealer picks one of these contracts and the game ends. 1
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EXTENSIVE-FORM REPRESENTATION OF SCREENING GAMES… (with two players) Suppose that the informed player has two types, a and b. Nature Type-a Type-b player 1 ( Uninformed) Menu A Menu B Menu A Menu B #2 #2 #2 #2 No Yes Yes No Yes No Yes No ( , ) … PAYOFFS ( , ) ( , ) ( , ) Why does the Uninformed player design a menu? -Because she wants to overcome her lack of information about the informed player’s “type.” What use is this information? -The uninformed player moves first and makes a “take-it-or-leave-it” menu offer. By carefully designing the menu of choices, he can extract a larger surplus from each type of the informed player… 2
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NileCO is a monopolist-seller of laptops and PharmSA is a potential buyer. NileCO does not exactly know what number of laptops PharmSA can buy and how much it can pay. Suppose there are two possible types of PharmSA: Type-a of PharmSA can at most pay 600YTL per laptop and buy up to 5 units (600YTL is the maximum it can pay); Type-b of PharmSA can buy up to 5 units at 450YTL price (maximum), and for each additional unit above 5, it is willing to pay 400YTL price (maximum). It cannot buy more than 9 units. PharmSA is of type-a with probability μ (a number between 0 and 1, which all players know). NileCO’s cost of producing each laptop is 300YTL. NileCO will design a menu and offer it to PharmSA. A MENU, in the present context, includes quantity-payment pairs (payment from PharmSA to NileCO, quantity to be purchased by PharmSA) . (Objectives) PAYOFFS : NileCO wants to maximize (expected) profits. PharmSA’s payoff from buying X units is X.(maximum willingness to pay for one unit – actual price) For example, if Pharmsa is of type-b and buys 9 units at the price 350YTL, its payoff is 5.(450-350) + 4.(400-350) = 700YTL. The Screening Game is depicted below
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This note was uploaded on 03/16/2012 for the course FENS 101 taught by Professor Selçukerdem during the Fall '12 term at Sabancı University.

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13.Screening - SCREENING GAMES The structure of a SCREENING...

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