M. A. Satterthwaite and S. R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....1 surveys double auction mechanisms known in the literature. As expected by the Myerson Satterthwaite impossibility theorem, no mechanism is (EFF) BB) and (IR) All mechanisms except the VCG DA are (BB) and (IR) but not (EFF) and all except the k DA mechanism are strategy proof. In the k DA [35, 6, 30], parameter k [0, 1] is chosen before the auction begins; the parameter is used to calculate a clearing price somewhere between A l and B l . The McAfee DA [20] computes price p # = A l 1 B l 1 ) 2, and implements this price if p # [A l , B l ] and trades l units, otherwise l 1 units ....

Mark A Satterthwaite and Steven R Williams. Bilateral trade with the sealed bid k-double auction: Existence and e#ciency. Journal of Economic Theory, 48:107--133, 1989.

....(EFF) IR) and (BB) 21 1 2 3 4 5 Q asks bids A l Figure 6: A standard double auction. Bid price vs. Ask price for successive quantities, Q,ofthe same item. In this example it is e#cient to trade l = 3 units, and there is a non discriminatory clearing price p [A l ,B l ] In the k DA [35, 6, 30], parameter k [0, 1] is chosen before the auction begins; the parameter is used to calculate a clearing price somewhere between A l and B l . The McAfee DA [20] computes price p # = A l 1 B l 1 ) 2, and implements this price if p # [A l ,B l ] and trades l units, otherwise l 1 units are ....

Mark A Satterthwaite and Steven R Williams. Bilateral trade with the sealed bid k-double auction: Existence and e#ciency. Journal of Economic Theory, 48:107--133, 1989.

.... (1 k) v(c) Adding the tvo equations and simplifying gives v(b) k; 1 k) vdc ) k: 1 k) We refer to auctions that set prices in accordance vith Theorem 4 as k bundle auctions. The k parameter here is directly analogous to the parameter used in the k double auction [23]. W and w bound the range of anonymous bundle prices for vhich supply equals demand. Reducing any price in w vould create excess demand for some of the items. There is a slightly veaker analogy for the upper bound. We cannot raise the price of any b B vithout disequilibrating supply and demand. ....

M. A. Satterthwaite and S. R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107 133, 1989.

....asynchronous system we need to perform the operation using only local message passing. In Chapter 7, I describe a protocol for detecting quiescence in general distributed negotiations, based on a well known termination detection algorithm. Each auction runs according to (M 1)st price rules [Satterthwaite and Williams, 1989; 1993; Wurman et al. 1998] The (M 1)st price auction is a variant of the (second price) Vickrey auction [Vickrey, 1961] generalized to allow for the exchange of multiple units of a good. Given a set of offers including M units offered for sale, the (M 1)st price auction sets a price equal ....

....obtained with any set of bidding policies is equal to the probability that the solution is computed by the combinatorial auction. The strategic game bears some similarity to the asymmetric information version of the Nash demand game [Chatterjee and Samuelson, 1983; Leininger et al. 1989; Satterthwaite and Williams, 1989] for which continua of equilibria exist in various forms. In the asymmetric information Nash demand game, there is a buyer with value v 0 and a seller with cost k 0 , each drawn from uniform distributions that are common knowledge. The buyer and seller place bids to exchange a good from the ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.

....demand bids B 1 B 2 : At this point the optimal trade quantity l is de ned to be maximal such that B l S l . Most real markets proceed by choosing a market clearing price anywhere in the range S l : B l (e.g. B l S l ) 2 the 1 2 DA which is a special case of the k Double Auction [15, 3, 10]) This pricing scheme is not incentive compatible but it has been shown to perform reasonably well in many cases under strategic behavior of the participants [1, 11] One may alternatively use the VCG auction rules setting separate prices for the winning demand bids p B = max(S l ; B l 1 ) and ....

M. Satterthwaite and S. Williams. Bilateral trade with the sealed bid kdouble auction: Existence and eciency. Journal of Economic Theory, 48:107-133, 1989. 20

....price, such as those often used to provide quantity discounts. These are just some of the possible fee structures. When an outside subsidy is present, these fees can flow the opposite direction from auctioneer to agents. Anderson et al. 1] explore the incentive properties of double auctions [36] with various fee structures. 3.3. Information Revelation Policy We formalize the auction s information revelation policy in terms of a quote function, which maps the set of current bids to a message we call the price quote, which represents some summary of the current bid state. 8 The ....

....A uniform price auction applying these rules can use any tie breaking policy and any algorithm for pairing the winning buy and sell bids. Having selecting the winning bids, we now turn our attention to setting the transaction price. The matching function , used in the double auction [36, 37], sets the transaction price according to , 4 . covers the full range of transaction prices that are uniform, separating, and support locally efficient allocations. Notice that the two extreme values of produce the ( st and th prices, respectively. Although ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.

....The question of whether large societies can help reconcile problems of finding approximately efficient, balanced, incentive compatible, still has many open facets. The mechanism described in Example 7 is due to McAfee (1993) The convergence discussed in footnote 18 has been explored by Gresik and Satterthwaite (1989), Satterthwaite and Williams (1989) and Rustichini, Satterthwaite and Williams (1995) see also Satterthwaite (1999) Example 8 illustrates ideas that are explored in Mailath and Postlewaite (1990) and Al Najjar and Smorodinsky (2000ab) The possibility of finding such approximately efficient ....

....large societies can help reconcile problems of finding approximately efficient, balanced, incentive compatible, still has many open facets. The mechanism described in Example 7 is due to McAfee (1993) The convergence discussed in footnote 18 has been explored by Gresik and Satterthwaite (1989) Satterthwaite and Williams (1989), and Rustichini, Satterthwaite and Williams (1995) see also Satterthwaite (1999) Example 8 illustrates ideas that are explored in Mailath and Postlewaite (1990) and Al Najjar and Smorodinsky (2000ab) The possibility of finding such approximately efficient mechanisms with large numbers in ....

Satterthwaite, M. and S. Williams (1989), "Bilateral Trade with the Sealed Bid kDouble Auction: Existence and Efficiency," Journal of Economic Theory, Vol. 48, pp. 107--133.

....Agent 1 6 6 5 10 7 8 12 Agent 2 3 3 2 8 5 6 11 Agent 3 4 2 1 7 6 5 10 Table 2: An example with three agents. AB C OE 3 Agent 1 10 5 0 Agent 2 8 2 0 Agent 3 7 1 0 Table 3: The pseudo assignment problem. 2. The k parameter here is analogous to the parameter used in the k double auction (Satterthwaite Williams 1989). P and P represent the range of prices for which supply equals demand. Reducing any price in P would create excess demand for some of the objects. There is a slightly weaker analogy for the upper bound side. We cannot raise the price of any b 2 B without disequilibrating supply and demand. ....

Satterthwaite, M. A., and Williams, S. R. 1989. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory 48:107--33.

....quote, and the (M 1)st price is the bid quote. Notice that this de nition generalizes the common notion of bid ask spread, since it applies even if the buy and sell bids overlap. In fact, the Mth and (M 1)st price rules belong to a more general class of mechanisms called k double auctions [17]. The parameter k 2 [0; 1] speci es the fraction between the (M 1)st and Mth prices at which the clearing price is set. The algorithm we present in Section 5 applies to the entire class of k double auctions. However, our analysis in the next section is concerned only with the two extreme points, ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and eciency. Journal of Economic Theory, 48:107-33, 1989.

....quote, and the (M 1)st price is the bid quote. Notice that this definition generalizes the common notion of bid ask spread, since it applies even if the buy and sell bids overlap. In fact, the Mth and (M 1)st price rules belong to a more general class of mechanisms called k double auctions [17]. The parameter k 2 [0# 1] specifies the fraction between the (M 1)st and Mth prices at which the clearing price is set. The algorithm we present in Section 5 applies to the entire class of k double auctions. However, our analysis in the next section is concerned only with the two extreme ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--33, 1989.

....price, such as those often used to provide quantity discounts. These are just some of the possible fee structures. When an outside subsidy is present, these fees can flow the opposite direction from auctioneer to agents. Anderson et al. 1] explore the incentive properties of k double auctions [36] with various fee structures. 3.3. Information Revelation Policy We formalize the auction s information revelation policy in terms of a quote function, which maps the set of current bids to a message we call the price quote, which represents some summary of the current bid state. 8 The ....

....A uniform price auction applying these rules can use any tie breaking policy and any algorithm for pairing the winning buy and sell bids. Having selecting the winning bids, we now turn our attention to setting the transaction price. The matching function k , used in the k double auction [36, 37], sets the transaction price according to p = kp (1 k)p, k 2 [0; 1] k covers the full range of transaction prices that are uniform, separating, and support locally efficient allocations. Notice that the two extreme values of k produce the (M 1)st and M th prices, respectively. Although no ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.

....k[v i (b) P b ] k[v i (c) P c ] and (1 k) v i (b) P b ] 1 k) v i (c) P c ] Adding the two equations and simplifying gives v i (b) kP b (1 k)P b v i (c) kP c (1 k)P c : 2. The k parameter here is analogous to the parameter used in the k double auction [17]. P and P represent the range of prices for which supply equals 6 A B C AB AC BC ABC Agent 1 6 6 5 10 7 8 12 Agent 2 3 3 2 8 5 6 11 Agent 3 4 2 1 7 6 5 10 Table 2: An example with three agents. AB C 3 Agent 1 10 5 0 Agent 2 8 2 0 Agent 3 7 1 0 Table 3: The pseudo assignment ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and eciency. Journal of Economic Theory, 48:107-33, 1989. 11

....k) v i (b) Gamma P b ] 1 Gamma k) v i (c) Gamma P c ] Adding the two equations and simplifying gives v i (b) Gamma kP b Gamma (1 Gamma k)P b v i (c) Gamma kP c Gamma (1 Gamma k)P c : 2. The k parameter here is directly analogous to the parameter used in the k double auction [17]. P and P represent the range of prices for which supply equals demand. Reducing any price in P would create excess demand for some of the objects. There is a slightly weaker analogy for the upper bound side. We cannot raise the price of any b 2 B without disequilibrating supply and demand. ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--33, 1989.

....price, such as those often used to provide quantity discounts. These are just some of the possible fee structures. When an outside subsidy is present, these fees can flow the opposite direction from auctioneer to agents. Anderson et al. 1] explore the incentive properties of k double auctions [35] with various fee structures. 21 3.3 Information Revelation Policy We formalize the auction s information revelation policy in terms of a quote function, ae, which maps the set of current bids to a message we call the price quote, which represents some summary of the current bid state. 8 The ....

....A uniform price auction applying these rules can use any tie breaking rule and any algorithm for pairing the winning buy and sell bids. Having selecting the winning bids, we now turn our attention to setting the transaction price. The matching function fl k , used in the k double auction [35, 36], sets the transaction price according to p = kp (1 Gamma k)p, k 2 [0; 1] fl k covers the full range of transaction prices that are uniform, separating, and support locally efficient allocations. Notice that the two extreme values of k produce the (M 1)st and Mth prices, respectively. ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.

....parse bid strings into machine manipulable representations. Classes at the third level implement specific clearing algorithms. Figure 3 diagrams the data structures at each level for an auctioneer that uses the 4heap algorithm [2] to implement the family of auctions based on the k double auctions [1]. 3 3.3.1 Auctioneer Event Handling When the auctioneer receives a LOAD message, it retrieves the auction description from the database and all bids that have an admitted state. Bids are loaded in order of submission and hashed by owner ID. If the bid has a fixed expiration time, the bid is ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--33, 1989.

....quote, and the (M 1)st price is the bid quote. Notice that this definition generalizes the common notion of bid ask spread, since it applies even if the buy and sell bids overlap. In fact, the Mth and (M 1)st price rules belong to a more general class of mechanisms called k double auctions [18]. The parameter k 2 [0; 1] specifies the fraction between the (M 1)st and Mth prices at which the clearing price is set. The algorithm we present in Section 5 applies to the entire class of k double auctions. However, our analysis in the next section is concerned only with the two extreme ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid K-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--33, 1989.

....to revise its bids, and no auction changes its allocation. At this point, the auctions clear ; each bidder is notified of the final prices and how many units it transacted in each good. Note that a quiescent economy may not be in a solution state. Each auction runs according to (M 1)st price rules [21, 22, 32]. The (M 1)st price auction is the uniform price generalization of the second price Vickrey auction [26] that allows for the sale and purchase of multiple units of a good. Given a set of bids including M units offered for sale, the (M 1)stprice auction sets a price equal to the (M 1)st highest ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.

....no auction changes its allocation. At this point, the auctions clear, and each bidder is notified of the final prices and how many units it transacted in each good. Note that a quiescent economy may not be in a solution state, valid or invalid. Each auction runs according to (M 1)st price rules [19, 20, 31]. The (M 1)st price auction is the uniform price generalization of the second price Vickrey Auction [24] that allows for the sale and purchase of multiple units of a good. Given a set of bids including M units offered for sale, the (M 1)st price auction sets a price equal to the (M 1)st ....

M. A. Satterthwaite and S. R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.

....parse bid strings into machine manipulable representations. Classes at the third level implement specific clearing algorithms. Figure 3 diagrams the data structures at each level for an auctioneer that uses the 4heap algorithm [2] to implement the family of auctions based on the k double auctions [1]. 3 3.3.1 Auctioneer Event Handling When the auctioneer receives a LOAD message, it retrieves the auction description from the database and all bids that have an admitted state. Bids are loaded in order of submission and hashed by owner ID. If the bid has a fixed expiration time, the bid is ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--33, 1989.

....rule serves a key role in establishing relationships between market quiescence and solution convergence of the economy [ Walsh and Wellman, 1998 ] In particular, the market al..ways reaches quiescence with the bidding policies described in Section 5.2. According to the the (M 1)st price rules [ Satterthwaite and Williams, 1989; Wurman et al. 1998 ] an auction balances reported supply and demand at a uniform clearing price . Winners include all buyers sellers strictly above below the price, and, to maximize the benefits from trade, some agents at the clearing price. 5.2 Bidding Policies Although multiagent system ....

Mark A. Satterthwaite and Steven R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.

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Satterthwaite, M. and S. Williams (1989), "Bilateral Trade with the Sealed-bid k- double Auction: Existence and E#ciency," Journal of Economic Theory 48: 107--133. 36

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M. A. Satterthwaite and S. R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.

No context found.

M. A. Satterthwaite and S. R. Williams. Bilateral trade with the sealed bid k-double auction: Existence and efficiency. Journal of Economic Theory, 48:107--133, 1989.

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