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Introduction Two of the most common non-price m...</title><content type='html'>1. Introduction Two of the most common non-price mechanisms that allocate &lt;BR/&gt;objects to individuals are auctions and lotteries. In auctions the probability &lt;BR/&gt;that player i wins depends on the other bids, as well as the size of payments. &lt;BR/&gt;In a lottery all agents have the same probability of wining the object, and the &lt;BR/&gt;actions of the other players might affect the winning prize (for example, when &lt;BR/&gt;there is more than one winner the winning prize will be divided equally) but do &lt;BR/&gt;not affect the probability of winning. In this paper we conduct - both &lt;BR/&gt;theoretical and empirical - analysis of a selling mechanism that combines &lt;BR/&gt;elements of an auction and a lottery. The mechanism studied is used by the &lt;BR/&gt;internet portal http://www.BestBidsAuction.com, which also provided data of its &lt;BR/&gt;auctions. Before each auction, the auctioneer determines three parameters of the &lt;BR/&gt;auction: the highest bidallowed (which is less than 10% of the retail value of &lt;BR/&gt;the object), the maximum number of bids allowed before the auction closes, and &lt;BR/&gt;the entry fee each bidder needs to pay when submitting his bid. All of these &lt;BR/&gt;values are made public before the bidding starts. After the bidders pay the &lt;BR/&gt;participation fee, they submit sealed bids, less than or equal to the highest &lt;BR/&gt;bid allowed. The winning bid is the highest unique bid (in the sense that no one &lt;BR/&gt;else bid exactly the same amount) among all bids received. The winner then pays &lt;BR/&gt;his bid price and obtains the object. We call the selling mechanism adopted by &lt;BR/&gt;the portal a Gambling Auction, because it has features that make it a &lt;BR/&gt;combination of an auction and a lottery. First, the bid and the probability of &lt;BR/&gt;winning are not monotonically related, because a lower bid might well win the &lt;BR/&gt;auction if many bidders are placing high bids. Consequently there is no obvious &lt;BR/&gt;bid that maximizes the probability of winning and, as we show, in equilibriumall &lt;BR/&gt;bids provide the same probability of winning. Second, this mechanism is not a &lt;BR/&gt;pure lottery either because the winning probability is determined by the action &lt;BR/&gt;of the biddersand not by an exogenous randomizing device: the winner is the one &lt;BR/&gt;that submits the highest unique bid. Note that, under the symmetric Nash &lt;BR/&gt;equilibrium of the game, the equal winning probabilities this auction creates &lt;BR/&gt;and the expected payments can be 2&lt;BR/&gt;&lt;BR/&gt;      &lt;BR/&gt;implemented using a lottery and thus the two types of mechanisms are outcome &lt;BR/&gt;equivalent if the bidders are risk neutral and follow the symmetric &lt;BR/&gt;equilibrium.2The theoretical analysis finds that in a symmetric equilibrium each &lt;BR/&gt;bidder chooses his bid using a distribution function over a support that has no &lt;BR/&gt;gap. This equilibrium strategy is increasing; namely the probability of placing &lt;BR/&gt;a higher bid is not less than that of a lower bid. The intuition is that &lt;BR/&gt;otherwise a higher bid would make winning more likely and thus be more &lt;BR/&gt;profitable than a lower bid, which would makeeveryone prefer it, destroying the &lt;BR/&gt;alleged equilibrium bidding pattern. We test this prediction with a novel data &lt;BR/&gt;set collected from the portal http://www.BestBidsAuction.com, which implements auctions &lt;BR/&gt;described above. The data confirms that the probability of a higher bid is not &lt;BR/&gt;less than a lower bid. We also find that an increase in the number of bidders &lt;BR/&gt;increases the number of bids for a given slot, although reduces the probability &lt;BR/&gt;that each bidder places his bid at this given slot. This leads to an increase of &lt;BR/&gt;the distance between the maximum bid allowed and the actual winning bid. We also &lt;BR/&gt;tested the theoretical prediction that each bid has the same probability of &lt;BR/&gt;winning by constructed a frequency table (Table 4). This table measures the &lt;BR/&gt;frequencywith which the highest bid wins by calculating the number of auctions &lt;BR/&gt;in which the highest bid won divided by the number of instances in which a &lt;BR/&gt;highest bid was placed. We repeat this exercise at lower bid levels and ask &lt;BR/&gt;whether the empirical frequencies are2This Gambling Auction is also interesting, &lt;BR/&gt;because it can be used in countries or U.S. states that forbid gambling, because &lt;BR/&gt;the rules of the mechanism do not meet the traditional definitions of lottery. &lt;BR/&gt;The mechanism might attract people who like participating in gambling &lt;BR/&gt;activities, since at a relatively low cost one have the opportunity to win a &lt;BR/&gt;sizable prize. The auctioneer will make more money using this mechanism than by &lt;BR/&gt;regular auction mechanisms if participants are risk lovers. Empirically, this is &lt;BR/&gt;the case since these auctions have a negative expected profit for a bidder. This &lt;BR/&gt;mechanism is similar to a rotating saving and credit associations (roscas) in &lt;BR/&gt;which group of people save for indivisible good. Each period allthe people &lt;BR/&gt;contribute to the rosca and it is given to someone randomly that is able to get &lt;BR/&gt;the good. In thenext period it is given to somebody else and so on (see Besley, &lt;BR/&gt;Coate and loury (1993)). In our mechanismthe good is also distributed eventually &lt;BR/&gt;randomly and each individual pays the participation fees, but theexpected payoff &lt;BR/&gt;is negative, since the auctioneer obtains a positive profit and the winner pays &lt;BR/&gt;extra amount of money (the winning bid) in order to get the good. 3&lt;BR/&gt;&lt;BR/&gt;      Page 4&lt;BR/&gt;indeed equal as suggested by the theory. Some formal chi-square tests and &lt;BR/&gt;informalanalysis suggest that the theoretical bid distribution is not consistent &lt;BR/&gt;with the data. In addition, unlike other studies that estimated the demand for &lt;BR/&gt;lottery games and found that consumers respond to the expected returns, we found &lt;BR/&gt;that consumer demand for this lottery is not sensitive to the expected payoff &lt;BR/&gt;but it is sensitive to the size of theprize. The paper is organized as follows. &lt;BR/&gt;In the next section we characterize the equilibrium strategies of the auction &lt;BR/&gt;game and provide some comparative static results. Section 3 describes the data, &lt;BR/&gt;while Section 4 performs empirical analysis. A final section offers some &lt;BR/&gt;concluding remarks. 2. Theoretical considerations We will first describe the &lt;BR/&gt;model we consider and then show that in a symmetric equilibrium a higher bid is &lt;BR/&gt;chosen with higher probability. There are kbidders3=3who all value the object at &lt;BR/&gt;the retail price, v. After paying an entry fee of c each bidder submits a sealed &lt;BR/&gt;bid that is less than a maximum value b &lt;&lt; v. We assume that each bidder places &lt;BR/&gt;only one bid. There is a minimum bid increment, which we normalize to 1. The &lt;BR/&gt;winner is the one who placed the highest bid that was not bid by anyone else. If &lt;BR/&gt;there is no such bid, then we assume that the seller runs the auctionagain with &lt;BR/&gt;the same set of bidders. The internet portal reports that, in the rare event of &lt;BR/&gt;no unique bid, the bidders will be notified about the situation and asked to &lt;BR/&gt;submit a new bid without additional charge. The winner has to pay an amount &lt;BR/&gt;equal to his bid, while the losers only pay the entry fee. In addition we assume &lt;BR/&gt;that k, v and b are such that inequilibrium the winning bid is close to b; in &lt;BR/&gt;other words, we assume that the bid increment is low compared to the value of &lt;BR/&gt;the object, and thus the winning bid is close to 3In the auction at the above &lt;BR/&gt;website only the maximum number of bidders is specified, but the number of &lt;BR/&gt;actual bidders is usually close to the allowed maximum number of bidders, so one &lt;BR/&gt;may assume that the number of bidders is a known constant, k.4&lt;BR/&gt;&lt;BR/&gt;      Page 5&lt;BR/&gt;the maximum allowed bid b.4Under such conditions we make the simplifying &lt;BR/&gt;assumption that each bidder is interested in maximizing his probability of &lt;BR/&gt;winning the object, ignoring the payment consequences of his bid.5The entry fee &lt;BR/&gt;is already sunk at the bidding stage, so it does not affect bidding strategies. &lt;BR/&gt;First, note that the above game has an equilibrium, since after imposing &lt;BR/&gt;aminimum bid requirement of 0, the auction becomes a finite game. Moreover, &lt;BR/&gt;using Kakutani�s fixed point theorem we may also show that a symmetric (mixed &lt;BR/&gt;strategy) equilibrium exists. Claim 1: In any symmetric equilibrium there is no &lt;BR/&gt;gap in the support of the equilibrium strategy. Proof: Suppose there was a gap &lt;BR/&gt;at b�. Then bidding b� would strictly dominate bidding the next available bid &lt;BR/&gt;b�-1, which yields a contradiction in that b�-1 is in the support of the &lt;BR/&gt;equilibrium strategy. Note, that the above claim also implies that the high end &lt;BR/&gt;of the support is the maximum allowed bid, b. Then a symmetric equilibrium is &lt;BR/&gt;characterized by the number of bidsemployed, n, and the probabilities of each of &lt;BR/&gt;those bids,)1Pr(+-=ibpiwhere i = 1,�,n. Theorem 1: In a symmetric equilibrium &lt;BR/&gt;the probability of a higher bid is not less than a lower bid: i &gt;j implies that &lt;BR/&gt;pi= pj. Moreover, pi = pjcan hold only when there are four bidders. In that &lt;BR/&gt;case, the unique equilibrium has p1= p2 = 1/2. Proof: See the appendix A. 4On &lt;BR/&gt;average, the distance between the winning bids and the maximum allowed bid in &lt;BR/&gt;our data is less than14 cents on average, and the maximum distance is less than &lt;BR/&gt;$1.5. 5The bidder�s problem is to choose bithat will maximize: P(bi)(V- bi)-C= &lt;BR/&gt;P(bi)(V-b+b-bi)-C= P(bi)(V-b)+P(bi)(b-bi)-C, where P(bi) is bidder i probability &lt;BR/&gt;of winning the object when placing a bid of bi, V is the object valuation, b is &lt;BR/&gt;the highest bid allowed and C is the participation cost. If all bidders follow a &lt;BR/&gt;symmetric equilibrium, then the probability of receiving the object is the same &lt;BR/&gt;for each bidder. Asmentioned before, the distance between the winning bids and &lt;BR/&gt;the maximum allowed bid in our data is lessthan 14 cents on average, and the &lt;BR/&gt;maximum distance is less than $1.5. So on average, when one maximizesthe &lt;BR/&gt;probability of winning the object and ignores the second part of the objective &lt;BR/&gt;function; one ignores a monetary incentive of only a few cents. If we drop this &lt;BR/&gt;simplifying assumption then our results do not hold as stated. It is no longer &lt;BR/&gt;necessarily true that the equilibrium does not have a gap, since the equilibrium &lt;BR/&gt;weidentify in the simplified game is not robust to large deviations, when a &lt;BR/&gt;bidder places a bid close to zero.However, since the largest admissible bid is &lt;BR/&gt;less than 10% of the value of the object, the incentive for this deviation might &lt;BR/&gt;be neglected in a first approach to model this game. This approach is also well &lt;BR/&gt;supportedby the data, since winning with a very low bid is very unlikely, as it &lt;BR/&gt;will be noted in the next section. 5&lt;BR/&gt;&lt;BR/&gt;      Page 6&lt;BR/&gt;The intuition behind these results is clear. Suppose, that the other bidders &lt;BR/&gt;randomize equally among the bids B = {b1., b2, �, bn}, where b1&gt; b2&gt; � &gt; bn. &lt;BR/&gt;Then it is easy to see that if bidder i places the bid b1, then he has a higher &lt;BR/&gt;probability of winning then with any other bid that belongs to B. But this &lt;BR/&gt;yields a contradiction, because in a symmetric equilibrium bidder i use a mixed &lt;BR/&gt;strategy with support on B, and thus he isindifferent between any of the bids &lt;BR/&gt;belonging to B. The incentive to bid high iseliminated only if a bidder expects &lt;BR/&gt;that there are more bidders who placed a high bid than who placed a lower one. &lt;BR/&gt;Thus, in equilibrium each bidder must place a higher bid with higher &lt;BR/&gt;probability. Let us consider some examples with a small number of bidders. &lt;BR/&gt;First, if there are three bidders, then, in the unique equilibrium all the bids &lt;BR/&gt;down to zero are used. With Tpossible bids including 0 it holds that for all 1 &lt; &lt;BR/&gt;i &lt; T, pi= 1/ 2T-iand p0=1/ 2T-1is theunique symmetric equilibrium of the game. &lt;BR/&gt;If k = 4, it is easy to show that the unique symmetric equilibrium is such that &lt;BR/&gt;p1= p2= �. In the case when k = 5 an equilibrium is such that &lt;BR/&gt;0.010}.p0.083,p0.197,p0.337,p0.372,{p54321=====We can confirm that it is indeed &lt;BR/&gt;equilibrium. A bidder�s utility is his probability of winning plus the &lt;BR/&gt;probability of a complete tie divided by five. Suppose that a bidder places the &lt;BR/&gt;maximum allowed bid. A bidder wins in this case if no one else placed thisbid, &lt;BR/&gt;i.e. with probability .)1(w411p-=A complete tie occurs, if one or two other &lt;BR/&gt;bidders placed the highest bid and the other two or three placed the same bid, &lt;BR/&gt;or if all others placed the highest bid. This probability is &lt;BR/&gt;.)(p})(p)(p)(p){(p)(p6})(p)(p)(p){(p4pt4125242322213534333211++++++++=Since in &lt;BR/&gt;equilibrium each bidder obtains a utility of 1/5 we obtain the following &lt;BR/&gt;condition:.515w11=+t6&lt;BR/&gt;&lt;BR/&gt;One can compute the corresponding probabilities, wi, tifor i = 2,3,4,5 and write &lt;BR/&gt;up thecondition that for all i:6.515wi=+itThen one obtains 5 equations in 5 &lt;BR/&gt;unknowns (the �s) and this system has a unique real valued solution, the vector &lt;BR/&gt;stated above. Finally, one needs to check that by placing a lower bid than bid &lt;BR/&gt;5, the achieved utility is not higher than 1/5. By placing such a bid the &lt;BR/&gt;deviating bidder wins if and only if the other four bidders tied. Then the &lt;BR/&gt;incentive constraint can be written as: ip.51622514=+???=jijiiipppThe proposed &lt;BR/&gt;strategy profile satisfies these conditions and thus it is equilibrium.For k = 5 &lt;BR/&gt;the distribution of the winning bid is &lt;BR/&gt;.}011.0,098.0,211.0,325.0,357.0{54321=====pppppFor k = 6, an equilibrium is &lt;BR/&gt;0.109},p0.248,p0.309,p0.334,{p4321====and the distribution of the winning bid is &lt;BR/&gt;}.122.0,247.0,303.0,329.0{4321====ppppFor k = 7 an equilibrium is &lt;BR/&gt;0.078},45p0.296,{54321=0.137=,0.22=,0.26==pppp7and the distribution of the &lt;BR/&gt;winning bid is .}084.0,137.0,219.0,272.0,287.0{54321=====pppppIt is apparent &lt;BR/&gt;that the size of the support of the equilibrium strategy is not monotonic. &lt;BR/&gt;Excluding the case of 3 bidders, which seems non-generic, one conjecture 6The &lt;BR/&gt;corresponding probabilities for wiand tiare different for every i. In order to &lt;BR/&gt;save space the complete set of equations is not reported here but it is &lt;BR/&gt;available upon request from the authors. 7We did not show that the above &lt;BR/&gt;equilibria are unique for a given k. For this one would need to show thatif one &lt;BR/&gt;considers a different number of bids for a given k than the one considered &lt;BR/&gt;above, then no solutionexists to the resulting system of incentive constraints. &lt;BR/&gt;We only showed at this point that there are no other equilibria for k=4, 5, 6, 7 &lt;BR/&gt;when we consider up to 7 possible bids. Our conjecture is that these equilibria &lt;BR/&gt;are unique in these cases and moreover, for any k there is a unique equilibrium &lt;BR/&gt;of the game.7&lt;BR/&gt;&lt;BR/&gt;      &lt;BR/&gt;that emerges is that the more bidders there are the less concentrated become the &lt;BR/&gt;equilibrium strategies. Although there is no monotonicity in the length of the &lt;BR/&gt;support with respect the number of bidders, our conjecture is that the expected &lt;BR/&gt;distance betweenthe maximum allowed bid and the winning bid (the Gap) increases &lt;BR/&gt;with the number ofbidders. Namely, it is more likely that a bid further from the &lt;BR/&gt;maximum becomes the winning bid when the number of bidders increases. &lt;BR/&gt;Theoretically this is the case when the number of bidders is 4, 5, 6 or 7.83. &lt;BR/&gt;The DataThis section describes the data. The data source is &lt;BR/&gt;BestBidsAuction.com 9which is the Internet website of Best Bids Auction, a &lt;BR/&gt;Arizona company that manages and implements private auctions designed to raise &lt;BR/&gt;money for selected charities and member non-profit fundraising organizations. &lt;BR/&gt;The internet auction process is a combination of a lottery and an auction. &lt;BR/&gt;Before each auction, the auctioneer determines, among other things, the highest &lt;BR/&gt;bid allowed and the maximum number of bids that will be accepted for the &lt;BR/&gt;auction, and makes this information available for the bidders. In order to &lt;BR/&gt;participate in an auction, bidders submit sealed bids, less than or equal to the &lt;BR/&gt;highest bid allowed in US dollars and cents and agree to pay a bidding fee for &lt;BR/&gt;each submitted bid. The auction is a sealed bid auction in the sense that when a &lt;BR/&gt;bidder submits a bid he does not know what the other bids are until the auction &lt;BR/&gt;is over. Each auction is closed when it receives the maximum number of bids or &lt;BR/&gt;meets the other closing requirements.10After the auction closes, the participant &lt;BR/&gt;that submitted the successful (winning) bid is determined. The successful bid &lt;BR/&gt;8The expected Gap when k = 4 is 5.04=g, and for the other cases it is, &lt;BR/&gt;078.1*4...*055515=++=ppg162.16=gand 458.17=gwhen the number of bidders are 5, 6, &lt;BR/&gt;and 7 respectively. 9All the information has been taken from &lt;BR/&gt;http://www.BestBidsAuction.com. 10An auction will remain open until either the maximum &lt;BR/&gt;number of bids allocated for the auction is reached or the auction reaches &lt;BR/&gt;maturation (63 days for auctions requiring less than 200 bids, and 183 days for &lt;BR/&gt;auctions requiring 200 or more bids) and has received the minimum number of bids &lt;BR/&gt;required to close. If the minimum number of bids has not been reached, the &lt;BR/&gt;auction will be extended until the minimum numberof bids is met. At that time, a &lt;BR/&gt;closing date of three days will be set and posted on the auction. 8&lt;BR/&gt;&lt;BR/&gt;      Page 9&lt;BR/&gt;is the highest unique bid out of all bids received in the auction.11Duplicate &lt;BR/&gt;bids are used to calculate the number of bids required to close an auction but &lt;BR/&gt;are disqualified from being selected as the successful bid. For example, if a &lt;BR/&gt;single auction includes the following four bids: $69.42, $69.42, $48.69 and &lt;BR/&gt;$65.44, the winner will be the one who submitted $65.44. In the very unlikely &lt;BR/&gt;event that an auction closes and there is not a unique bid, all participants &lt;BR/&gt;receive an e-mail describing the situation and are asked to submit a new bid &lt;BR/&gt;without additional fees. Table 1 gives summary statistics from the different &lt;BR/&gt;auctions that took place during 2003 and 2004. The information provided on the &lt;BR/&gt;website includes all auctions that havebeen conducted in this period. The &lt;BR/&gt;products auctioned were electronic appliances (computers, TV�s, video games etc) &lt;BR/&gt;and gift cards (provided by Target, Shell, Wall-Mart, Starbucks etc). The mean &lt;BR/&gt;retail value of the items auctioned was $414.169. The most expensive item &lt;BR/&gt;auctioned was a Panasonic 42�� Plasma TV with a retail price of $4999, while the &lt;BR/&gt;cheapest item was a Nintendo Game Boy with a retail price of $79.99. The Maximum &lt;BR/&gt;Allowed Bid was almost always identical to the Maximum Submitted Bid, which &lt;BR/&gt;means that in almost all the auctions the highest submitted bid was the highest &lt;BR/&gt;allowed bid.12On average, the maximum allowed bid was 7.2% of the retail &lt;BR/&gt;price,13and it had a mean of $30.83. The highest Maximum Allowed Bid, $624.38, &lt;BR/&gt;occurred in the case of the Panasonic 42�� Plasma TV, while smallest Maximum &lt;BR/&gt;Allowed Bid, $2.94, was in the case of a $100 Starbucks gift card. The average &lt;BR/&gt;winning bid was $30.70, and it was, on average, 13.69 cents below the Maximum &lt;BR/&gt;Allowed Bid (and the maximum submitted bid). We define Gap as thedifference &lt;BR/&gt;between the maximum allowed bid and the winning bid. The minimum of this &lt;BR/&gt;variable is 0, which mean that the maximum allowed bid was the winner. The &lt;BR/&gt;maximum 11A unique bid is a bid that is not a duplicate bid. A "duplicate bid" &lt;BR/&gt;is a bid submitted by a participant in anauction where another participant(s) &lt;BR/&gt;has submitted a bid(s) for the identical amount.12There are 15 cases out of 310 &lt;BR/&gt;in which the highest submitted bid is less than the maximum allowed bid. In 10 &lt;BR/&gt;cases the difference is 1 cent. 13It seems that the auctioneer choose the &lt;BR/&gt;Maximum Allowed Bid such that it will be, on average, less than 10% of the &lt;BR/&gt;retail price. An OLS regression of the Maximum Allowed Bid on the retail price &lt;BR/&gt;yield a coefficient of 0.072 with standard error of 0.0024 (t-value of 29.59) &lt;BR/&gt;and R squared of 0.7398. It seems that the Maximum Allowed Bid is also &lt;BR/&gt;positively correlated with the Number of Bids per auction. An OLSregression of &lt;BR/&gt;the Maximum Allowed Bid on the Number of Bids yield a coefficient of 0.375 with &lt;BR/&gt;standarderror of 0.020 (t-value of 18.37) and R squared of 0.5228. An OLS &lt;BR/&gt;regression of the Maximum Allowed Bid on both the Retail Price and the Number of &lt;BR/&gt;Bids per auction yields coefficients of 0.1765 on the retailprice and -0.6648 on &lt;BR/&gt;the Number of Bids, both significant at 1% level. 9</content><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/10973959/112956726920843699/comments/default/117058666355662277'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/10973959/112956726920843699/comments/default/117058666355662277'/><link rel='alternate' type='text/html' href='http://behindthebadge.blogspot.com/2005/10/questions-about-marriage.html?showComment=1170586620000#c117058666355662277' title=''/><author><name>design</name><uri>http://www.bestbidsauction.com/product_detail.php?bid_id=59</uri><email>noreply@blogger.com</email></author><thr:in-reply-to xmlns:thr='http://purl.org/syndication/thread/1.0' href='http://behindthebadge.blogspot.com/2005/10/questions-about-marriage.html' ref='tag:blogger.com,1999:blog-10973959.post-112956726920843699' source='http://www.blogger.com/feeds/10973959/posts/default/112956726920843699' type='text/html'/></entry><entry><id>tag:blogger.com,1999:blog-10973959.post-116884409763258944</id><published>2007-01-14T22:54:00.000-08:00</published><updated>2007-01-14T22:54:00.000-08:00</updated><title type='text'>Hey nice blog. 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title=''/><author><name>lennykline61394461</name><uri>http://www.blogger.com/profile/16812071923410333212</uri><email>noreply@blogger.com</email></author><thr:in-reply-to xmlns:thr='http://purl.org/syndication/thread/1.0' href='http://behindthebadge.blogspot.com/2005/10/questions-about-marriage.html' ref='tag:blogger.com,1999:blog-10973959.post-112956726920843699' source='http://www.blogger.com/feeds/10973959/posts/default/112956726920843699' type='text/html'/></entry><entry><id>tag:blogger.com,1999:blog-10973959.post-114493297048259043</id><published>2006-04-13T05:56:00.000-07:00</published><updated>2006-04-13T05:56:00.000-07:00</updated><title type='text'>Here's a useful resources on gift giving for breas...</title><content type='html'>Here's a useful resources on &lt;A HREF="http://breast-cancer1.com/" REL="nofollow"&gt;gift giving for breast cancer&lt;/A&gt; worth a look: http://breast-cancer1.com/</content><link rel='edit' type='application/atom+xml' 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