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While earlier research suggested that children with TS demonstrated signi cant impairment on measures of executive function, more recent research with better-de ned groups of children with TS only and TS with comorbidity suggests that many de cits are accounted for by comorbid ADHD among children with TS. For example, TS has been characterized as a disorder of inhibitory control, and de cits in inhibition are often reported among children with TS (Stern, Blair, & Peterson, 2008), which would be consistent with disruption of the cortico-striatal-thalamic-cortical circuitry and basal ganglia function described previously (S. V. Muller et al., 2003). In contrast, Ozonoff et al. (1998) found that de cits in inhibition were largely dependent on comorbidity, as children with TS alone performed similarly to controls but children with TS plus ADHD and/or OCD showed de cits compared to the control group. Interestingly, inhibition de cits also were related to number and severity of TS symptoms. In another study, children with TS alone and children with ADHD alone showed more intrusions (i.e., inhibition errors) than controls on one verbal list learning task, but the children with TS performed in the average

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Subtracting from both sides the square of the expected value of the winner s bid, ie Evn 1/ /2 , we see that the winner s bid has a smaller variance in the rst-price auction, and so a risk-averse seller would prefer a rst-price auction Let us verify this for two bidders whose valuations are uniformly distributed on [0; 1] In the rst-price auction, each bidder bids half his valuation, so the revenue is 1=2/ maxfv1 ; v2 g In the second-price auction each bids his valuation and the revenue is minfv1 ; v2 g Both have expectation 1=3, but the variances are 1=72 and 1=18, respectively Thus, a risk-averse seller prefers the rst-price auction 1416 Collusion It is important when running an auction to take steps to prevent bidders from colluding.

[0] [0] [0] 1. Choose starting values: [0] = [ 1 , 2 , . . . , J ]. 2. At the tth step starting at t = 1, complete the single cycle by drawing values from the J conditional distributions given by [t] [t 1] [t 1] [t 1] [t 1] 1 ( 1 | 2 , 3 , . . . , J 1 , J ) [t] [t] [t 1] [t 1] [t 1] , . . . , J 1 , J ) 2 ( 2 | 1 , 3 [t] [t] [t] [t 1] [t 1] ) 3 ( 3 | 1 , 2 , . . . , J 1 , J

Collusion occurs when two or more bidders make arrangements not to bid as high as their valuations suggest, and so reduce the seller s revenue Antique auctions are notorious for this A number of bidders form a ring and agree not to bid against one another and on whom the winner will be This lowers the winning bid Later, the winner distributes his gain amongst all the bidders, in proportion to their market power, so that all do better than they would have done by not colluding In some spectrum auctions in the US, there have been instances of bidders using the nal four digits of their multimillion dollar bids to signal to one another the licenses they want to buy Thus, a critical characteristic of an auction is how susceptible it is to collusion.

This depends upon what incentives there are for players to stand by the promises they make to one another when agreeing to collude We can see that an ascending English auction is susceptible to collusion Suppose the bidders meet and determine that bidder 1 has the greatest valuation They agree that bidder 1 should make a low bid and win the object for a payment close to zero No other bidder has an incentive to bid against bidder 1, since he cannot win without ultimately outbidding bidder 1; yet if he does so he would incur a loss Thus, the agreement between the bidders is self-enforcing and the auction is susceptible to collusion In contrast, collusion is dif cult in a Dutch auction, or in a rst-price sealed-bid auction There is nothing to stop a ring member bidding higher than was agreed.