differences are positive showing that ATTac-2000 outscored all other agents on average 5 Statistical significance was computed from paired T tests all results are significant at the level except for the one marked in italics  As mentioned before if the number of high bidders is greater than or equal to we expect the price for contentious hotels to rise and in all such scenarios ATTac-2000 significantly outperforms all the other agents  The large score differences appearing in the top rows of Table are mainly due to the fact that the other agents get large  negative scores since they end up buying many expensive hotel rooms In these experiments ATTac-200 always uses its adaptive hotel price expectations  even when there are only high bidders In the last row when the number of high bidders is very little bidding up of hotel prices is expected and in this case  we do not get statistical significance relative to the two high bidders agent and agent since their strategies are nnarly identical to ATTac-2000s in this case We do get high statistical significance relative to all the other agents  copies of variant     however  Thus  ATTac-2000 s adaptivity to hotel prices seems to help a lot when hotel prices do skyrocket and does not seem to prevent ATTac-2000 from winning on average when they don t The results of Table provide strong evidence for ATTac-2000 s ability to adapt robustly to varying number of competing agents that bid up hotel prices near the end of the game Note that ATTac-200 is not designed to perform well against itself  If   copies of ATTac200 play against each other repeatedly they will all favor the same hotel rooms and thus consistently all get large negative scores  It would be interesting to determine whether there exists a strategy that is both harmful to ATTac and beneficial to the adversary

## 5. Related Work

Although there has been a good deal of research on auction theory  especially from the per spective of auction mechanisms  Klemperer studies of autonomous bidding  agents and their interactions are relatively few and recent  TAC is one example  FM
is an other auction test bed  which is based on fishmarket auctions  Rodriguez Aguilar  Martin Noriega Garcia   Sierra Automatic bidding agents have also been created in this domain  Gimenez Funes  Godo  Rodriguez Aguiolar     Garcia Calves There have been a number of studies of agents bidding for a single good in multiple auctions  Ito Fukuta Shintani   Sycara      Anthony Hall Dang   Jennings  Preist Bartolini Outside of  but  related to  the  auction  scenario  automatic shopping  and Phillips pricing agents for internet commerce have been studied within a simplified model  Green Kephart wald The control of the contr of which qualified to compete in the semi finals and finals in Boston The designs of these agents were motivated by a wide variety of research interests including machine learning  artificial life  experimental to economics  real time systems  and choice theory   Greenwald Stone Our own approach was motivated by our research interests in multiagent learning   Littman Singh Kearns Mansour Based on the problem description Stone we expected to find several learning opportunities in the domain  As noted above  detailed