
$$\mathrm{For~all}$$

$$\in\ \{$$

![0_image_0.png](0_image_0.png)

The demand for resources from the selected travel packages must not exceed the sum of the owned and bought resources constraint s

- For all The total quantity of each entertainment ticket allocated does not exceed what is owned cn straint s
- For all An entertainment ticket can and E 
AI
only be used if its day is between the arrival and departure day of the selected travel package con straint s
- For all and E {
4 entertainment ticket per day constraint s I N
Each client can only use one
- For all   and   E {.

entertainment ticket once

$$\begin{array}{c c c}{{}}&{{\}}&{{\sum}}\\ {{\tt o n c e}}&{{}}&{{\tt o n s t r\,a i n t\,s}}\end{array}$$

Each client can only use each type of
- All variables are integers
The solution to the resulting integer linear program is a value maximizing allocation of owned resources to customers along with a list of resources that need to be purchased Using the linear programming package  LPsolve" ATTac-2000 is usually able to find the ing globally optimal solution in under one second on a MHz Pentium II
Note that this is not by any means the only possible formulation of the allocation Greenwald  Boyan  Kirby  and Reiter   
studied a variant and found that it performed extremely well on a collection of large random allocation problems The above approa is guaranteed to find the optimal allocation  and usually does so quickly   However  since integer linear programming is an NP complete problem  some inputs can lead to significantly longer solution times  In a sample of    games taken shortly before the finals the allocator was called times In of the cases the optimization took a ss were all over a minute and all came from the same game  ATTac-2000 used the strategy that if an integer linear program takes or more seconds to solve the above mentioned greedy strategy over random client orderings is used as a fall back strategy for the rest of the game  This fall back strategy was not needed during the tournament finals

## 3.3 Adapt Ivity

In a TAC game instance the only information available to agents is the ask prices individual bids are not visible After each game transaction by transaction data is available but the lack of within game information precluded competitors from using detailed models of opponent strategies in decision making ATTac-2000 instead adapts its behavior on line in three different ways  adaptable timing of bidding modes  adaptable allocation strategy and adaptable hotel bidding