Entertainment Tickets

ATTac-2000's bidding strategy for the entertainment tickets hypothesizes that for each ticket, the opponent buy (sell) price remains constant over the course of a single game (but may vary from game to game). So as to avoid underbidding (overbidding) for that price, ATTac-2000 gradually decreases (increases) its bid over the course of the game. The initial bids are always as optimistic as possible, but by the end of the game, ATTac-2000 is willing to settle for deals that are minimally profitable. In addition, this strategy serves to hedge against ATTac-2000's early uncertainty in its final allocation of goods to clients.

On every bidding iteration, ATTac-2000 places a buy bid for each type of entertainment ticket, and a sell bid for each type of entertainment ticket that it currently owns. In all cases, the prices depend on the amount of time left in the game (T_l), becoming less aggressive as time goes on (see Figure 1).

  

Figure 1: ATTac-2000's bidding strategy for entertainment tickets. The black circles indicate the calculated values of the tickets to ATTac-2000. The lines indicate the bid prices corresponding to those values. For example, the solid line (which increases over time) corresponds to the buy price relative to the buy value. Correspondence between the text and the lines is indicated by similar line types and boxes surrounding the text.

For each owned entertainment ticket E, if E is assigned in G^*, let V(E) be the value of E to the client to whom it is assigned in G^* (``owned, allocated sell value'' in Figure 1). ATTac-2000 offers to sell E for $\min(200,V(E) + \delta)$ where $\delta$decreases linearly from 100 to 20 based on T_l.¹ If there is a current bid price greater than the resulting sell price, then ATTac-2000 raises its sell price to 1 cent lower than the current bid price in order to get as high a price as possible.

If E is owned but not assigned in G^* (because all clients are either unavailable that night or already scheduled for that type of entertainment in G^*), let V(E) be the maximum value for E over all clients, i.e. the greatest possible value of E given the client profiles (``owned, unallocated sell value'' in Figure 1). ATTac-2000 offers to sell E for $\max(50,V(E) - \delta)$ where $\delta$ increases linearly from 0 to 50 based on T_l. Once again, ATTac-2000 raises its price to meet an existing bid price that is greater than its target price. This strategy reflects the increasing likelihood as the game progresses that G^* will be close to the final client allocation, and thus that any currently unused tickets will not be needed in the end. When in active mode, ATTac-2000 assumes that G^* is final and offers to sell any unneeded tickets for $30 in order to obtain at least some value for them (represented by the discrete point at the bottom right in Figure 1). Below $30, ATTac-2000 would rather waste the ticket than allow a competitor to make a large profit.

Finally, ATTac-2000 bids to buy each type of entertainment ticket E(including those that it is also offering to sell) based on the increased value that would be derived by owning E. Let ${G^*}_E^\prime$ be the optimal allocation that would result were E owned (``buy value'' in Figure 1). Note that ${G^*}_E^\prime$ could have different flight and hotel assignments than G^* so as to make most effective use of E. Then, ATTac-2000 offers to buy E for $V({G^*}_E^\prime) - V({G^*}) - \delta$, where $\delta$ decreases linearly from 100 to 20 based on T_l.

All of the parameters described in this section were chosen arbitrarily without detailed experimentation. Again our intuition is that, unless opponents know and explicitly exploit these values, ATTac-2000's performance is not very sensitive to them.