The Trading Agent Competition is a multiple auction-type game competition held every year. A trading agent is a computer program that tries to satisfy the preferences of its client(s) by attempting to assemble a variety of travel packets through different types of auctions and competitions. The agent who fulfills his client’s preferences best wins.

This creates several problems that this computer program has to deal with. They have to deal with multiple auctions occurring at the same time, and try to package everything to meet their client(s) preferences. They also have to deal with the strategies of other agents trying to compete for the same goods.

A more complete explanation of the game and rules can be found here:
TAC Competition

In 2002 Ioannis Vetsikas, a Cornell student, won the competition. He also wrote a paper dealing with one of the sub-problems and how it relates to different types of auctions and Nash Equilibrium.

The paper can be found here:
Vetsikas Paper

This paper leads to a very interesting analysis of Nash Equilibrium. It links auctions and equilibrium to develop an optimal strategy to play this game. This analysis allows for development of algorithms that have better chances to win the TAC game. It is a good example of taking the theory (albeit much more advance) we learned in class and applying it to a practical situation.

In the Trading Agent the agents are competing for airline tickets, hotel rooms, and event tickets. In his paper, Vetsikas analyzes the sub-problem of the hotel room reservations.

There are 16 hotels rooms available each night at each of two hotels. Rooms are sold by the day by each hotel room in a separate, ascending, multi-unit, 16th price auction. A random auction will close every minute through-out the game. Agents place their bids between closing times in a sealed price auction. Every consecutive round agents who didn’t win a unit place another sealed bid auction equal to or higher than the previous round. Agents can also not retract bids.

They propose a theorem which states a differential equation that all equilibriums are solutions too. This guarantees that an equilibrium does exist and is unique.

To expand upon this theorem they analyze the Nash Equilibrium for a single unit auction, with N agents, using a first price sealed bid auction. They then move on to the multi-unit auction with N agents. They derive several differential equations necessary to compute an auction that closes at multiple possible times. They explicitly compute the solution for the last two rounds, and then recursively compute the solutions for the previous rounds.