Research in the field of algorithmic game theory that explores a relatively new class of auctions with interdependent values.
This research focuses on a topic from algorithmic game theory. In this field, we study how we can design mechanisms with multiple selfish agents to guarantee that they behave in a certain way. The topic of this research focuses on auctions with interdependent values where multiple agents have some information about an item being auctioned, but their value for the item can depend on information of other agents. Our goal as the mechanism designer is to design an auction which obtains this information from the agents and allocates it to the agent who values it the most (i.e. this would get us the optimal welfare). We want to ensure that the agents tell the truth, and we have a guarantee on how much of the optimal welfare we can obtain. A classic example of this setting in the real world is with oil drilling. Say that someone offers up a certain patch of land for oil drilling and multiple oil companies study the land and obtain different information about it. It is possible that some companies may value the land more if they knew what other companies did. To effectively auction off the land, the auctioneer asks each of the companies for this information to make it public knowledge. However, many companies may be incentivized to lie so other companies do not know the true value of the land. In this research, we explore many settings similar to the one described above, but we assume that there are restrictions on how an agent’s value can depend on the information of other agents (note that it is assumed that information is some numeric value). An example of this would be restricting the valuation functions of agents to be linear. We can also make assumptions on how the auction is run. An example of this is running a clock auction where we tentatively set winners of an auction and ask other agents if they are willing to increase their bid until we are left with a set of feasible bidders. The focus of this research is mostly on randomized mechanisms, and we look at how much of the optimal welfare we can get in expectation. We hope to get new results from this research.