In a recent post tekhn3 mentioned an interesting auction type that we have not discussed in class. It seems to be a form of an all-pay auction. In an all-pay auction every bidder pays their bid, but only the highest bidder wins the good being sold. Lobbying can be viewed as an all-pay auction as every lobbyist pays, but only one is successful. You might think that since every bidder pays, the seller would generate more revenue with this form of auction than with a second price auction. But optimal bids are very different here than in a second price auction. In particular, bidding your true value is obviously not an optimal strategy in this auction. The Revenue Equivalence Theorem shows that expected seller revenue is the same for an all-pay auction as for a second price auction (or a first price auction). A good reference for this is the on-line book by Paul Klemperer.

Recent posts by peterk9286 and by sonja379 discuss applications of game theory to viruses and to animal behavior. In class we have discussed games in which the payers are people, but the theory applies to any setting in which the payoffs to those playing the game depend on their own actions and on the actions of other payers. In evolutionary biology, animals or genes are the players, and the payoffs are often taken to be fitness. A branch of game theory, called Evolutionary Game Theory, deals with the dynamics of populations in these games. John Maynard Smith formulated the concept of Evolutionarily Stable Strategies to deal with these games.

In a recent post arcanus wrote about various ways to visualize networks. In class we typically draw very simple graphs in which the important structural properties are immediately apparent. But how you represent the graph can make patterns easy or difficult to see. There is a literature describing various ways of representing networks. One key element is dividing the nodes into communities in which the nodes in a community interact more with each other than with those outside of the community. Structural equivalence is one criterion that is used to group nodes; nodes are structurally equivalent if they have identical relationships to other nodes. Matt Jackson presented an alternative approach that classifies nodes into communities using within and across group interactions in an Institute for Social Sciences seminar this past Fall.