The frequency of posts on our class weblog has grown to about eight per day. We are still reading and enjoying them, and we are grading them. But given the rate at which posts are arriving we will begin commenting on the digest post only on those where we want to add something.

Fifo writes about combinatorial auctions in which the seller has many objects to sell and the buyers are interested in buying packages of objects. The idea is that a buyer’s value for one object depends on whether or not he wins another object. This makes the problem much more complex than the auctions we have talked about in class. Interestingly, with a bit of generalization, Vickery’s results on second-price auctions also solve a simple version of this problem with independent, private values. If bidders bid on all packages of objects, then in a second-price-like auction, truthful bidding is a dominant strategy. Many issues remain because this auction may be too complex to actually run, values may not be simple and they may not be easy for buyers to access. The extension of the Vickery auction that solves the problem is called a Vickery-Clarke-Groves mechanism. We will discuss this mechanism later in the course.

Princess Felicia Octavia Gabrielle del Granditois raises interesting questions about fairness and justice in games. We have seen similar issues in our discussion of the ultimatum game and in network exchange where individuals are willing to fore-go small amounts of money rather than accept unfair deals. The behavioral economics literature discusses many such departures from narrowly defined rationality. One question that this discussion raises is: what are the payoffs in a game? In class we have taken payoffs to be the value of some private good that the individual receives, like money. In principle, there is nothing in game theory (or the decision theory that underlies it) that requires this choice. An individual’s payoff could just as well be some function of the amount of money they receive and the amount of money the other player receives. This post also relates Nash equilibrium to a process of natural selection. Later in the course we will discuss Evolutionary Game Theory which begins with natural selection and derives an equilibrium which is similar to, but not quite the same as, Nash equilibrium.

Spero discusses preferential attachment models (and their limitations) as a way to think about growth in networks. In the models we have discussed in class the networks are static. This is clearly a limitation and Spero discusses interesting ideas about how networks might evolve if power affects who joins or leaves a network. For example, think about the 4-node network exchange model in which the interior nodes have weak power over the end nodes. Now suppose that one of the end nodes adds a friend so that we have a 5-node network. Who gains and who loses? Or what happens if one of the end nodes decides to quit?