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# A Simplified Model of the UMDL

In order to capture the main characteristics of the UMDL, and to facilitate the development and testing of agents, we have defined an ``abstract'' economic model. We define an economic society of agents as one where each agent is either a buyer or a seller. The set of buyers is B and the set of sellers is S. These agents exchange goods by paying some price , where P is a finite set. The buyers are capable of assessing the quality of a good received and giving it some value , where Q is also a finite set.

The exchange protocol, seen in Figure 1, works as follows: When a buyer wants to buy a good g, she will advertise this fact. Each seller that sells that good will give his bid in the form of a price . The buyer will pick one of these and will pay the seller. The seller will then return the specified good. Note that there is no law that forces the seller to return a good of any quality. It is up to the buyer to assess the quality q of the good. Each buyer b also has a value function for each good that it might wish to buy. The value function, returns a number that represents the value that b assigns to that particular good at that particular price and quality. Each seller , on the other hand, has a cost associated with each good it can produce. Therefore, if seller s gets paid p for good g, his profit will be . Since we assume that cost and payments are expressed in the same unit (i.e. money), the profit equation simplifies to . The buyers, therefore, have the goal of maximizing the value they get for their transactions, and the sellers have the goal of maximizing their profits.

Figure 1: View of the protocol. We show only one buyer B and three sellers S1, S2, and S3. At time 1 the buyer requests bids for some good. At time 2 the sellers send their prices for that good. At time 3 the buyer picks one of the bids, pays the seller the amount and then, at time 4, she receives the good.

Jose M. Vidal
jmvidal@umich.edu
Wed Aug 21 07:12:37 EDT 1996