Wei Dai <weidai@eskimo.com> writes:
The first step toward a theory of reputation is defining what reputation is. The definition should correspond closely enough to our common sense notion of reputation so that our intuitions about it are not completely useless. I think a good definition is this: Alice's reputation of Bob is her expectation of the results of future interactions with Bob. If these interactions are mainly economic in nature, then we can represent Alice's reputation of Bob by a graph with the horizontal axis labeled price and the vertical axis labeled expected utility. A point (x,y) on the graph means that Alice expects to get y utils in a business transaction where she pays Bob x dollars. Given this definition, it is natural to say the Bob's reputation is the set of all other people's reputations of Bob.
This is an interesting approach. However this seems to fold in issues of reliability with issues of quality and value. If I have a choice of two vendors, one of whom produces a product which is twice as good, but there is a 50% chance that he will abscond with my money, I am not sure how to value him compared with the other. It seems like the thrust of the analysis later is to determine whether people will in fact try to disappear. But that is not well captured IMO by an analysis which just ranks people in terms of "utility" for the price.
A reputation system consists of a set of entities, each of whom has a reputation and a method by which he changes his reputation of others. I believe the most important question for a theory of reputation to answer is what is a good method (reputation algorithm) by which a person changes his reputation of others. A good reputation algorithm must serve his self-interest; it must not be (too) costly to evaluate; its results must be stable; a reputation system where most people use the algorithm must be stable (i.e., the reputation system must be an evolutionarily stable system).
I am not sure about this last point. It seems to me that a good reputation is one which is most cost-effective for its owner. Whether it is good for social stability is not relevant to the person who is deciding whether to use it. ("But what if everyone behaved that way? How would you feel then?") It may be nice for the analyst but not for the participant.
In a reputation based market, each entity's reputation has three values. First is the present value of expected future profits, given the reputation (let's call it the operating value). Note that the entity's reputation allows him to make positive economic profits, because it makes him a price-maker to some extent. Second is the profit he could make if he threw away his reputation by cheating all of his customers (throw-away value). Third is the expected cost of recreating an equivalent reputation if he threw away his current one (replacement cost).
I don't really know what the first one means. There are a lot of different ways I can behave, which will have impact on my reputation, but also on my productivity, income, etc. There are other ways I can damage my reputation than by cheating, too. I can be sloppy or careless or just not work very hard. So the first two are really part of a continuum of various strategies I may apply in life. The second is pretty clear but the first seems to cover too wide a range to give it a value.
Now it is clear that if a reputation's throw-away value ever exceeds its operating value or replacement cost, its owner will, in self-interest, throw away his reputation by cheating his customers. In a stable reputation system, this should happen very infrequently. This property may be difficult to achieve, however, because only the reputation's owner knows what its values are, and they may fluctuate widely. For example the operating value may suddenly decrease when his competitor announces a major price cut, or the replacement cost may suddenly decrease when he succeeds subverting a respected reputation agency.
It would be useful to make some of the assumptions a bit clearer here. Is this a system in which cheating is unpunishable other than by loss of reputation, our classic anonymous marketplace? Even if so, there may be other considerations. For example, cheating may have costs, such as timing the various frauds so that people don't find out and extricate themselves from vulnerable situations before they can get stung. Also, as has been suggested here in the past, people may structure their interactions so that vulnerabilities to cheating are minimized, reducing the possible profits from that strategy.
One way to answer some of these questions may be to create a model of a reputation system with a simple reputation algorithm and a simplified market, and determine by analysis or simulation whether it has the desirable properties. I hope someone who has an economist friend can persuade him to do this.
It might be interesting to do something similar to Axelrod's Evolution of Cooperation, where (human-written) programs played the Prisoner's Dilemma against each other. In that game, programs had reputations in a sense, in that each program when it interacted with another remembered all their previous interactions, and chose its behavior accordingly. The PD is such a cut-throat game that it apparently didn't prove useful to try to create an elaborate reputation-updating model (at least in the first tournaments; I understand that in later versions some programs with slightly non-trivial complexity did well). What you might want to do, for simplicity, is to have your universe consist of just one good (or service, or whatever), with some producers who all have the same ability, and some consumers, all with the same needs. Where they differ would be in their strategies for when to cheat, when to be honest, when to trust, and when to be careful. At any given time a consumer must choose which producer to buy from. The details of their interaction would appear to greatly influence the importance of reputation. Maybe there could be a tradeoff where if the consumer is willing to pay in advance he gets a better price than if he will only provide cash on delivery. (Unfortunately it seems like the details of this tradeoff will basically determine the outcome of the experiment. However maybe some values will lead to interesting behavior.) Producers who want to cheat could do so by offering greater discounts for payment in advance, offering low prices in order to attract as many customers as possible before disappearing. Consumers might rightly be suspicious of an offer that looks too good. Maybe it could be set up so consumers could cheat, too. No, I think that is too complicated. Then producers would have to know consumers' reputations and I think it gets muddy. Probably it would be simplest to just have producers have reputations. Hal