towards a theory of reputation

[Wei Dai <weidai@eskimo.com>]

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Many of the topics discussed on this list are economic in nature.  
Unfortunately cypherpunks haven't attracted the attention of professional 
economists who might be willing to apply their analytic tools to these 
issues.  Reputation is one of these issues that is especially important.  
I'm not an economist, so I hope these ramblings do not discourage real 
economists from tackling reputation as a serious research project.

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.

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).

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).

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.

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.

Wei Dai

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