|Ph.D Student||Hon-Snir Shlomit|
|Subject||Utility Equivalence in Auctions|
|Department||Department of Industrial Engineering and Management||Supervisor||PROFESSOR EMERITUS Dov Monderer|
We analyze auctions from the buyers' point of view in a
(non-symmetric) independent-private-value model of valuations.
It is well-known that the revenue equivalence
theorem is derived for risk- neutral agents from a utility
equivalence principle: For a fixed agent, for any two auction
mechanisms, the difference between the utility in equilibrium
functions is a constant function, if the probability of winning
(in equilibrium) functions coincide.
We show that this
utility equivalence principle holds only for a risk-neutral
agent. We generalize the definition of utility equivalence
principle. The generalized principle is discussed only for pairs
of auction mechanisms, which specify the same payments when the
agent does not win. It is shown that the generalized principle
holds if and only if the agent has constant absolute risk
attitude. The (generalized) utility equivalence principle
implies that an agent is indifference to any two auctions in
which both, her probability to win and her expected utility at her
lowest possible type ( or at any other type) coincide. The
(generalized) utility equivalence principle is further
generalized to a model that allows random participation. In
addition, we show that this principle takes a very special form
for standard auction mechanisms, and that it can be used in
analyzing competition in auction design.
In order to prove our results we have made a comprehensive
equilibrium analysis of auctions. This analysis is performed in
the most general model: The agents may have any attitude toward
risk, and the distribution of types may contain atoms.