Ph.D Thesis

Ph.D StudentHon-Snir Shlomit
SubjectUtility Equivalence in Auctions
DepartmentDepartment 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.