Luciano I. de Castro

Parametric representation of preferences

A preference is invariant with respect to a set of transformations if the ranking of acts is unaffected by reshuffling the states under these transformations. For example, transformations may correspond to the set of finite permutations, or the shift in a dynamic choice model. Our main result is that any invariant preference must be parametric: there is a unique sufficient set of parameters such that the preference ranks acts according to their expected utility given the parameters. Parameters are characterized in terms of objective frequencies, and can thus be interpreted as objective probabilities. By contrast, uncertainty about parameters is subjective. The preferences for which the above results hold are only required to be reflexive, transitive, monotone, continuous, and mixture linear.

EQUILIBRIA EXISTENCE AND CHARACTERIZATION IN AUCTIONS: ACHIEVEMENTS AND OPEN QUESTIONS

Establishing existence and characterizing equilibria are both important achievements in the study of auctions. However, we recognize that equilibria existence results form the basis for well accepted characterizations. In this survey, we review the landmark results and highlight open questions regarding equilibria existence and characterizations in auctions. In addition, we review the standard assumptions underlying these results, and discuss the suitability of the Nash equilibrium solution concept. We focus our review on single‐object auctions, but also review results in multi‐unit, divisible, combinatorial and double auctions.

Prediction markets for electricity demand

Load forecasting is a central task for operating, maintaining, and planning power systems. Because of this importance, many different methods are proposed to forecast load, but none of them is proved clearly superior. This paper proposes a prediction market to forecast electricity demand that has the advantage of allowing aggregation and competition among the many available methods. We describe how to implement a simple prediction market for continuous variables, using only contracts based on binary variables. We also discuss possible pitfalls in the implementation of such a market.

Pure Strategy Equilibria of Single and Double Auctions with Interdependent Values

We prove the existence of monotonic pure strategy equilibrium for many types of asymmetric auctions with n bidders and unitary demands, interdependent values and independent types. The assumptions require monotonicity only in the own bidders type. The payments can be a function of all bids. Thus, we provide a new equilibrium existence result for asymmetrical double auctions and a small number of bidders. The generality of our setting requires the use of special tie-breaking rules. We present a reasonable counterexample for interdependent values auctions that shows that sometimes all equilibria are trivial, that is, they have zero probability of trade. Nevertheless, we give sufficient conditions for non-trivial equilibrium existence.