Some preliminary remarks on the relevance of topological essentiality in general equilibrium theory and game theory

We define an algebro-topological concept of essential map and we use it to prove several results in the theory of general equilibrium and nash equilibrium refinement.fixed point theory, game theory, equilibrium theory, stability of Nash equilibrium, multiplicity of equilibria

The communication complexity of private value single item auctions

In this paper we present a new auction, the bisection auction, that can be used for the sale of a single indivisible object. We discuss the issue concerning the information revelation requirement of this auction and the associated amount of data that needs to be transmitted. We show that in the truthtelling equilibrium the bisection auction is economical in its demand for information on the valuations of the players. It requires the players to transmit less information bits to the auctioneer than the Vickrey and English auctions. In particular, we prove that for integer valuations uniformly distributed on the interval [0,L) the bisection auction of n players requires in expectation transmission of at most 2n + log L information bits by the players. Compared with the corresponding number in the Vickrey auction which is n log L, and in the English auction which is on average at least (1/3) nL, the bisection auction turns out to be the best performer.mathematical economics;

Fraction auctions: the tradeoff between effciency and running time

This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [13] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders. We discuss the running time and the efficiency in the ex-post equilibrium of the auction. We show that by changing the parameter c of the auction we can trade off efficiency against running time.operations research and management science;

Inefficiency of equilibria in query auctions with continuous valuations

Query auctions are iterative auctions in which bidders have to select in each round an action from a finite set. We show that, when bidders have continuous valuations, any ex post equilibrium in an ex post individually rational query auction can only be ex post efficient when the running time of the auction is infinite for almost all realizations of valuations of thebidders. Thus, when valuations are drawn from a continuous probability distribution, efficiency can only be bought at the expense of a running time that is infinite with probability one. For two bidders we even show this to be true when we only require efficiency with probability one.mathematical economics;

On The Fastest Vickrey Algorithm

We investigate the algorithmic performance of Vickrey-Clarke-Groves mechanisms in the single item case. We provide a formal definition of a Vickrey algorithm for this framework, and give a number of examples of Vickrey algorithms. We consider three performance criteria, one corresponding to a Pareto criterion, one corresponding to worst case analysis, and a third criterion related to first-order stochastic dominance. We show that Pareto optimal Vickrey algorithms do not exist and that worst case analysis is of no use in discriminating between Vickrey algorithms. For the case of two bidders, we show the bisection auction to be optimal according to the third criterion. The bisection auction istherefore optimal in a very strong sense.operations research and management science;

Inefficiency of equilibria in query auctions with continuous valuations

We show that, when bidders have continuous valuations, any ex post equilibrium in an ex post individually rational query auction can only be ex post efficient when the running timeof the auction is infinite for almost all realizations of valuations of the bidders. We also show that this result applies to the general class of bisection auctions. In contrast we show that, when we allow for inefficient allocations with arbitrarily small probability, there is a query auction (to be more specific, a bisection auction) that attains this level of approximate efficiency in equilibrium, while additionally the running time of the auction in equilibrium is finite for all realizations of valuations.mathematical economics;

The family of c-bisection auctions: efficiency and running time

In this paper we analyze the performance of a recently proposed sequential auction, called the c-bisection auction, that can be used for a sale of a single indivisible object. We discuss the running time and the e±ciency in the ex-post equilibrium of the auction. We show that by changing the parameter c of the auction we can trade o® e±ciency against running time. Moreover, we show that the auction that gives the desired level of e±ciency in expectation takes the same number of rounds for any number of players.computer science applications;

Firm investment and monetary policy transmission in the Euro Area

This paper presents a comparable set of results on the monetary transmission channels on firm investment (the interest rate channel and the broad credit channel) for the four largest euro-areacountries (Germany, France, Italy and Spain), using particularly rich micro datasets for eachcountry containing over 215,000 observations from 1985 to 1999. For each of those countries,investment relationships are estimated explaining investment by its user cost, sales and cash flow.A first result is that investment is sensitive to user cost changes in all those four countries. Thisimplies an operative interest channel in these euro-area countries. A second result is that investmentin all countries is quite sensitive to cash flow movements. However, only in Italy do smaller firmsreact more to cash flow movements than large firms, implying that a broad credit channel might notbe equally pervasive in all countries.Investment, Monetary Transmission Channels, User Cost of Capital

Firm Investment and Monetary Policy Transmission in the Euro Area

We present a comparable set of results on the monetary transmission channels on firm investment for the four largest euro-area countries (Germany, France, Italy and Spain). With particularly rich micro datasets for each country containing over 215,000 observations from 1985 to 1999, we explore what can be learned about the interest channel and the broad credit channel. For each of those countries, we estimate neo-classical investment relationships, explaining investment by its user cost, sales and cash flow. We find investment to be sensitive to user cost changes in all those four countries. This implies an operative interest channel in these euro-area countries. We also find investment in all countries to be quite sensitive to cash flow movements. However, only in Italy do smaller firms react more to cash flow movements than large firms, implying that a broad credit channel might not be equally pervasive in all countries.investment, monetary transmission, user cost of capital