Bidding Behavior and Equilibrium Excursion of Uniform Price Auction Mechanism

Multiple equilibria (equilibrium excursion) affects the auction proceeds, and is bad for estimating auction efficiency. This paper examines the relationship between bidding behavior and equilibrium excursion. We analyze a uniform price auction mechanism based on a rationing strategy and common value information. In this uniform price auction mechanism, bidders (strategic and non-strategic) participate in an auction simultaneously, and the auctioneer rations the strategic bidders after observing their bids. The conclusions drawn suggest that a rationing strategy can effectively limit the strategic bidders from manipulating the auction, and the Nash equilibrium may not be unique (i.e., there exists an equilibrium excursion). As the number of bidders increases, or when the quantity that can be allocated to the non-strategic bidders is unconstrained, there exists asymptotically a unique equilibrium price which is the highest price the auctioneer could obtain. Based on these conclusions, we provide some strategies and suggestions on how to induce the equilibrium excursion state to a desired unique equilibrium state.

Entropy approximation versus uniqueness of equilibrium for a dense affine space of continuous functions

We show that for a [Formula: see text]-action (or [Formula: see text]-action) on a non-empty compact metrizable space [Formula: see text], the existence of a affine space dense in the set of continuous functions on [Formula: see text] constituted by elements admitting a unique equilibrium state implies that each invariant measure can be approximated weakly[Formula: see text] and in entropy by a sequence of measures which are unique equilibrium states.

Large deviation principles for non-uniformly hyperbolic rational maps

We show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called ‘Topological Collet–Eckmann’. More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages. For this purpose we show that each Hölder continuous potential admits a unique equilibrium state, and that the pressure function can be characterized in terms of iterated preimages, periodic points, and Birkhoff averages. Then we use a variant of a general result of Kifer.

On t-conformal measures and Hausdorff dimension for a family of non-uniformly hyperbolic horseshoes

In this paper we consider horseshoes with homoclinic tangencies inside the limit set. For a class of such maps, we prove the existence of a unique equilibrium state μt, associated to the (non-continuous) potential −tlog Ju. We also prove that the Hausdorff dimension of the limit set, in any open piece of unstable manifold, is the unique number t0 such that the pressure of μt0 is zero. To deal with the discontinuity of the jacobian, we introduce a countable Markov partition adapted to the dynamics, and work with the first return map defined in a rectangle of it.