Related papers: $k$th price auctions and Catalan numbers
In this (partly expository) paper we give a short overview about the close relationship between the sequence of Catalan numbers and Hankel determinants from the point of view of orthogonal polynomials and show that an analogous situation…
Following Benjamin et al., a matrix with entries being sums of two neighbouring Catalan numbers is considered. Its LU-decomposition is given, by guessing the results and later prove it by computer algebra, with lots of human help.…
The enhanced competition paradigm is an attempt at bridging the gap between simple and optimal auctions. In this line of work, given an auction setting with $m$ items and $n$ bidders, the goal is to find the smallest $n' \geq n$ such that…
We study the dynamic pricing of discrete goods over a finite selling horizon. One way to capture both the elastic and stochastic reaction of purchases to price is through a model where sellers control the intensity of a counting process,…
This paper studies an environment of simultaneous, separate, first-price auctions for complementary goods. Agents observe private values of each good before making bids, and the complementarity between goods is explicitly incorporated in…
We study the complexity of computing Bayes-Nash equilibria in single-item first-price auctions. We present the first efficient algorithms for the problem, when the bidders' values for the item are independently drawn from the same…
Using mechanised reasoning we prove that combinatorial Vickrey auctions are soundly specified in that they associate a unique outcome (allocation and transfers) to any valid input (bids). Having done so, we auto-generate verified executable…
We study the problem of designing revenue-maximizing auctions for allocating multiple goods to flexible consumers. In our model, each consumer is interested in a subset of goods known as its flexibility set and wants to consume one good…
This paper establishes quantitative correlation inequalities between monotone events and structured threshold objects in both the discrete cube and Gaussian space. We prove that for any increasing balanced family, there exists a linear…
The declining price anomaly states that the price weakly decreases when multiple copies of an item are sold sequentially over time. The anomaly has been observed in a plethora of practical applications. On the theoretical side, Gale and…
We consider the question of whether collusion among bidders (a "bidding ring") can be supported in equilibrium of unrepeated first-price auctions. Unlike previous work on the topic such as that by McAfee and McMillan [1992] and Marshall and…
We develop extensions to auction theory results that are useful in real life scenarios. 1. Since valuations are generally positive we first develop approximations using the log-normal distribution. This would be useful for many finance…
We generalise the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting and annihilating particles by presenting a model of the velocity on each side (buy…
We introduce draft auctions, which is a sequential auction format where at each iteration players bid for the right to buy items at a fixed price. We show that draft auctions offer an exponential improvement in social welfare at equilibrium…
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…
We define an extension of parity from the integers to the rational numbers. Three parity classes are found -- even, odd and `none'. Using the 2-adic valuation, we partition the rationals into subgroups with a rich algebraic structure. The…
We introduce the new concept of weighted $K$-$k$-Schur functions -- a novel family within the broader class of Katalan functions -- that unifies and extends both $K$-$k$-Schur functions and closed $k$-Schur Katalan functions. This new…
We quantify the value of the monopoly's bargaining power in terms of competition complexity--that is, the number of additional bidders the monopoly must attract in simple auctions to match the expected revenue of the optimal mechanisms…
Signaling is an important topic in the study of asymmetric information in economic settings. In particular, the transparency of information available to a seller in an auction setting is a question of major interest. We introduce the study…
This paper proposes a simple descriptive model of discrete-time double auction markets for divisible assets. As in the classical models of exchange economies, we consider a finite set of agents described by their initial endowments and…