Bid distributions of competing agents in simple models of auctions

The distribution of returns in financial time series exhibits heavy tails. In empirical studies, it has been found that gaps between the orders in the order book lead to large price shifts and thereby to these heavy tails. We set up an agent based model to study this issue and, in particular, how the gaps in the order book emerge. The trading mechanism in our model is based on a double-auction order book, which is used on nearly all stock exchanges. In situations where the or...

We consider a class of auctions (Lowest Unique Bid Auctions) that have achieved a considerable success on the Internet. Bids are made in cents (of euro) and every bidder can bid as many numbers as she wants. The lowest unique bid wins the auction. Every bid has a fixed cost, and once a participant makes a bid, she gets to know whether her bid was unique and whether it was the lowest unique. Information is updated in real time, but every bidder sees only what's relevant to the...

First price auctions are widely used in government contracts and industrial auctions. In this paper, we consider the Bayesian Nash Equilibrium (BNE) in first price auctions with discrete value distributions. We study the characterization of the BNE in the first price auction and provide an algorithm to compute the BNE at the same time. Moreover, we prove the existence and the uniqueness of the BNE. Some of the previous results in the case of continuous value distributions do ...

The connection between games and no-regret algorithms has been widely studied in the literature. A fundamental result is that when all players play no-regret strategies, this produces a sequence of actions whose time-average is a coarse-correlated equilibrium of the game. However, much less is known about equilibrium selection in the case that multiple equilibria exist. In this work, we study the convergence of no-regret bidding algorithms in auctions. Besides being of theo...

This survey outlines a general and modular theory for proving approximation guarantees for equilibria of auctions in complex settings. This theory complements traditional economic techniques, which generally focus on exact and optimal solutions and are accordingly limited to relatively stylized settings. We highlight three user-friendly analytical tools: smoothness-type inequalities, which immediately yield approximation guarantees for many auction formats of interest in th...

As computational agents are developed for increasingly complicated e-commerce applications, the complexity of the decisions they face demands advances in artificial intelligence techniques. For example, an agent representing a seller in an auction should try to maximize the seller's profit by reasoning about a variety of possibly uncertain pieces of information, such as the maximum prices various buyers might be willing to pay, the possible prices being offered by competing s...

The use of kinetic modelling based on partial differential equations for the dynamics of stock price formation in financial markets is briefly reviewed. The importance of behavioral aspects in market booms and crashes and the role of agents' heterogeneity in emerging power laws for price distributions is emphasized and discussed.

We propose a model for price formation in financial markets based on clearing of a standard call auction with random orders, and verify its validity for prediction of the daily closing price distribution statistically. The model considers random buy and sell orders, placed following demand- and supply-side valuation distributions; an equilibrium equation then leads to a distribution for clearing price and transacted volume. Bid and ask volumes are left as free parameters, per...

In this study, we develop a theoretical model of strategic equilibrium bidding and price-setting behaviour by heterogeneous and boundedly rational electricity producers and a grid operator in a single electricity market under uncertain information about production capabilities and electricity demand. We compare eight different market design variants and several levels of centralized electricity production that influence the spatial distribution of producers in the grid, the...

We study the price competition in a duopoly with an arbitrary number of buyers. Each seller can offer multiple units of a commodity depending on the availability of the commodity which is random and may be different for different sellers. Sellers seek to select a price that will be attractive to the buyers and also fetch adequate profits. The selection will in general depend on the number of units available with the seller and also that of its competitor - the seller may only...