Equilibrium Of Auction Research Articles

Bayesian Nash equilibrium in all-pay auctions with interdependent types

We prove the existence of a behavioral-strategy Bayesian Nash equilibrium in all-pay auctions with statistically interdependent types (signals) under quite general assumptions on the values, costs and tie-breaking rules. Moreover, the set of equilibria is shown to be the same for any tie-breaking rule used in the auction.

Computing Bayes–Nash Equilibrium Strategies in Auction Games via Simultaneous Online Dual Averaging

Determining equilibria in auction games is computationally hard in general, and no exact solution theory is known. We introduce an algorithmic framework in which we discretize type and action space and then learn distributional strategies via online optimization algorithms. We show that the equilibrium of the discretized auction game approximates an equilibrium in the continuous game. In a wide variety of auction games, we provide empirical evidence that the approach approximates the analytical (pure) Bayes–Nash equilibrium closely. In standard models in which agents are symmetric, we find equilibrium in seconds. The method allows for interdependent valuations and different types of utility functions, and it can be used to find equilibrium in auction markets and beyond.

Freight Flow Assignment in the Intermodal Logistics Network

Intermodal logistics networks have received increased attention from researchers in recent decades. The growing importance of strategic supply chain management in light of issues such as road congestion, environmental concerns, and traffic safety is forcing firms to revise traditional freight transportation. As a result, the study of intermodal logistic service development has become urgent for multiple branches of science. This work is focused on the mathematical model of the freight flow assignment problem under auction equilibrium. We formulate this model as a non-linear optimization problem and show that its solution corresponds to the equilibrium assignment pattern in an intermodal logistics network. The developed model can be applied for long-term planning and management since its basic assumption is that in the long run, the activities carried out by shippers are in equilibrium. The findings of the paper contribute to the theory of transportation and can give fresh managerial insights for engineers.

Equilibrium Learning in Auction Markets

My dissertation investigates the computation of Bayes-Nash equilibria in auctions via multiagent learning. A particular focus lies on the game-theoretic analysis of learned gradient dynamics in such markets. This requires overcoming several technical challenges like non-differentiable utility functions and infinite-dimensional strategy spaces. Positive results may open the door for wide-ranging applications in Market Design and the economic sciences.

Trade, equilibrium prices and rents in European auctions for emission allowances

This paper analyzes the price behavior of Phase III (2013–2020) EU-ETS emission allowances of CO2 by focusing on the dynamics of daily auction equilibrium prices and on the changes of the volatility of the underlying stochastic process. The paper derives the main testable statistical hypotheses (particularly that about the determinants of the conditional variance of prices) on the results derived in a model of optimal bidders’ behavior given the ETS auction rules. Tests are conducted by estimating various versions of GARCH models for both mean and variance equations of price return. Results show that the price dynamics is affected by factors including a measure of excess demand/offer and the number of winning bidders and that, contrary to expectations, reforms of the auction rules introduced at the end of Phase III explain a great part of the increased price volatility. The increased volatility is also positively associated with the bid spread and negatively associated with the number of bidders active in each auction round.

Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players

I characterize the optimal accuracy level r of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner’s expected valuation by choosing a contest with an all-pay auction equilibrium (r≥2). By contrast, if she aims at maximizing the expected aggregate effort or the winner’s expected effort, she will choose a contest with a pure-strategy equilibrium, and the optimal accuracy level r<2 decreases in the players’ heterogeneity. Finally, a contest designer who faces a tradeoff between selection quality and minimum (maximum) effort will never choose a contest with a semi-mixed equilibrium.

Price discovery using a double auction

We investigate equilibrium in the buyer's bid double auction (BBDA) in a model with correlated private values/costs. Using a combination of theorems and computed examples, we demonstrate that simple equilibria exist even in small markets. Moreover, we bound traders' strategic behavior as a function of market size and derive rates of convergence to zero of (i) inefficiency in the allocation caused by strategic behavior and (ii) the error in the market price as an estimate of the rational expectations price. These rates together with computed examples suggest that strategic behavior can be inconsequential even in small markets in its effect on allocational efficiency and information aggregation. The BBDA thus simultaneously accomplishes both the informational and allocational goals that markets ideally fulfill; it does this perfectly in large markets and approximately in small markets, with the error due mainly to the smallness itself and not the strategic behavior of traders.

A new resource allocation method in fog computing via non-cooperative game theory

IoT-based network systems use a modern architecture called fog computing, In which data providing data services is economical with low latency. This paper tends to solve the challenge of resource allocation in fog computing. Solving the resource allocation challenge leads to increased profits, economic savings, and optimal computing systems use. Here resource allocation is improved by making use of the combined algorithm Nash equilibrium and auction. In the proposed method, each player is assigned a matrix. Each player matrix includes fog nodes (FNs), data service subscribers (DSSs), and data service operators (DSOs). Each player generates the best strategy based on the other players strategy in all stages of the algorithm. The simulation results show that FNs profit in the combined Nash and Auction equilibrium algorithms is superior to the Stackelberg game algorithm.

Product-Mix Auctions and Tropical Geometry

In a recent and ongoing work, Baldwin and Klemperer explore a connection between tropical geometry and economics. They give a sufficient condition for the existence of competitive equilibrium in product-mix auctions of indivisible goods. This result, which we call the unimodularity theorem, can also be traced back to the work of Danilov, Koshevoy, and Murota in discrete convex analysis. We give a new proof of the unimodularity theorem via the classical unimodularity theorem in integer programming. We give a unified treatment of these results via tropical geometry and formulate a new sufficient condition for competitive equilibrium when there are only two types of products. Generalizations of our theorem in higher dimensions are equivalent to various forms of the Oda conjecture in algebraic geometry.

Potential heterogeneity in target’s value and jump bidding in takeover auctions

ABSTRACTThis ticle analyses the pre-emptive jump bidding equilibrium in takeover auctions when bidders’ valuations of the target firm follow truncated normal distribution. It shows that potential heterogeneity of the targets’ value, measured by the standard deviation of the bidders’ valuation function, is especially important when it is small and, for extremely small values, the second bidder is almost always pre-empted. It also shows that, contrary to regular clock-style auctions, the increase in standard deviation may negatively affect the expected profit of the first bidder.

Separating equilibria in auctions with two types of bidders

We consider two simultaneous, private value, second-price auctions with identical objects for sale and two types of bidders, strong and weak, in the sense of hazard rate stochastic dominance. We show that if the strong bidders are not too strong with respect to the weak bidders, then, by setting an appropriate reserve price, a separating equilibrium exists in which strong bidders will participate in the auction with only strong bidders, and weak bidders will participate in the auction with only weak bidders.

Alternative Policy Responses to Increased Use of Formula Pricing

Abstract This article determines the potential effects of policies to address concerns about lower producer prices due to increased use of marketing agreements. Policies considered are banning alternative marketing agreements, compensating producers who sell on the cash market, and restricting the quantity of marketing agreements. We use an agent-based model in a common-value auction framework to analyze these policies. The common-value auction framework is used because it closely resembles how livestock are actually purchased. The agent-based model is used to find the common-value auction equilibrium. A ban on marketing agreements reduces social welfare and the other policy interventions have little effect on prices. Past theoretical studies predict marketing agreements will cause large reductions in prices paid to producers. Conversely, empirical studies show slight effects. This article offers an alternative theory that more closely matches livestock markets and our results reduce the gap between theoretical and empirical research. The common-value auction model predicts negative effects on producer prices close to those found in past empirical research.

Auction Mechanism of Micro-Grid Project Transfer

Micro-grid project transfer is the primary issue of micro-grid development. The efficiency and quality of the micro-grid project transfer directly affect the quality of micro-grid project construction and development, which is very important for the sustainable development of micro-grid. This paper constructs a multi-attribute auction model of micro-grid project transfer, which reflects the characteristics of micro-grid system and the interests of stakeholders, calculates the optimal bidding strategy and analyzes the influence of relevant factors on auction equilibrium by multi-stage dynamic game with complete information, and makes a numerical simulation analysis. Results indicate that the optimal strategy of auction mechanism is positively related to power quality, energy storage quality, and carbon emissions. Different from the previous lowest price winning mechanism, the auction mechanism formed in this paper emphasizes that the energy suppliers which provide the comprehensive optimization of power quality, energy storage quality, carbon emissions, and price will win the auction, when both the project owners and energy suppliers maximize their benefits under this auction mechanism. The auction mechanism is effective because it is in line with the principle of individual rationality and incentive compatibility. In addition, the number of energy suppliers participating in the auction and the cost of the previous auction are positively related to the auction equilibrium, both of which are adjusting the equilibrium results of the auction. At the same time, the utilization rate of renewable energy and the comprehensive utilization of energy also have a positive impact on the auction equilibrium. In the end, this paper puts forward a series of policy suggestions about micro-grid project auction. The research in this paper is of great significance to improve the auction quality of micro-grid projects and promote the sustainable development of micro-grid.

The network equilibrium problem with mixed demand

We formulate the network equilibrium problem with mixed demand which generalizes the problems of network equilibrium with fixed and elastic demand. We prove the equilibrium conditions for this problem and propose some conditions of existence of a solution that are based on the coercivity property.We establish a connection between the problem of network equilibrium with mixed demand and the problem of auction equilibrium. The results of test calculations are presented for a model example.

Penny auctions

This paper studies penny auctions, a novel auction format in which every bid increases the price by a small amount, but placing a bid is costly. Outcomes of real-life penny auctions are often surprising. Even when selling cash, the seller may obtain revenue that is much higher or lower than its nominal value, and losers in an auction sometimes pay much more than the winner. This paper characterizes all symmetric Markov-perfect equilibria of penny auctions and studies penny auctions’ properties. The results show that a high variance of outcomes is a natural property of the penny auction format and high revenues are inconsistent with rational risk-neutral participants.

Insider Trading with Non-Fiduciary Market Makers

The single auction equilibrium of Kyle's (1985) is studied, in which market makers are not fiduciaries. They have some market power which they utilize to set the price to their advantage, resulting in positive expected profits. This has several implications for the equilibrium, the most important being that by setting a relatively modest fee, the market maker is able to obtain a profit of the order of magnitude, and even better than, a perfectly informed insider. Our model indicates why speculative prices are more volatile than predicted by fundamentals. Noise traders may be uninformed, or partially informed. We analyze a situation where the market maker has private information as well as being non-fiduciary. In our model this leads to a more efficient market where the insider trades less and the market maker's profit increases.

Selective bi-coordinate variations for resource allocation type problems

We suggest a modification of the coordinate descent methods for resource allocation problems, which keeps the basic convergence properties of the gradient ones, but enables one to reduce the total computational expenses and to provide all the computations in a distributed manner. We describe applications to economic (auction) equilibrium problems and give preliminary results of computational tests.

Asymmetric Information about Rivals' Types: Existence of Equilibrium in First-Price Auction

This paper establishes the equilibrium existence in the first-price auction in the setup where bidders are partitioned into ``knowledge groups'' so that each bidder observes the types of rival bidders in the same group but not the others' types.

On Pure Strategy Equilibria in Simultaneous Auctions for Complementary Goods

We explore existence and properties of Bayesian Nash equilibrium in simultaneous first-price auctions for complementary goods. We introduce a novel partial order on bidder types and apply methodology in Athey (2001), McAdams (2003) and Reny (2011) to demonstrate existence of monotone equilibria in these auctions when the bid space is finite. We then apply this finding to demonstrate two new results on monotone equilibria in continuous bid spaces. The first of these establishes existence of monotone equilibria in a setting similar to Krishna and Rosenthal (1996), in which a single global bidder bids for multiple objects against a set of local bidders who bid for single objects only. The second considers equilibria with communication as in Jackson, Simon, Swinkels and Zame (2002), showing that in our setting their statements on distributional strategies can be refined to be monotone. Finally, we discuss conditions under which these results can be extended to all-pay, second-price and other standard simultaneous auctions.

On auction equilibrium models with network applications

We consider a general auction market model with divisible commodities and price functions of participants and show that it can be suitable for proper description of complex systems with active elements. Using its equivalent variational inequality reformulation, we obtain a general existence result under mild additional conditions on price functions. We show that the basic network flow equilibrium problems are particular cases of this auction market model. Besides, we describe a new auction based model for resource allocation problems in wireless communication networks. This enables us to obtain new existence results for these models as simple adjustments of that for the general auction model.