On the evaluation of bidding strategies in sequential auctions

This paper provides further insight into the structure of the procurement strategy for a firm that in order to fill the demand of its market builds inventory by participating in sequential auctions. The analysis herein extends previous work by endogenizing the probability of winning an auction using the rise function in order to obtain a concrete characterization of the optimal strategy. Further, an efficient computational algorithm is given and evaluated for specific valuation models for the market.     

Entry coordination in auctions and social welfare: An experimental investigation

Most of the literature on auctions with endogenous entry assumes that, in equilibrium, the number of entrants is deterministic. We discuss a series of experiments designed to test the alternative hypothesis that, even in equilibrium, the number of entrants is stochastic. This distinction has strong implications for auction performance, the design of optimal mechanisms, and social welfare. Our results strongly reject the hypothesis of deterministic entry and tend to confirm the alternative hypothesis that entry is stochastic. Revised February 2000     

Asymptotic revenue equivalence of asymmetric auctions with interdependent values

We prove an asymptotic revenue equivalence among weakly asymmetric auctions with interdependent values, in which bidders have either asymmetric utility functions or asymmetric distributions of signals.     

On bidding for a fixed number of items in a sequence of auctions

We consider the problem of a firm (“the buyer”) that must acquire a fixed number (L) of items. The buyer can acquire these items either at a fixed buy-it-now price in the open market or by participating in a sequence of N > L auctions. The objective of the buyer is to minimize his expected total cost for acquiring all L items. We model this problem as a Markov Decision Process and establish monotonicity properties for the optimal value function and the optimal bidding strategies.     

Exploring the VCG mechanism in combinatorial auctions: The threshold revenue and the threshold-price rule

We explore interesting potential extensions of the Vickrey–Clarke–Groves (VCG) rule under the assumption of players with independent and private valuations and no budget constraints. First, we apply the VCG rule to a coalition of bidders in order to compute the second price of the coalition. Then, we introduce and formulate the problem of determining that partition of players into coalitions which maximize the auctioneer’s revenue in the case whereby such coalitions take part to a VCG auction each one as a single agent; in particular, we provide an integer linear formulation of this problem. We also generalize this issue by allowing players to simultaneously belong to distinct coalitions in the case that players’ valuation functions are separable. Finally, we propose some applications of these theoretical results. For instance, we exploit them to provide a class of new payment rules and to decide which bids should be defined as the highest losing ones in combinatorial auctions.     

Equilibrium cooperation in two-stage games: Experimental evidence

This paper reports results of an experiment design ed to investigate the nature of cooperation and punishment. Subjects are matched in a series of two-person, two-stage games with a sequential equilibrium that supports first-stage cooperation with a credible threat of subsequent punishment. Participants sometimes used a consistent punish/reward strategy, and when they did, cooperation rates increased dramatically. The results thus contradict “payoff relevance”: second-stage behavior can be influenced by first-stage outcomes that have no effect on the payoff structure. Nevertheless, high cooperation rates were often not observed, even with a Pareto undominated “punishment” equilibrium in the second stage. Received: November 1993/final version: July 1995     

Communication, credible improvements and the core of an economy with asymmetric information

We analyze an economy with asymmetric information and endogenize the possibilities for information transmission between members of a coalition. We then define a concept of the Core that takes into account these communication possibilities. The internal consistency of the improvements is considered and an Internally Consistent Core, which requires credibility from the improvements is introduced. Received: September 1998/revised version: June 1999     

On the role of heterogeneous and imperfect information in a laboratory financial market

In this paper, we analyze the behavior of a group of heterogeneously informed investors in an laboratory asset market. Our experimental setting is inspired by Huber et al. (On the benefit of information in markets with heterogeneously informed traders: an experimental study, 2004). However, instead of their system of cumulative and exogenously given information structure, we introduce an information market where the traders can buy an imperfect prediction of the future value of the dividend with a maximum anticipation of four periods. The accuracy of the prediction decreases with the chosen time horizon, whereas its price remains constant. Our results confirm a non-strictly monotonic increasing value of the information.     

Optimal bidding in auctions of mixed populations of bidders

A mixed population of bidders consists of two asymmetric groups. Members of the first group are game-theoretic players, who maximize their expected profit and incorrectly believe that their opponents act similarly. The second group of bidders adopts an irrational strategy: they either choose their bids randomly following a given probability distribution, in a “naïve” form of bidding, or follow a decision-theoretic approach, maximizing their expected profit under the assumption that all other bids are random. In a sealed bid private-value procurement auction we examine the optimal strategy of a new player, who has perfect knowledge of the structure of the mixed bidder population and enters the auction. The optimal bid of the new bidder is derived when the cost and mark-up follow a uniform distribution in [0, 1]. The effect of the relative size of the group of game-theoretic bidders and the population size on the optimal bid price is established.     

Unboundedness of the large solutions of an asymmetric oscillator

In this paper, we consider the unboundedness problem of solutions for the following asymmetric oscillator:

(φp(x^′)^)′+(p−1)[αφp(x⁺)−βφp(x⁻)]=f(x,x^′,t),     

On the impact of an event

Given an information structure a function that measures how the inferences made by the agents spread among the states is defined; it specifies for each event its impact at each state, for each agent. Several properties are established. Received November 1994/Revised version September 1996     

Unboundedness of the large solutions of some asymmetric oscillators at resonance

In this paper, we consider the unboundedness of solutions of the following differential equation (φ_p(x′))′ + (p ? 1)[αφ_p(x⁺) ? βφ_p(x^?)] = f(x)x′ + g(x) + h(x) + e(t) where φ_p(u) = |u|^{p? 2} u, p > 1, x^± = max {±x, 0}, α and β are positive constants satisfying with m, n ∈ N and (m, n) = 1, f and g are continuous and bounded functions such that lim_x→±∞g(x) ? g(±∞) exists and h has a sublinear primitive, e(t) is 2π_p‐periodic and continuous. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于试验设计的效率及有关问题

效率是试验设计的根本出发点和追求目标,但实际上它是一个抽象和模糊的概念,容易误解和产生偏颇,至今还很少有文献对它专门进行过很好的阐述和研究。常见的各种试验设计方法所追求的效率一般都是单一地在某种数学模型及相应的数学准则下要求实现最优而已。本文将探讨试验设计的基本原理,解释和研究到底什么是试验设计的效率?应该怎样来追求试验设计的效率?并指出现有试验设计学科的一些不足和问题,提出一个改进的试验设计框架和学说。     

Lattice hydrodynamic model of pedestrian flow considering the asymmetric effect

The original lattice hydrodynamic model of traffic flow is extended to single-file pedestrian movement at middle and high density by considering asymmetric interaction (i.e., attractive force and repulsive force). A new optimal velocity function is introduced to depict the complex behaviors of pedestrian movement. The stability condition of this model is obtained by using the linear stability theory. It is shown that the modified optimal velocity function has a remarkable influence on the neutral stability curve and the pedestrian phase transitions. The modified Korteweg-de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method, and its kink-antikink soliton solution can better describe the stop-and-go phenomenon of pedestrian flow. From the density profiles, it can be found that the asymmetric interaction is more efficient than the symmetric interaction in suppressing the pedestrian jam. The numerical results are consistent with the theoretical analysis.     

On the robustness of non-linear personalized price combinatorial auctions

Though the VCG auction assumes a central place in the mechanism design literature, there are a number of reasons for favoring Iterative Combinatorial Auctions (ICAs). Several promising ICA formats were developed based on primal–dual and subgradient algorithms. Prices are interpreted as a feasible dual solution and the provisional allocation is interpreted as a feasible primal solution. iBundle(3), dVSV and Ascending Proxy Auction result in VCG payoffs when the coalitional value function satisfies buyer submodularity and bidders bid straightforward, which is an ex-post Nash equilibrium in this case. iBEA and CreditDebit auctions do not even require the buyer submodularity and achieve the same properties for general valuations. Often, however, one cannot assume straightforward bidding and it is not clear from the theory how these non-linear personalized price auctions (NLPPAs) perform in this case. Robustness of auctions with respect to different bidding behavior is a critical issue for any application. We conducted a large number of computational experiments to analyze the performance of NLPPAs with respect to different bidding strategies and valuation models. We compare NLPPAs with the VCG auction and with ICAs with linear prices, such as ALPS and the Combinatorial Clock Auction. While NLPPAs performed very well in case of straightforward bidding, we observe problems with revenue, efficiency, and speed of convergence when bidders deviate.     

Effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effect of variable viscosity on the peristaltic flow of a Newtonian fluid in an asymmetric channel has been discussed. Asymmetry in the flow is induced due to travelling waves of different phase and amplitude which propagate along the channel walls. A long wavelength approximation is used in the flow analysis. Closed form analytic solutions for velocity components and longitudinal pressure gradient are obtained. The study also shows that, in addition to the effect of mean flow parameter, the wave amplitude also effect the peristaltic flow. This effect is noticeable in the pressure rise and frictional forces per wavelength through numerical integration.     

The impact of preventive activities on the economics of production systems: Modeling and application

In this paper, the impact of preventive activities on the economics of production systems has been discussed. A defective production system has been used to evaluate the financial return of a system with and without preventive activity. A mathematical model has been developed to simulate the situation. A practical case in the automotive industry has been used to verify the model. According to this research, it has been found that preventive activities will affect the return of the production system, and the effect depends on the cost of the action that has been taken.     

Construction of asymmetric copulas and its application in two-dimensional reliability modelling

Copulas offer a useful tool in modelling the dependence among random variables. In the literature, most of the existing copulas are symmetric while data collected from the real world may exhibit asymmetric nature. This necessitates developing asymmetric copulas that can model such data. In the meantime, existing methods of modelling two-dimensional reliability data are not able to capture the tail dependence that exists between the pair of age and usage, which are the two dimensions designated to describe product life. This paper proposes a new method of constructing asymmetric copulas, discusses the properties of the new copulas, and applies the method to fit two-dimensional reliability data that are collected from the real world.     

On the expected optimal value of random assignment problems: Experimental results and open questions

In the paper, we study the expected optimal value of random linear assignment problems, whose data are random variables with the uniform and the exponential distributions. An interior point approach is used to solve large-scale dense assignment problems with size up to 10,000 nodes and 100 million edges. Our computational results indicate the validity of a long-standing conjecture about the limiting value of the expected optimal assignment. Some interesting open problems and extensions are discussed.