Entrepreneurial Chess

Although the combinatorial game Entrepreneurial Chess (or Echess) was invented around 2005, this is our first publication devoted to it. A single Echess position begins with a Black king vs. a White king and a White rook on a quarter-infinite board, spanning the first quadrant of the xy-plane. In addition to the normal chess moves, Black is given the additional option of “cashing out”, which removes the board and converts the position into the integer \(x + y\), where [x, y] are the coordinates of his king’s position when he decides to cash out. Sums of Echess positions, played on different boards, span an unusually wide range of topics in combinatorial game theory. We find many interesting examples.     

Weighted Matching in Chess Tournaments

In many chess tournaments, e.g. when the Swiss system is used, the number of players is much larger than the number of rounds to be played. In such tournaments the pairing for a round depends on the results in earlier rounds, and the pairing process can be very complicated. In these pairing systems the main goals are to let players with equal scores play together, and that each player should alternately play white and black, with the restriction that no player may face the same opponent more than once. The paper describes how a weighted matching algorithm is used to find ‘the best pairing’ by converting the pairing rules into penalty points.     

Competitive Bidding

This paper considers the problem of making simultaneous bids for a number of objects against competition by an unknown number of competitors. A method of solution is given which has been successfully applied in practice.     

熵率在中国象棋上的应用

本文通过对加权图上的随机游动熵率的研究,引进了中国象棋各棋子的熵率,从而可以比较中国象棋各棋子的自由度.     

On Some Optimal Constructions of Chess Tournament Combinations

An optimal solution for the following “chess tournament” problem is given. Let n, r be positive integers such that r<n. Put N=2n, R=2r+1. Let X_N,R be the set of all ordered pairs (T, A) of matrices of degree N such that T=(t_ij) is symmetric, A=(a_ij) is skew-symmetric, t_ij ∈,{0, 1, 2,…, R), a_ij ∈{0,1,–1}. Moreover, suppose t_ii=a_ii=0 (1?i?N). t_ij = t_ik>0 implies j=k, t_ij=0 is equivalent to a_ij=0, and |a_i1|+|a_i2|+…+|a_iN|=R (1?i?N). Let p(T, A) be the number of i such that 1?i?N and a_i1 + a_i2 + … + a_iN >0. The main result of this note is to show that max p(T, A) for (T, A)∈X_{N, R} is equal to [n(2r+1)/(r+1)], and a pair (T₀, A₀) satisfying p(T₀, A₀)=[n(2r+1)/(r+1)] is also given.     

Recurrent Competitive Bidding

A competitive bidding policy can be formulated if prior probability distributions of competitors' bids for future contracts have been determined. A method for determining these prior probability distributions is described for markets where there are a large number of customers. The identity of each winning company and its bid are assumed to be available to competitors and other customers so that the market reacts quickly to changes. A real example of the use of the method is given. The suppliers' general levels of bidding and their variation with individual types of customer are evaluated quantitatively. The results are consistent with qualitative knowledge of the market.     

Distributions in Competitive Bidding

Analyses of historical tendering data for a company selling concrete farm buildings have called into question the usual assumption of normality or lognormality for the probability distribution. The desirability of modelling individual competitors' strategies is reinforced. Complex problems of parameter estimation and testing have been overcome by adopting a likelihood approach, with values examined for plausibility.     

Implementing a Bidding Model

A major British construction company spent 4 years developing, experimenting, evolving and implementing a probabilistic bidding model. This paper chronicles the progress and describes the results achieved. Over the course of the project the model evolved from a simple algorithm into a sophisticated tool for corporate planning.     

A Stochastic Model for Bidding

Competitive bidding situations involve considering a multiplicity of factors. Organizations must be able to weigh the relative probability of potential projects based on resource usage, project duration and competitor actions to decide which of many possible bids to submit. A bidding strategy designed to maximize expected long run return is crucial, since an organization can usually submit only one bid per project.This paper presents a family of stochastic dynamic programming models considering different bidding situations. Several projects, each with several potential bids, are available for each situation. The objective is to determine what bidding strategy will maximize expected returns. Models are developed for two principle bidding situations: sequential, where projects are bid individually; and simultaneous, where several projects are bid at one time. Next, the effects of over- or under-commitment of resources are incorporated into the models. Finally, changes in project timing and the resultant effects on bidding strategy are included.A numerical example traces the changes in bidding strategy which occur as the models are expanded. The general formulation of bidding problems is also discussed, including changing the bid success probabilities due to competitor actions, the possibility of crashing projects and alternate methods of performing projects.     

多风险因素的投标报价决策方法

本文讨论工程项目投标报价的多风险因素层次模型，系统地介绍了90年代以来发展出的多风险因素条件下投标报价的5种主要决策方法，即层次分析法（AHP）、人工神经网络（ANN）、模糊评价法（Fuzzy）、专家系统（ES）和基于事例推理（CBR）。本文也对中国在该领域的研究现状作一个简单的评述。     

Problems in Determining Bidding Strategies

A methodology for estimating the bidding strategy of a collaborating company in an apparently complex market, as exemplified by a heating and ventilating contractor, has been developed. In the absence of sufficient detailed price data on all identified competitors, the market lowest bid strategy was determined sufficiently accurately to allow possible strategy changes to be simulated.     

Cost Uncertainty in Competitive Bidding Models

In this paper a number of issues will be examined regarding uncertainty about cost estimates in competitive bidding models. First, the value of information is derived when the relevant parameters are known. Next, it is shown how the usual procedure for finding the optimal price can be improved by taking into account information regarding the relation between the ratio of estimated cost to real cost for winning bids, and markup. Finally, a trial-and-error procedure is presented for determining the parameters needed to estimate the value of information.     

A Bidding Game with Heterogeneous Players

A one-sided limit order book is modeled as a noncooperative game for several players. Agents offer various quantities of an asset at different prices, competing to fulfill an incoming order, whose size is not known a priori. Players can have different payoff functions, reflecting different beliefs about the fundamental value of the asset and probability distribution of the random incoming order. In a previous paper, the existence of a Nash equilibrium was established by means of a fixed point argument. The main issue discussed in the present paper is whether this equilibrium can be obtained from the unique solution to a two-point boundary value problem, for a suitable system of discontinuous ordinary differential equations. Some additional assumptions are introduced, which yield a positive answer. In particular, this is true when there are exactly two players, or when all players assign the same exponential probability distribution to the incoming order. In both of these cases, we also prove that the Nash equilibrium is unique. A counterexample shows that these assumptions cannot be removed, in general.     

A Bidding Simulation for Training Estimators

A simulation for training estimators and managers is described. The game simulates a bidding situation in the construction industry, with the participants split into teams which bid against each other for government contracts. The contracts are differentiated in terms of workload implications and location, and the teams are encouraged to use discriminating bidding strategies. The cost estimates provided include substantial uncertainty, and the teams can purchase more accurate estimates as well as buying competitive information. As a result of playing the game, participants appreciated the importance of expenditure on estimates, keeping good records, and using simple bidding models.     

Managerial Judgement in a Competitive Bidding Model

The basic Friedman model is extended to allow for bias in cost estimates and the use of management judgement on market trends. The estimated mean bid is used as a parameter. Simulation, using data from four construction companies, is used to evaluate the performance of the resulting model. A sensitivity analysis is used to determine the required accuracy for the management estimate. A brief account is given of the introduction of the model as a practical tool of top management in a major construction firm.     

Bidding and sequential coalition formation with externalities

We study coalition formation games with externalities where each agent’s payoff depends on the entire partition. As in Bloch (Games Econ Behav 14:90–123, 1996) and Ray and Vohra (Games Econ Behav 26:268–336, 1999), we assume that coalitions form sequentially and agreements are irreversible. Instead of a fixed order protocol, we use a “bidding mechanism” (see Pérez-Castrillo and Wettstein in Am Econ Rev 92(5):1577–1587, 2002) to determine proposals and transfers among the agents. We show that such a mechanism facilitates the attainment of efficiency; in particular, our game admits a Markov perfect equilibrium with the property of full dynamic efficiency. In addition, the aggregate equilibrium payoffs of our game exhibit monotonicity in time. Nevertheless, inefficient equilibria can also emerge.     

基于改进数据包络分析的建设工程评标模型

建设工程评标是一项复杂的系统工程.为建立合理的评标决策支持系统,根据实际评标建立以商务标为目标函数,以技术标为约束条件的评标模型.引入数据包络分析(DEA)方法,建立第二目标函数为决策单元非效率值总和最小模型,进行交叉评价,解决了CCR模型在实际应用中不能完全确定中标顺序的问题.通过实际案例分析,交叉评价模型能够产生独立效率值并进行有效排序,证明了评标模型的可操作性与适用性.     

基于灰靶理论的工程项目投标决策

针对承包商投标决策问题,结合建设工程项目特点,提出工程项目投标决策灰靶分析与评价方法.首先,分析投标决策中可能存在的影响因素,从环境条件、工程条件、业主条件、市场竞争条件、自身条件等5个方面建立投标决策指标体系;其次,综合考虑投标决策的不确定性和复杂性,构建工程项目投标灰靶决策模型,提出一种在没有最优项目情况下的投标决策算法;最后,通过工程实例分析,验证了该方法的可行性与有效性.研究结果表明:投标灰靶决策模型能够辨证考虑投标决策中的确定和不确定因素,评价结果较客观地反映各拟投标项目优劣水平,为投标项目评审提供了一个新思路.