在消费者偏好不确定下双寡头定位定价博弈

本文通过建立在企业对消费者偏好信息不确定情形下,双寡头企业动态定位、定价博弈模型,研究企业的定位策略、定价策略以及产品差异化问题。证明了该动态博弈存在唯一的子博弈精炼均衡。均衡结果表明,偏好不确定性是一种差异化力量,与消费者偏好信息确定情形相比,企业的不确定性能够提高均衡价格、增加均衡利润。最后,分析了偏好不确定性对社会最优定位和社会最优差异化的影响。     

基于CAPM框架下的创业企业风险资本融资契约设计

从组合的视角出发,考虑创业企业家的风险厌恶程度,通过等价利率将创业企业的风险资本融资契约适应到CAPM框架下,利用纳什议价解刻画双方在信息不对称下的均衡解,基于风险-收益的角度建立了最优融资契约设计模型,为创业企业融资提供了契约设计和风险资本类型选择的一个依据,并通过算例说明了模型的可行性。研究还表明,创业企业引入风险资本优于纯债务融资,而股权的分配则取决于双方的议价力。同时,风险厌恶程度越低的创业企业家越趋向于选择独立的风险投资机构;风险厌恶程度越高的创业企业家越趋向于选择公司背景的风险投资机构;而风险厌恶程度不高,考虑后期贷款的创业企业家则趋向于选择银行背景的风险投资机构。     

常数相对风险厌恶多单位拍卖的比较静态与定价结构

考虑竞价者具有常数相对风险厌恶时的多单位拍卖问题,讨论均衡出价与风险偏好以及价值分布之间的关系.在竞价者具有相同的风险偏好的对称拍卖情形,利用风险中性等价导出了比较静态的充要条件,这一充要条件综合了风险偏好和价值分布的变化.在竞价者具有不同的风险偏好的非对称拍卖中,导出了均衡出价关于风险偏好的线性定价结构,依据这一结构,对任意给定出价,竞价者要求的剩余是其风险厌恶参数的线性函数,并且可以分解为竞争性剩余和风险厌恶剩余.     

均值-CVaR零售商的供应链服务决策及协调契约

研究零售商具有风险偏好行为下,同时考虑价格、质量和服务水平的供应链联合决策问题。运用均值-CVaR准则来刻画零售商风险偏好行为,它包括风险厌恶、风险中性和风险追求,同时具有损失规避的特性。首先得到供应链集中系统、制造商提供服务（模型$\mbox{I}$）和零售商提供服务（模型$\mbox{II}$）下的最优决策和最优利润（期望效用）。其次,证明了成本共担契约在零售商风险厌恶时可以实现供应链协调.第三,对模型$\mbox{I}$和模型$\mbox{II}$协调后的最优利润（期望效用）进行比较,证明两种模型下制造商利润相同,而与模型$\mbox{I}$相比,模型$\mbox{II}$下零售商获得更多的期望效用。最后,数值例子证明了得到的研究结果。     

具有损失厌恶偏好的Muthoo交替出价谈判博弈研究

现实的谈判中往往存在谈判破裂的风险,Muthoo基于参与人理性,提出了刻画具有谈判破裂风险的交替出价谈判博弈模型.然而实验经济学和心理学研究表明,决策主体通常具有损失厌恶行为.文章对具有损失厌恶行为的Muthoo交替出价谈判博弈进行研究.首先将在过去谈判阶段的最高出价作为参与人的参考点,这使得收益与均衡策略依赖于谈判历史.然后构建子博弈完美均衡,该均衡通过当前阶段的参考点依赖于谈判历史;基于子博弈完美均衡策略满足静态的马尔科夫策略、立刻接受以及接受-拒绝无差异性等三条性质,证明了子博弈完美均衡的唯一性;最后分析子博弈完美均衡关于损失厌恶行为的敏感性及其收敛性.发现:参与人受益于对手的损失厌恶行为,而因自身的损失厌恶行为遭受损失.     

基于CVaR方法的房地产组合投资最优化模型研究

房地产开发项目投资是具有高风险高回报的典型的风险投资.在这个高风险的投资环境中要想达到预期目标,就必须对整个项目进行开发投资风险分析.本文运用CVaR对房地产项目投资存在的风险进行识别度量,通过建立基于CVaR下的房地产组合投资模型,达到项目风险防范的目的,提高投资回报的稳定性.     

连续区间策略下二人零和对策问题研究

考虑连续区间策略下的二人零和对策问题,研究其均衡策略的存在性。首先分析了完全信息下的二人零和对策问题,证明了该问题均衡策略的存在性并给出求解方法。然后进一步研究了收益函数不确定的不完全信息二人零和对策问题,在各局中人都认为对方是风险厌恶型的假设下,分析该类对策纯策略均衡的存在性,并通过研究纯策略均衡存在的充要条件给出判断并寻找纯策略均衡解的方法。最后给出一个数值算例,验证本文所提出方法的可行性。     

基于双边过度自信及风险厌恶的委托-代理问题研究

研究了委托人与代理人双边过度自信倾向及风险厌恶偏好情形下的委托-代理问题.结论表明最优风险分担水平随着委托人风险厌恶程度及代理人过度自信水平的增大而增加,随着代理人风险厌恶程度和委托人过度自信水平的减少而减少.最优努力水平随代理人风险厌恶程度及委托人过度自信水平的增大而提高,随委托人风险厌恶程度和代理人过度自信水平的减少而减少.     

具有公平偏好成员的供应链定价决策与利润分析

将公平偏好因素引入供应链定价决策中,以零售商和制造商均为公平中性时的决策结果为参照,基于FS公平偏好效用函数分析了仅零售商具有不利不公平厌恶偏好、仅制造商具有有利不公平厌恶偏好和二者均具有公平偏好三种情形下公平偏好对供应链双方的均衡定价策略及利润的影响.结果表明:在仅零售商具有不利不公平厌恶偏好情形下,制造商降低批发价格,零售商最优零售价格保持不变,供应链整体利润保持不变;另外两种情形下,制造商和零售商均采取降价策略,供应链整体利润大于双方均为公平中性情形;三种情形下,零售商将获得与公平中性情形相比更多的供应链利润.     

基于风险厌恶的下游供应链转运问题研究

当需求面临较大不确定性并且供货周期很长的情况下,转运策略成为提高供应链效率的重要解决方案。本文以条件风险价值（Conditional Value—at—Risk,简称CVaR）为风险度量准则,定量地研究了集中决策下的两级供应链系统的转运问题。我们得出了下游批发商的最优订货决策主要依赖于需求分布、单位缺货成本和风险厌恶程度等因素的一般性结论,并得出了均衡最优订货组合所需要满足的条件,重点分析了当需求基于均匀分布时,单位缺货成本和风险厌恶程度对最优订货组合的影响。     

Equilibria for networks with malicious users

We consider the problem of characterizing user equilibria and optimal solutions for selfish routing in a given network. We extend the known models by considering malicious behavior. While selfish users follow a strategy that minimizes their individual cost, a malicious user will use his flow through the network in an effort to cause the maximum possible damage to the overall cost. We define a generalized model, present characterizations of flows at equilibrium and prove bounds for the ratio of the social cost of a flow at equilibrium over the cost when centralized coordination among users is allowed. An extended abstract of this work appeared in the Proceedings of the 14th Annual International Symposium on Algorithms and Computation (ISAAC) 2003. G. Karakostas’ research was supported by an NSERC Discovery research grant and MITACS. Part of this research was done when Viglas was a postdoctoral fellow at the University of Toronto, Canada.     

Bottleneck routing with elastic demands

Bottleneck routing games are a well-studied model to investigate the impact of selfish behavior in communication networks. In this model, each user selects a path in a network for routing her fixed demand. The disutility of a user only depends on the most congested link visited. We extend this model by allowing users to continuously vary the demand rate at which data is sent along the chosen path. As our main result we establish tight conditions for the existence of pure strategy Nash equilibria.     

Stability vs. optimality in selfish ring routing

We study asymmetric atomic selfish routing in ring networks, which has diverse practical applications in network design and analysis. We are concerned with minimizing the maximum latency of source-destination node-pairs over links with linear latencies. We show that there exists an optimal solution that is a 9-approximate Nash equilibrium, significantly improving the existing upper bound of 54 on the instability factor. We present fast implementation of the best response dynamics for computing a Nash equilibrium. Furthermore, we perform empirical study on the price of stability, narrowing the gap between the lower and upper bounds to 0.7436.     

Firm behavioral response to multiple sources of risky cash flow

We extend previous research to demonstrate that risk-averse firms can appear to be risk-seeking when facing multiple sources of risky cash flow. While our model requires that cash flows from operations are independently, uniformly distributed, we are able to demonstrate that three previous derived results hold with multiple sources of risk. Using chance constrained programming, we demonstrate that binding probability constraints can cause (1) a higher degree of aversion to illiquidity to induce increased risk taking; (2) apparent risk-seeking behavior; and (3) an increase in endowment to lead to lower expected profit.     

Repeated congestion games with bounded rationality

We consider a repeated congestion game with imperfect monitoring. At each stage, each player chooses to use some facilities and pays a cost that increases with the congestion. Two versions of the model are examined: a public monitoring setting where agents observe the cost of each available facility, and a private monitoring one where players observe only the cost of the facilities they use. A partial folk theorem holds: a Pareto-optimal outcome may result from selfish behavior and be sustained by a belief-free equilibrium of the repeated game. We prove this result assuming that players use strategies of bounded complexity and we estimate the strategic complexity needed to achieve efficiency. It is shown that, under some conditions on the number of players and the structure of the game, this complexity is very small even under private monitoring. The case of network routing games is examined in detail.     

Nash equilibria in all-optical networks

We consider the problem of routing a number of communication requests in WDM (wavelength division multiplexing) all-optical networks from the standpoint of game theory. If we view each routing request (pair of source-target nodes) as a player, then a strategy consists of a path from the source to the target and a frequency (color). To reflect the restriction that two requests must not use the same frequency on the same edge, conflicting strategies are assigned a prohibitively high cost.Under this formulation, we consider several natural cost functions, each one reflecting a different aspect of restriction in the available bandwidth. For each cost function we examine the problem of the existence of pure Nash equilibria, the complexity of recognizing and computing them and finally, the problem in which we are given a Nash equilibrium and we are asked to find a better one in the sense that the total bandwidth used is less. As it turns out some of these problems are tractable and others are NP-hard.     

A note on a selfish bin packing problem

In this paper, we consider a selfish bin packing problem, where each item is a selfish player and wants to minimize its cost. In our new model, if there are k items packed in the same bin, then each item pays a cost 1/k, where k ≥ 1. First we find a Nash Equilibrium (NE) in time O(n log n) within a social cost at most 1.69103OPT + 3, where OPT is the social cost of an optimal packing; where n is the number of items or players; then we give tight bounds for the worst NE on the social cost; finally we show that any feasible packing can be converged to a Nash Equilibrium in O(n ²) steps without increasing the social cost.     

Firm behavior under illiquidity risk

We develop a model of firm behavior in the presence of risk, resource constraints, and a cash flow constraint. Given imperfect capital markets, the producer confronts an uncertain cash flow. Utilizing chance constrained programming, we show that an increase in aversion to liquidity risk can cause an increased allocation to high-risk production alternatives. With a binding cash flow constraint, risk-averse firms appear to demonstrate risk-seeking behavior over losses and risk-averse behavior over gains.     

Selfish Square Packing

We consider a game-theoretical bin packing problem. The 1D (one dimensional) case has been treated in the literature as the ʼselfish bin packing problemʼ. We investigate a 2D version, in which the items to be packed are squares and the bins are unit squares. In this game, a set of items is packed into bins. Each player controls exactly one item and is charged with a cost defined as the ratio between the area of the item and the occupied area of the respective bin. One at a time, players selfishly move their items from one bin to another, in order to minimize the costs they are charged. At a Nash equilibrium, no player can reduce the cost he is charged by moving his item to a different bin. In the 2D case, to decide whether an item can be placed in another bin with other items is NP-complete, so we consider that players use a packing algorithm to make this decision. We show that this game converges to a Nash equilibrium, independently of the packing algorithm used. We prove that the price of anarchy is at least 2.27. We also prove that, using the NFDH packing algorithm, the asymptotic price of anarchy is at most 2.6875.     

Computing approximate Nash equilibria in general network revenue management games

Computing optimal capacity allocations in network revenue management is computationally hard. The problem of computing exact Nash equilibria in non-zero-sum games is computationally hard, too. We present a fast heuristic that, in case it cannot converge to an exact Nash equilibrium, computes an approximation to it in general network revenue management problems under competition. We also investigate the question whether it is worth taking competition into account when making (network) capacity allocation decisions. Computational results show that the payoffs in the approximate equilibria are very close to those in exact ones. Taking competition into account never leads to a lower revenue than ignoring competition, no matter what the competitor does. Since we apply linear continuous models, computation time is very short.