Kalai-Smorodinsky Bargaining Solution Equilibria

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don’t have an a-priori opinion on the relative importance of all these criteria. Roemer (Econ. Bull. 3:1–13, 2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution (see Kalai and Smorodinsky in Econometrica 43:513–518, 1975). We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered by Roemer (Econ. Bull. 3:1–13, 2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations; in particular, we consider the extension to multicriteria games of the Selten’s trembling hand perfect equilibrium concept (see Selten in Int. J. Game Theory 4:25–55, 1975) and prove that perfect Kalai-Smorodinsky bargaining solution equilibria exist and properly refine both the perfect equilibria and the Kalai-Smorodinsky bargaining solution equilibria.     

最低工资与经济增长:一个新理论模型

近年来,最低工资问题越来越受到理论界以及政府部门的重视.考虑了最低工资标准对国家经济增长的影响,提出了一个最低工资经济增长的理论模型,并求得该模型的均衡解,得出了最低工资标准的提高将降低就业率,由此引发的失业扩大将会促进经济增长的结论.     

Conflict resolution in fuzzy environment

Conflict resolution methodology is discussed with fuzzified Pareto frontier. Four solution concepts, namely, the Nash solution, the generalized Nash solution, the Kalai-Smorodinsky concept, and a solution method based on a special bargaining process are examined. The solutions are also fuzzy, the corresponding payoff values are fuzzy numbers, the membership functions of which are determined. Three particular cases are considered in the paper. Linear, quadratic, and general nonlinear Pareto frontiers with known shape are examined.     

The compromise value for NTU-games

The compromise value is introduced as a single-valued solution concept for NTU-games. It is shown that the compromise value coincides with the -value for TU-games and with the Kalai-Smorodinsky solution for bargaining problems. In addition the axiomatic characterizations of both the two-person Kalai-Smorodinsky solution and the -value can be extended to the compromise value for large classes of NTU-games.We also present an alternative NTU-extension of the TU -value (called the NTU -value) which coincides with the Nash solution for two-person bargaining problems. The definition of the NTU -value is analogous to that of the Shapley NTU-value.     

Bargaining over the division of a shrinking pie: An axiomatic approach

The Bargaining Problem paradigm is extended to time-consuming conflict situations. Such a situation can be represented by a chain of bargaining domains, each representing the conflict at a different point in time. The solution function selects a point in the union of all these domains. We characterize a solution function which satisfies several requirements and explore its properties. One of the results is that an extension of the Adding requirement (Thomson-Myerson 1980) is enough, under some conditions, to yield a solution point, so there is no need to extend the stronger requirements of Independence of Irrelevant Alternatives (Nash 1950) or Monotonicity (Kalai-Smorodinsky 1975).     

Individual and collective opportunities

We consider the bargaining problem in the context of a variable number of agents. When new agents enter the scene but the opportunities open to the enlarged group do not expand, some solutions paradoxically may recommend that some of the agents originally present gain. We propose a quantitative measure of the extent to which a solution allows this phenomenon to occur and we rank the major solutions on that basis. The Kalai-Smorodinsky solution performs better than all weakly pareto-optimal and anonymous solution, and in particular strictly better than the Nash solution. However, the two solutions are equivalent when it is the opportunities for gains offered to initial groups, instead of individuals, that are being compared.     

Bargaining solutions at work: Qualitative differences in policy implications

Traditional bargaining theory characterizes solutions to bargaining problems by their properties in the utility space. In applications, however, one is usually interested in the implications of the conflict resolution within the economic environment, where the properties of axiomatic bargaining solutions are less well understood. By means of a standard bargaining model for the labor market we demonstrate that economic policy implications may be very sensitive to the choice of the bargaining solution. More specifically, the induced employment effects of a change in the reservation wage under the Nash-solution may differ substantially from those under the Kalai–Smorodinsky, the egalitarian, or the equal-loss solution. Hence, the choice of the bargaining solution is not innocuous, even if one is only interested in qualitative policy conclusions.     

Guarantee structures for problems of fair division

We study the problem of fair division in situations where the number of individuals involved may vary while the resources at their disposal remain fixed. We are interested in minimizing the loss that an agent originally present may incur in such circumstances. Given a solution, i.e., a systematic method of solving any division problem in some class, we introduce the notion of its guarantee structure as a measure of the protection it offers to the original agents. We show that the Kalai-Smorodinsky solution offers greater guarantees than any weakly Pareto-optimal and anonymous solution and in particular than the Nash solution.     

Replication invariance of bargaining solutions

This note is concerned with the behavior of bargaining solutions under replication of bargaining problems. A notion of replication, alternative to that studied by Kalai, is proposed, and it is shown that for both the Nash and Kalai-Smorodinsky solutions, the sum of what the agents of each type obtain in the replicated problem is equal to what the agent they are representing would obtain in the original problem under an application of the asymmetric generalization of the solution with weights proportional to the orders of replication of the different types. This similarity in behavior of the two solutions is in contrast with the conclusions reached by Kalai.     

A Differential Games Solution to a Logarithmic Advertising Model

A logarithmic excess-advertising model of a duopoly is presented, and Nash optimal open-loop advertising strategies are determined. It turns out that if the two firms use different discount rates, then the optimal strategies will be exponentially decreasing. However, in this case the state equation has no nice solution and must be solved by numerical methods. When both firms use the same discount rate, then the state equation has a simple solution. This solution is also valid for the case where no discounting is performed. Furthermore, when no discounting is performed, the optimal strategies will be simple time-linear decreasing strategies. Finally, it is studied how the optimal strategies and trajectories depend on the parameters of the model.     

Cooperating and Non-cooperating Firms in Inventive and Absorptive Research

We consider a duopoly competing in quantity, where firms can invest in both innovative and absorptive research and development to reduce their unit production cost, and where they benefit from free spillovers between them. We analyze the case where firms act non-cooperatively and the case where they cooperate by forming a research joint venture. We show that, in both modes of play, there exists a unique symmetric solution. We find that the level of investment in innovative research and development is always the highest and that the efficiency of investment in absorptive research has almost no impact on the equilibrium solution.     

Optimal co-investment in supply chain infrastructure

This paper considers co-investment in a supply chain infrastructure using an inter-temporal model. We assume that firms’ capital is essentially the supply chain’s infrastructure. As a result, firms’ policies consist in selecting an optimal level of employment as well as the level of co-investment in the supply chain infrastructure. Several applications and examples are presented and open-loop, as well as feedback solutions are found for non-cooperating firms, long- and short-run investment cooperation and non-simultaneous moves (Stackelberg) firms. In particular, we show that a solution based on Nash and Stackelberg differential games provides the same level of capital investment. Thus, selecting the leader and the follower in a co-investment program does not matter. We show that in general, co-investments by firms vary both over time and across firms, and thereby render difficult the implementation of co-investment programs for future capital development. To overcome this problem, we derive conditions for firms’ investment share to remain unchanged over time and thus be easily planned.     

The Kalai-Smorodinsky bargaining solution with loss aversion

We consider bargaining problems under the assumption that players are loss averse, i.e., experience disutility from obtaining an outcome lower than some reference point. We follow the approach of Shalev (2002) by imposing the self-supporting condition on an outcome: an outcome z in a bargaining problem is self-supporting under a given bargaining solution, whenever transforming the problem using outcome z as a reference point, yields a transformed problem in which the solution is z.We show that n-player bargaining problems have a unique self-supporting outcome under the Kalai-Smorodinsky solution. For all possible loss aversion coefficients we determine the bargaining solutions that give exactly these outcomes, and characterize them by the standard axioms of Scale Invariance, Individual Monotonicity, and Strong Individual Rationality, and a new axiom called Proportional Concession Invariance (PCI). A bargaining solution satisfies PCI if moving the utopia point in the direction of the solution outcome does not change this outcome.     

Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach

We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero-coupon bond, the inflation-linked real money account and a risky share described by jump-diffusion processes. Using the theory of quadratic-exponential backward stochastic differential equation (BSDE) with jumps approach, we derive the optimal strategy for the two typical utilities (exponential and power) and the value function is characterized as a solution of BSDE with jumps. Finally, we derive the explicit solutions for the optimal investment in both cases of exponential and power utility functions for a diffusion case.     

Supply chain networks,wages, and labor productivity: insights from Lagrange. analysis and computations

The COVID-19 pandemic has dramatically demonstrated the importance of labor to supply chain network activities from production to distribution with shortfalls in labor availability, for numerous reasons, resulting in product shortages and the reduction of profits of firms. Even as progress has been made through vaccinations, issues associated with labor are still arising. Increasing wages is a strategy to enhance labor productivity and, also to ameliorate, in part, labor shortages, but has not, until this work, been explored in a full supply chain network context. Specifically, in this paper, a game theory supply chain network model is constructed of firms competing in producing a substitutable, but differentiated, product, and seeking to determine their equilibrium product path flows, as well as hourly wages to pay their workers, under fixed labor amounts associated with links, and wage-responsive productivity factors. The theoretical and computational approach utilizes the theory of variational inequalities. We first introduce a model without wage bounds on links and then extend it to include wage bounds. Lagrange analysis is conducted for the latter model, which yields interesting insights, as well as an alternative variational inequality formulation. A series of numerical examples reveals that firms can gain in terms of profits by being willing to pay higher wages, resulting in benefits also for their workers, as well as consumers, who enjoy lower demand market prices for the products. However, sensitivity analysis should be conducted to determine the range of such wage bounds. Ultimately, we observed, that the profits may decrease and then stabilize. This work adds to the literature on the integration of concepts from economics and operations research for supply chain networks and also has policy implications.

     

经济增长转型与就业促进

创造就业机会,解决失业问题,已经成为中国政府亟待解决的首要经济发展目标。本文深入分析了改革开放以来经济增长与就业增长之间、资本增长与就业增长之间、工资增长与就业增长之间的关系,并进一步深讨了经济转轨各个阶段就业模式的变化,以及正规就业与非正规就业对就业增长的影响。在此基础上,作者明确指出,经济增长与投资增长对扩大就业的作用正逐渐削弱,宏观经济政策与就业政策的改革也不足以彻底缓解就业压力,解决失业问题的关键在于实现经济增长模式从"经济增长优先"向"就业增长优先"型的转变,正确处理和协调劳动力密集型产业与资本密集型产业之间、劳工利益与资本利益之间、扩大内需与创造就业之间的关系。     

A note on the ‘underadjustment phenomenon’

In recent work in the area of employment discrimination statistics we have noticed that a basic formula quantifying the degree of underadjustment bias in regression coefficients seems not to have been clearly stated and proved. We believe the underadjustment phenomenon to be of great importance in assessing the validity of multiple regression studies of wage disparities in equal employment litigation, and of observational studies involving two populations in general. Since the argument is based entirely on some simple mathematical features of the linear model, the result should be of interest in other fields of application as well.     

The destabilizing effects of the social norm to work under a social security system

We study employment dynamics in an OLG model with unemployment benefits financed by taxing wages, and with a defined contribution plan. The novelty with respect to recent studies of the effects of social security in this context is that we introduce a social norm to work, shaping the worker’s participation decision, and hence affecting the reservation wage. We find that a strong social norm to work destabilizes conventional wisdom by reversing the negative effects of social security on employment, and destabilizes the economy by facilitating the emergence of endogenous fluctuations.     

高科技企业与知识型员工劳资之间的薪酬博弈模型

近年来,一些高科技企业的知识型员工过劳、猝死和自杀事件层出不穷,学者们从工作压力等不同角度对此现象进行了探讨。本文引入不完全信息动态博弈模型,从工资水平和工作压力强度两个方面建立了科技企业和知识型员工的劳资双方多阶段动态薪酬博弈模型,并基于理论推演给出科技企业和知识型员工的博弈效益虚拟数值,进而得到模型的“高薪高工作强度”均衡解。文章揭示了当前高科技企业及其员工倾向于高薪高强度模式的内在机理,也解释了知识型员工采取极端行为的原因,为探究有效平衡经济利益和社会责任的雇佣关系新模式提供借鉴。