The Expected Number of Nash Equilibria of a Normal Form Game

Fix finite pure strategy sets _S1,…,_Sn , and let S=_S1×⋯×_Sn . In our model of a random game the agents' payoffs are statistically independent, with each agent's payoff uniformly distributed on the unit sphere in ℝ^S. For given nonempty _T1⊂_S1,…,_Tn⊂_Sn we give a computationally implementable formula for the mean number of Nash equilibria in which each agent i's mixed strategy has support T_i. The formula is the product of two expressions. The first is the expected number of totally mixed equilibria for the truncated game obtained by eliminating pure strategies outside the sets T_i. The second may be construed as the “probability” that such an equilibrium remains an equilibrium when the strategies in the sets _Si∖_Ti become available.     

我国现行个人所得税制的博弈分析

在我国现行个人所得税制下,扣缴人、纳税人、征税人之间的博弈形成了不完全信息动态博弈。将博弈引入税收征管,结合我国的个人所得税以源泉扣缴为主的特点,建立博弈模型求解博弈均衡路径,不但可以检验我国个人所得税制是否达到立法者的预期,而且可以提供优化个人所得税征管机制的各项政策建议。     

Implementation with Near‐Complete Information

Many refinements of Nash equilibrium yield solution correspondences that do not have closed graph in the space of payoffs or information. This has significance for implementation theory, especially under complete information. If a planner is concerned that all equilibria of his mechanism yield a desired outcome, and entertains the possibility that players may have even the slightest uncertainty about payoffs, then the planner should insist on a solution concept with closed graph. We show that this requirement entails substantial restrictions on the set of implementable social choice rules. In particular, when preferences are strict (or more generally, hedonic), while almost any social choice function can be implemented in undominated Nash equilibrium, only monotonic social choice functions can be implemented in the closure of the undominated Nash correspondence.     

Computing Supergame Equilibria

We present a general method for computing the set of supergame equilibria in infinitely repeated games with perfect monitoring and public randomization. We present a three‐stage algorithm that constructs a convex set containing the set of equilibrium values, constructs another convex set contained in the set of equilibrium values, and produces strategies that support them. We explore the properties of this algorithm by applying it to familiar games.     

Bayesian Learning,Smooth Approximate Optimal Behavior,and Convergence to ε‐Nash Equilibrium

In this paper, I construct players' prior beliefs and show that these prior beliefs lead the players to learn to play an approximate Nash equilibrium uniformly in any infinitely repeated slightly perturbed game with discounting and perfect monitoring. That is, given any ε > 0, there exists a (single) profile of players' prior beliefs that leads play to almost surely converge to an ε‐Nash equilibrium uniformly for any (finite normal form) stage game with slight payoff perturbation and any discount factor less than 1.     

不确定交货条件下两供应商-单制造商协同供货模型

研究了不确定交货条件下两供应商-单制造商系统基于惩罚策略的协同供货模型。首先建立了基于惩罚策略的供应商和制造商模型,接着对模型中供应商和制造商的最优决策进行了分析,得出两供应商的最优生产批量决策存在唯一纳什均衡,且最优期望利润间接地受其单位缺货成本的影响,而制造商最优订货批量大于等于市场需求。其次建立了集中决策下供应链利润函数模型,并证明了该函数是决策变量的联合凹函数,存在唯一的最优解。为了达到集中决策下的供应链利润最大化,推导出基于惩罚策略的供应链协同机制。制造商通过调整订货批量和零件单位缺货惩罚成本,在供应链利润最大化前提下获得最大的剩余利润。最后数例分析说明制造商如何通过控制该惩罚成本系数使得供应链协同并获得最大的剩余利润。     

Coordination of Supply Chains with Risk‐Averse Agents

The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk‐averse agents. We take up this issue and begin with defining a coordinating contract as one that results in a Pareto‐optimal solution acceptable to each agent. Our definition generalizes the standard one in the risk‐neutral case. We then develop coordinating contracts in three specific cases: (i) the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint; (ii) the supplier and the retailer each maximizes his own mean‐variance trade‐off; and (iii) the supplier and the retailer each maximizes his own expected utility. Moreover, in case (iii), we show that our contract yields the Nash Bargaining solution. In each case, we show how we can find the set of Pareto‐optimal solutions, and then design a contract to achieve the solutions. We also exhibit a case in which we obtain Pareto‐optimal sharing rules explicitly, and outline a procedure to obtain Pareto‐optimal solutions.     

The Unemployment Volatility Puzzle: Is Wage Stickiness the Answer?

I discuss the failure of the canonical search and matching model to match the cyclical volatility in the job finding rate. I show that job creation in the model is influenced by wages in new matches. I summarize microeconometric evidence and find that wages in new matches are volatile and consistent with the model's key predictions. Therefore, explanations of the unemployment volatility puzzle have to preserve the cyclical volatility of wages. I discuss a modification of the model, based on fixed matching costs, that can increase cyclical unemployment volatility and is consistent with wage flexibility in new matches.     

第四方物流企业作业承接不完全信息双边讨价还价分析

第四方物流(4PL)企业承接物流作业后要依靠第三方物流(3PL)企业来完成物流作业,因而4PL企业承接物流作业的价格决策会受到它与3PL企业交易情况的影响.本文利用不完全信息双边讨价还价博弈得出了4PL企业承接物流作业的价格,分析了价格的影响因素和4PL企业与生产企业达成交易的条件.通过对比4PL企业已知其与3PL企业交易情况和未知其与3PL企业交易情况时的报价,得出了在与生产企业交易过程中,4PL企业在前一情况下的报价高于后一情况下的报价的结论,并分析了产生这一结论的原因.     

考虑零售商风险规避的生鲜供应链区块链技术投资决策及协调

鲜活度信息具有供应商私有性,实际供应链中可能存在谎报现象,投资区块链技术可以抑制供应商的谎报行为。本文分析该技术投入前后供应链均衡解的变化,寻求不同情形下区块链技术成本投资阈值,并设计收入共享契约、回购补偿契约进行供应链协调,提出非对称纳什均衡谈判来分配盈余收益。研究表明:合作博弈下,区块链的成本投资阈值、供应链系统收益大小取决于单位产品区块链技术投入成本、交易缩短后的时间及单位产品交易节约成本,与供应链成员的风险规避度无关;三种Stackelberg博弈都存在一个技术投资临界值,且供应商和零售商所能接受的投资阈值不同,是否投资区块链取决于供应商,信息共享度越高越倾向于投资,且投资成本分担比例只影响批发价格。收入共享契约、回购补偿契约协调均使供应链成员收益达到双赢效果,通过非对称纳什均衡谈判能够实现契约协调后动态盈余收益的分配。最后,本研究给出算例分析验证了相关结论。