A single-shot game of multi-period inspection

This paper deals with an inspection game of Customs and a smuggler during some days. Customs has two options of patrolling or not. The smuggler can take two strategies of shipping its cargo of contraband or not. Two players have several opportunities to take an action during a limited number of days but they may discard some of the opportunities. When the smuggling coincides with the patrol, there occurs one of three events: the capture of the smuggler by Customs, a success of the smuggling and nothing new. If the smuggler is captured or no time remains to complete the game, the game ends. There have been many studies on the inspection game so far by the multi-stage game model, where both players at a stage know players’ strategies taken at the previous stage. In this paper, we consider a two-person zero-sum single-shot game, where the game proceeds through multiple periods but both players do not know any strategies taken by their opponents on the process of the game. We apply dynamic programming to the game to exhaust all equilibrium points on a strategy space of player. We also clarify the characteristics of optimal strategies of players by some numerical examples.     

Non-zero-sum stochastic differential reinsurance and investment games with default risk

This paper investigates the implications of strategic interaction (i.e., competition) between two CARA insurers on their reinsurance-investment policies. The two insurers are concerned about their terminal wealth and the relative performance measured by the difference in their terminal wealth. The problem of finding optimal policies for both insurers is modelled as a non-zero-sum stochastic differential game. The reinsurance premium is calculated using the variance premium principle and the insurers can invest in a risk-free asset, a risky asset with Heston’s stochastic volatility and a defaultable corporate bond. We derive the Nash equilibrium reinsurance policy and investment policy explicitly for the game and prove the corresponding verification theorem. The equilibrium strategy indicates that the best response of each insurer to the competition is to mimic the strategy of its opponent. Consequently, either the reinsurance strategy or the investment strategy of an insurer with the relative performance concern is riskier than that without the concern. Numerical examples are provided to demonstrate the findings of this study.     

On stability of collaborative supplier selection

This note discusses the possibility of fair gain sharing in cooperative situations where players optimally partition themselves across a number of alternative channels. An example is group purchasing among a set of buyers facing with a range of suppliers. We introduce channel selection games as a new class of cooperative games and give a representation of their cores. With two channels (suppliers), the game has a non-empty core if the gain functions across every individual channel is supermodular.     

双人静态博弈纯战略纳什均衡存在性判别

本文给出了双人有限静态博弈纯战略纳什均衡存在性的一种判别方法。并且，在纳什均衡存在的条件下，本判别法将给出纳什均衡解及解的唯一性判别。     

A supply chain model with direct and retail channels

We study a dual channel supply chain in which a manufacturer sells to a retailer as well as to consumers directly. Consumers choose the purchase channel based on price and service qualities. The manufacturer decides the price of the direct channel and the retailer decides both price and order quantity. We develop conditions under which the manufacturer and the retailer share the market in equilibrium. We show that the difference in marginal costs of the two channels plays an important role in determining the existence of dual channels in equilibrium. We also show that demand variability has a major influence on the equilibrium prices and on the manufacturer’s motivation for opening a direct channel. In the case that the manufacturer and the retailer coordinate and follow a centralized decision maker, we show that adding a direct channel will increase the overall profit. Our numerical results show that an increase in retailer’s service quality may increase the manufacturer’s profit in dual channel and a larger range of consumer service sensitivity may benefit both parties in the dual channel. Our results suggest that the manufacturer is likely to be better off in the dual channel than in the single channel when the retailer’s marginal cost is high and the wholesale price, consumer valuation and the demand variability are low.     

Submodularity of some classes of the combinatorial optimization games

Submodularity (or concavity) is considered as an important property in the field of cooperative game theory. In this article, we characterize submodular minimum coloring games and submodular minimum vertex cover games. These characterizations immediately show that it can be decided in polynomial time that the minimum coloring game or the minimum vertex cover game on a given graph is submodular or not. Related to these results, the Shapley values are also investigated.Supported by the Berlin-Zürich Joint Graduate Program Combinatorics, Geometry, and Computation (CGC), financed by ETH Zürich and the German Science Foundation (DFG).     

Algorithms for non-convexS n -games

We considerS-games in which the setS is the parametric curve{(p ₁ (t),, p _n(t)): t [0, 1]} and thep _i(t) are real polynomials. These games will be referred to asS _n -games. Two iterative algorithms are given in the case ofn = 2. One gives linear convergence to an optimal of player I, and the other gives monotone convergence. In the case of arbitraryn we give an algorithm of the cutting plane family converging to the value. The principal features of this algorithm are that the hyperplanes arise intrinsically as tangents to an associated concave function which is not in general differentiable, and the linear subproblems arise as matrix games. Because of the latter property inactive constraints are in principle automatically dropped. We give a game theoretic convergence proof. This algorithm may be used multiply for bounding optimals of player I.     

强场下的Li-like氖复合机制X光激光的数值模拟

论述了隧道电离和阈上电离加热过程。并把此二过程加到一个non-LTE平均原子模型,用此模型来研究强场下光致电离类锂氖复合机制X射线激光。计算结果表明,当驱动激光脉冲为100fs、波长为0.248μm、功率密度为2×10¹⁷Wcm^-2,氖气的密度为10^-3gcm^-3时,类锂氖精细结构跃迁3d_5/2→2p_3/2(λ=98Å)的最大增益系数约为100cm^-1,其维持时间约为1.5ps。     

Coordination in decentralized assembly systems with uncertain component yields

The literature on assembly systems with random component yields has focused on centralized systems, where a single decision maker chooses all components’ production quantities and incurs all the costs. We consider a decentralized setting where the component suppliers choose their production quantities based solely on their own cost/reward structure, and the assembly firm makes ordering decisions based on its own cost/reward structure. When the suppliers control their inputs but the outputs exhibit random yields, coordination in such systems becomes quite complex. In such situations, incentive alignment control mechanisms are needed so that the suppliers will choose production quantities as in the centralized system case. One such mechanism is to penalize the supplier with the worse delivery performance. We analyze the conditions under which system coordination is achieved while respecting participation constraints. Further, we determine the optimal component ordering policy for the assembly firm and derive the optimal coordinating penalties.     

On extremal pure Nash equilibria for mixed extensions of normal-form games

In this paper we derive conditions under which mixed extensions of normal-form games have least and greatest Nash equilibria in pure strategies, and either of them gives best utilities among all mixed Nash equilibria when strategy spaces are complete separable metric spaces equipped with closed partial orderings, and the values of utility functions are in separable ordered Banach spaces. The obtained results are applied to supermodular normal-form games whose strategy spaces are multidimensional.