基于现货市场的供应链博弈模型

构建了现货市场价格及市场需求均不确定的供应链博弈模型,分析了风险中性供应商的批发价决策、风险厌恶制造商的采购决策,证明博弈均衡存在且唯一。通过解析分析及数值实验探讨了风险态度、现货价格和需求波动及其相关性对供应链博弈的影响。结果表明:1)制造商因规避风险会减小采购,这降低了供应链总效用;2)现货市场存在时制造商会减小向供应商采购的数量,这降低了供应商的利润,但提高了供应链总效用;3)现货价格与市场需求的相关关系让供应商掌握主动,但会降低制造商及整个供应链的绩效。     

Coalitional games: Monotonicity and core

We characterize a monotonic core solution defined on the class of veto balanced games. We also discuss what restricted versions of monotonicity are possible when selecting core allocations. We introduce a family of monotonic core solutions for veto balanced games and we show that, in general, the per capita nucleolus is not monotonic.     

Mean field games with controlled jump–diffusion dynamics: Existence results and an illiquid interbank market model

We study a family of mean field games with a state variable evolving as a multivariate jump–diffusion process. The jump component is driven by a Poisson process with a time-dependent intensity function. All coefficients, i.e. drift, volatility and jump size, are controlled. Under fairly general conditions, we establish existence of a solution in a relaxed version of the mean field game and give conditions under which the optimal strategies are in fact Markovian, hence extending to a jump–diffusion setting previous results established in Lacker (2015). The proofs rely upon the notions of relaxed controls and martingale problems. Finally, to complement the abstract existence results, we study a simple illiquid inter-bank market model, where the banks can change their reserves only at the jump times of some exogenous Poisson processes with a common constant intensity, and provide some numerical results.     

An agreeable collusive equilibrium in differential games with asymmetric players

We study a class of collusive equilibria in differential games with asymmetric players discounting the future at different rates. For such equilibria, at each moment, weights of players can depend on the state of the system. To fix them, we propose using a bargaining procedure according to which players can bargain again at every future moment. By choosing as threat point the feedback noncooperative outcome, the corresponding solution, if it exists, is agreeable. An exhaustible resource game illustrates the results.     

Survey on applications of semi-tensor product method in networked evolutionary games

Semi-tensor product (STP) method of matrices has received more and more attention from the communities of both engineering and economics in recent years. This paper presents a comprehensive survey on the applications of STP method in the theory of networked evolutionary games. In the beginning, some preliminary results on STP method are recalled. Then, the applications of STP method in many kinds of networked evolutionary games, such as general networked evolutionary games, networked evolutionary games with finite memories, networked evolutionary games defined on finite networks, and random networked evolutionary games, are reviewed. Finally, several research problems in the future are predicted.     

How fast can Maker win in fair biased games?

We study $(a:a)$ Maker–Breaker games played on the edge set of the complete graph on $n$ vertices. In the following four games — perfect matching game, Hamilton cycle game, star factor game and path factor game, our goal is to determine the least number of moves which Maker needs in order to win these games. Moreover, for all games except for the star factor game, we show how first player can win in the strong version of these games.     

Mayer control problem with probabilistic uncertainty on initial positions

In this paper we introduce and study an optimal control problem in the Mayer's form in the space of probability measures on ${\mathbb{R}}^n$ endowed with the Wasserstein distance. Our aim is to study optimality conditions when the knowledge of the initial state and velocity is subject to some uncertainty, which are modeled by a probability measure on ${\mathbb{R}}^d$ and by a vector-valued measure on ${\mathbb{R}}^d$, respectively. We provide a characterization of the value function of such a problem as unique solution of an Hamilton–Jacobi–Bellman equation in the space of measures in a suitable viscosity sense. Some applications to a pursuit-evasion game with uncertainty in the state space is also discussed, proving the existence of a value for the game.     

How to play the Majority game with a liar

The Majority game is played by a questioner () and an answerer (). holds n elements, each of which can be labeled as 0 or 1. is trying to identify some element holds as having the Majority label or, in the case of a tie, claim there is none. To do this asks questions comparing whether two elements have the same or different label. ’s goal is to ask as few questions as possible while ’s goal is to delay as much as possible. Let q^∗ denote the minimal number of questions needed for to identify a Majority element regardless of ’s answers.In this paper we investigate upper and lower bounds for q^∗ in a variation of the Majority game, where is allowed to lie up to t times. We consider two versions of the game, the adaptive (where questions are asked sequentially) and the oblivious (where questions are asked in one batch).     

具有区间联盟值n人对策的Shapley值

本文提出了一类具有区间联盟收益值n人对策的Shapley值.利用区间数运算有关理论,通过建立公理化体系,对具有区间联盟收益值n人对策的Shapley值进行深入研究,证明了这类n人对策Shapley值存在性与唯一性,并给出了此Shapley值的具体表达式及一些性质.最后通过一个算例检验了其有效性与正确性.