Noncooperative exchange using money and broker-dealers

This paper presents a model of exchange where a single commodity serves as a means of payment and trade must pass through designated brokers. Broker buy and sell prices, trader allocations, and broker profits depend on the buy and sell decisions of all the market participants, and the exchange problem is described as a noncooperative game. The existence of an equilibrium is established and bounds are placed on the price spread on each commodity. Finally, the properties of the noncooperative equilibria under replication are examined.     

A closed economy with exogenous uncertainty,different levels of information,money, futures and spot markets

AMoney Game is a model of trade (and production) in which there is a distinguished commodity (real or fiat) which is used as a money; and in which complete rules for the formation of price, as a result of individual strategies, are given. The explicit definition of the games does not necessarily imply the type of solution concept to be used. In this paper we limit our enquiry to the noncooperative equilibrium and its relationship with the competitive equilibrium.     

A Differential Game of Transboundary Industrial Pollution with Emission Permits Trading

Transboundary pollution is a particularly serious problem as it leads people located at regional borders to disproportionately suffer from pollution. In 2007, a cooperative differential game model of transboundary industrial pollution was presented by Yeung. It is the first time that time-consistent solutions are derived in a cooperative differential game on pollution control with industries and governments being separate entities. In this paper, we extend Yeung’s model to an even more general model, in which emission permits trading is taken into account. Our objective is to make use of optimal control theory to find the two regions’ noncooperative and cooperative optimal emission paths such that the regions’ discounted stream of net revenues is maximized. We illustrate the results with a numerical example.     

设施选址博弈问题的无支付机制设计研究

选址博弈是目前国际相关学术领域的重要前沿课题之一. 在选址博弈问题中, 存在n个相互影响的``理性"居民, 他们的住址等信息是其私有信息;设计者需要设计选址机制, 以居民汇报的住址信息为输入, 输出设施位置. 在进行机制设计的过程中, 如何在没有金钱的刺激下, 保证所有居民``说真话", 设计出防策略性无支付机制是其中的重要研究内容. 设施选址博弈问题的无支付机制设计是组合优化和理论计算机科学的交叉学科课题, 在管理科学、信息科学以及社会经济学等领域有着重要的应用, 具有重要的理论意义和实际的应用价值. 现根据不同设施类型及个数、不同个人偏好、不同度量空间以及不同社会总体目标等条件, 介绍各种类型的设施选址博弈模型, 罗列相关的研究成果, 并总结其中尚待解决的问题.     

On implementation via demand commitment games

A simple version of the Demand Commitment Game is shown to implement the Shapley value as the unique subgame perfect equilibrium outcome for any n-person characteristic function game. This improves upon previous models devoted to this implementation problem in terms of one or more of the following: a) the range of characteristic function games addressed, b) the simplicity of the underlying noncooperative game (it is a finite horizon game where individuals make demands and form coalitions rather than make comprehensive allocation proposals and c) the general acceptability of the noncooperative equilibrium concept. A complete characterization of an equilibrium strategy generating the Shapley value outcomes is provided. Furthermore, for 3 player games, it is shown that the Demand Commitment Game can implement the core for games which need not be convex but have cores with nonempty interiors. Received March 1995/Final version February 1997     

A solution for noncooperative games

In this paper, we study solutions of strict noncooperative games that are played just once. The players are not allowed to communicate with each other. The main ingredient of our theory is the concept of rationalizing a set of strategies for each player of a game. We state an axiom based on this concept that every solution of a noncooperative game is required to satisfy. Strong Nash solvability is shown to be a sufficient condition for the rationalizing set to exist, but it is not necessary. Also, Nash solvability is neither necessary nor sufficient for the existence of the rationalizing set of a game. For a game with no solution (in our sense), a player is assumed to recourse to a standard of behavior. Some standards of behavior are examined and discussed.This work was sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and by the National Science Foundation under Grant No. MCS-75-17385-A01. The author is grateful to J. C. Harsanyi for his comments and to S. M. Robinson for suggesting the problem.     

Monotonicity of the mapping associated with a noncooperative multiperson game

A noncooperative multiperson game can be associated with a mapping that generates a variational inequality. The problem of searching for Nash points in the game is equivalent to solving this inequality. Numerical methods for solving the variational inequality rely heavily on the monotonicity of the mapping generating the inequality. At the same time, the mapping associated with the noncooperative multiperson game may not be monotone. Necessary and sufficient conditions are established under which the mapping associated with a finite noncooperative mixed-strategy game of three or more persons is monotone.     

A Bidding Game with Heterogeneous Players

A one-sided limit order book is modeled as a noncooperative game for several players. Agents offer various quantities of an asset at different prices, competing to fulfill an incoming order, whose size is not known a priori. Players can have different payoff functions, reflecting different beliefs about the fundamental value of the asset and probability distribution of the random incoming order. In a previous paper, the existence of a Nash equilibrium was established by means of a fixed point argument. The main issue discussed in the present paper is whether this equilibrium can be obtained from the unique solution to a two-point boundary value problem, for a suitable system of discontinuous ordinary differential equations. Some additional assumptions are introduced, which yield a positive answer. In particular, this is true when there are exactly two players, or when all players assign the same exponential probability distribution to the incoming order. In both of these cases, we also prove that the Nash equilibrium is unique. A counterexample shows that these assumptions cannot be removed, in general.     

An analytic derivation of admissible efficient frontier with borrowing

The admissible efficient portfolio selection problem for risky assets has been discussed by Zhang and Nie. In this paper, the admissible efficient portfolio model is proposed under the assumption that there exists the borrowing (money or a risk free asset) case. The admissible efficient frontiers are developed by the spreads of expected return and risk from admissible errors. The analytic forms of the admissible efficient frontiers when short sales are not allowed on all risky assets are derived from two cases: the borrowing with an upper bound constraint, or without an upper bound constraint. The influence on the admissible efficient frontier is explained under the different interest rates of the borrowing. The differences between the results with the borrowing and the results without the borrowing is revealed by a real numerical example.     

Cooperative Hedging in Incomplete Markets

Abstract

The problem of (partial) hedging contingent claims for a single agent is well studied. This paper studies the problem for the multiagent case in incomplete markets. For this case, a cooperative hedging game is posed as follows: First, all agents contribute some money and collect the money together as the initial total capital, then invest the initial total capital in a trading strategy, and, finally, divide the terminal wealth of the trading strategy and each of them gets a part. We give a characterization of the optimal cooperative hedging strategy and prove that the core of the cooperative hedging game, as a cooperative game with side payment, is nonempty.     

Infinite horizon noncooperative differential games with nonsmooth costs

For a noncooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we study a class of infinite-horizon scalar games with either piecewise linear or piecewise smooth costs, exponentially discounted in time. By the analysis of the value functions, we find that results about existence and uniqueness of admissible solutions to the HJ system, and therefore of Nash equilibrium solutions in feedback form, can be recovered as in the smooth costs case, provided the costs are globally monotone. On the other hand, we present examples of costs such that the corresponding HJ system has infinitely many admissible solutions or no admissible solutions at all, suggesting that new concepts of equilibria may be needed to study games with general nonlinear costs.     

Competitive equilibria in economies with multiple divisible and indivisible commodities and without money

A general equilibrium model is considered with multiple divisible and multiple indivisible commodities. In models with indivisibles it is typically assumed that an indivisible commodity, called money, is present that is needed to transfer the value of amounts of indivisible goods. For economies with divisible and indivisible goods and money and without producers it is well understood in the literature that a general equilibrium exists if the individual demands and supplies for the indivisible goods all belong to the same class of discrete convexity. In this paper we consider economies with multiple divisible and multiple indivisible commodities, but without money as one specific commodity for value transfer. Moreover, we allow for one or more producers that own a nonincreasing returns to scale technology. However, one of the producers has a production technology which is linear in producing divisible goods. In this way the composite of the divisible goods takes over the role of money in the model. Individual endowments being large enough for production together with discrete convexity guarantees the existence of a competitive equilibrium using Kakutani’s fixed point theorem.     

A convergence method for stochastic differential games with a small parameter

A stochastic differential game problem for wideband noise driven system is considered. Often in applications, one have a single realization, then expectation is not appropriate in the cost function. First we will consider the payoff structure in the pathwise but not necessarily in the expected value sense. For N-person noncooperative games, under very general conditions, it will be shown that the optimal equilibrium policies of the limit diffusion when applied to the physical processes, will be δ-equilibrium as the parameters ε > 0 and T→ ∞. A combination of direct averaging and perturbed test function techniques will be used in convergence analysis. Results are shown to hold when mathematical expectations are used in the payoff structure. Two person zero sum games can also be considered in this framework     

Two Game Models for Cooperation with Implicit Noncooperation

We propose two flexible game models to represent and analyze cases that cannot be modeled by current game models. One is called sharing creditability game (SCG) and the other is called bottomline game (BLG). The new models transform cooperative games into new games that incorporate auxiliary information (noncooperative in nature) usually neglected in previous theories. The new games will be solved only by traditional noncooperative game theory. When the new solutions are applied to the original games, the solutions can reflect the auxiliary information in addition to the original objectives of the decision makers or players. Generally, the new solutions are different from the cooperative and the noncooperative solutions of the original games. Existing transferable utility (TU) games and noncooperative games will coincide with special cases of the two new game models. Using SCG and BLG, the prisoner’s dilemma can be reformulated and a richer set of decisions can be considered for the players. The two new game models have potential applications in military and socioeconomic situations.This research was partly funded by the College Engineering, Ohio State University.     

A Markov Model of Production, Trade, and Money: Theory and Artificial Life Simulation

The paper generalizes the Kiyotaki-Wright trade model by treatingthe trading period as a finite game, so Nash's theorem can be used to provethe existence of equilibrium, and by treating the economy as a Markovprocess, so an ergodic theorem can be used to show the existence ofequilibria with desirable properties (e.g., in which money exists). A Markovmodel of trade also allows us to add complexity to the economy withoutadding corresponding complexity to the analysis of the model's properties.The paper also provides artificial life simulations of the Markov economysuggesting that monetary equilibria are dynamically stable and do notrequire high levels of learning or information processing on the part ofagents.     

基于时隙ALOHA协议的数据传输二人随机博弈模型

在一个给定的拓扑网络中研究关于数据传输的二人随机博弈模型.两个局中人（源节点）试图通过一个公共节点向目的节点传输随机数据包,这些数据包被分为重要的数据包和不重要的数据包两类,假设每个局中人都有一个用于存储数据包的有限容量的缓冲器.通过构造数据传输的成本分摊和奖励体系,把这种动态的冲突控制过程建模为具有有限状态集合的随机博弈,研究局中人在这种随机博弈模型下的非合作以及合作行为.在非合作情形下,给出纳什均衡的求解算法;在合作情形下,选择Shapley值作为局中人支付总和的分配方案,并讨论其子博弈一致性,提出使得Shapley值为子博弈一致的分配补偿程序.     

Equilibria of the Games in Choice Form

Equilibrium in choice is a solution-concept for noncooperative games defined in a general framework??the game in choice form. There are two leading ideas of the new definition. One is that the players?? preferences need not be explicitly represented, but earlier accepted solution concepts should be formally derived as particular cases. Secondly, the choice of a player need not be a best reply to the strategy combination of the others, if the choices of the other players are motivated for themselves and a best reply does not exist. It is shown that in the present framework are included classical models of game theory, and the new concept extends various known noncooperative solutions. The main technical results of the paper concern the existence of the equilibrium in choice. As particular cases, known results on the existence of classical solutions are found. Thus, our approach can be also seen as a general method for proving the existence of different solutions for noncooperative games.     

Conflict dissolution by reframing game payoffs using linear perturbations

Human beings have a prevailing drive to achieve their self-interest goals or equilibrium states, which may subsume their social interests. An ideal working environment or cooperative game situation would be one in which each participant or player maximizes his/her own interest while maximizing his/her contribution to the collective group interest. This paper addresses the feasibility, methods, and bounds for reframing a generaln-person game into an ideal game in which full cooperation or a targeted solution can be induced and maintained by the players' self-interest maximization. Criteria for good reframing are introduced. Monotonic games, self-interest cooperative and noncooperative games, and a decomposition theory of general games are also introduced to facilitate the study. It is shown that everyn-person game can be written as the sum of a self-interest cooperative game and a self-interest noncooperative game. Everyn-person game can be reframed so that full cooperation can be achieved by the players' self-interest maximization. Everyn-person game can be reframed so that a targeted solution can be obtained and maintained through the players' self-interest maximization.     

Co-op advertising models in manufacturer–retailer supply chains: A game theory approach

In the literature of cooperative (co-op) advertising, the focus of research is on a relationship in which a manufacturer is the leader and retailers are followers. This relationship implies the dominance of the manufacturer over retailers. Recent market structure reviews have shown a shift of retailing power from manufacturers to retailers. Retailers have equal or even greater power than a manufacturer when it comes to retailing. Based on this new market phenomenon, we intend to explore the role of vertical co-op advertising efficiency with respect to transactions between a manufacturer and a retailer through brand name investments, local advertising expenditures, and sharing rules of advertising expenses. Three co-op advertising models are discussed which are based on two noncooperative games and one cooperative game. In a leader–follower noncooperative game, the manufacturer is assumed to be a leader who first specifies the brand name investment and the co-op subsidization policy. The retailer, as a follower, then decides on the local advertising level. In a noncooperative simultaneous move game, the manufacturer and the retailer are assumed to act simultaneously and independently. In a cooperative game, the system profit is maximized for every Pareto efficient co-op advertising scheme, but not for any other schemes. All Pareto efficient co-op advertising schemes are associated with a single local advertising level and a single brand name investment level, but with variable sharing policies of advertising expenses. The best Pareto efficient advertising scheme is obtained taking members' risk attitudes into account. Utilizing the Nash bargaining model, we discuss two situations that (a) both members are risk averse, and (b) both members are risk neutral. Our results are consistent with the bargaining literature.     

Two noncooperative games between a coalition and its surrounding in a class of n-person games with constant sum

A cooperative game engendered by a noncooperative n-person game (the master game) in which any subset of n players may form a coalition playing an antagonistic game against the residual players (the surrounding) that has a (Nash equilibrium) solution, is considered, along with another noncooperative game in which both a coalition and its surrounding try to maximize their gains that also possesses a Nash equilibrium solution. It is shown that if the master game is the one with constant sum, the sets of Nash equilibrium strategies in both above-mentioned noncooperative games (in which a coalition plays with (against) its surrounding) coincide.