On a class of nash-solvable bimatrix games and some related nash subsets

This work is concerned with a particular class of bimatrix games, the set of equilibrium points of which games possess many of the properties of solutions to zero-sum games, including susceptibility to solution by linear programming. Results in a more general setting are also included. Some of the results are believed to constitute interesting potential additions to elementary courses in game theory.     

空间pNA''与对策的NA一致连续性

pNA是无原子对策理论中极其重要的Banach空间,Kohlberg和Tauman已经刻划了pNA中某类对策的特征。本文从另一角度来研究这一困难的问题,目的是刻划比pNA更大,但又与PNA极为相似的Banach空间pNA′中的对策之特征。我们证得pNA′中的对策可用NA一致连续性来刻划。     

A saddle-point theorem for a class of infinite games

In this paper, the existence of a saddle point for two-person zero-sum infinite games of a special type is proved. The games have continuous bilinear payoff functions and strategy sets which are convex, noncompact subsets of an infinite-dimensional vector space. The closures of the strategy sets are, however, compact. The payoff functions satisfy conditions which allow the use of dominance arguments to show that points in the closure of a strategy set are dominated by or are strategically equivalent to points in the strategy set itself. Combining the dominance arguments with a well-known existence theorem produces the main result of the paper. The class of games treated is an extension of a class studied by J. D. Matheson, who obtained explicit solutions for the saddle points by using necessary conditions.     

One-person games of economic survival

This paper discusses the one-person economic survival game model with a discrete probability distribution for the contribution to surplus variable. The general game model and strategies in these games are examined, and necessary conditions which an undominated, stationary strategy must satisfy are obtained. For a special class of these games a mathematical formulation of the value of the game is given, and examples and theorems which relate to undominated strategies in this class are presented. This paper, in some sense, is a sequel to a portion of a paper by Shubik and Thompson [7] which appeared in this journal.     

A note on values and multilinear extensions

An axiomatic formulation is given of a class of values for cooperative games. This class includes the Shapley value and the Banzhaf index, and is related to the multilinear extension of a game.     

A family of games on 1,∞)2 with payoff a function of y/x

A two-parameter class of games on 1,∞)² is studied. The games may be regarded as analogs of Silverman games, having continuous payoff function in place of a step function of y/x. This change is motivated by a desire to move toward a model for competitive situations where the penalty for overspending increases with the amount of overspending. There are some similarities to games with bell-shaped kernel. For most of the region considered in the plane of the two parameters there are solutions of finite type, which are obtained explicitly. There are, however, pockets in this plane where no optimal strategies have been found and possibly where none of finite type exist.     

A note concerning asymmetric games on graphs

We consider a class of asymmetric two-person games played on graphs, and characterize all the positions in the game.     

Game theoretic analysis of maximum cooperative purchasing situations

This article introduces maximum cooperative purchasing (MCP)‐situations, a new class of cooperative purchasing situations. Next, an explicit alternative mathematical characterization of the nucleolus of cooperative games is provided. The allocation of possible cost savings in MCP‐situations, in which the unit price depends on the largest order quantity within a group of players, is analyzed by defining corresponding cooperative MCP‐games. We show that a decreasing unit price is a sufficient condition for a nonempty core: there is a set of marginal vectors that belong to the core. The nucleolus of an MCP‐game can be derived in polynomial time from one of these marginal vectors. To show this result, we use the new mathematical characterization for the nucleolus for cooperative games. Using the decomposition of an MCP‐game into unanimity games, we find an explicit expression for the Shapley value. Finally, the behavior of the solution concepts is compared numerically. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 607–624, 2013     

A multi‐objective model for bank ATM networks

In this paper we present an application of the core solution concepts for multi‐objective games to a bank ATM network model. In these games, the worth of a coalition is given by a subset of vectors of the k‐dimensional space rather than by a scalar. The paper investigates how an ATM network model based on multi‐objective cooperative game theory could be used as an alternative way of setting interchange fees paid by the customer's bank to the one that owns the ATM. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Zero-sum games with multiple goals

This paper investigates a class of two-person zero-sum multiple payoff games in which each component is deterministic. The problem of minimizing a player's total underachievement of a fixed set of goals is shown to reduce to a linear programming problem. Applications are discussed and illustrative examples are presented.     

Probabilistic resource pooling games

We study a setting with a single type of resource and with several players, each associated with a single resource (of this type). Unavailability of these resources comes unexpectedly and with player‐specific costs. Players can cooperate by reallocating the available resources to the ones that need the resources most and let those who suffer the least absorb all the costs. We address the cost savings allocation problem with concepts of cooperative game theory. In particular, we formulate a probabilistic resource pooling game and study them on various properties. We show that these games are not necessarily convex, do have non‐empty cores, and are totally balanced. The latter two are shown via an interesting relationship with Böhm‐Bawerk horse market games. Next, we present an intuitive class of allocation rules for which the resulting allocations are core members and study an allocation rule within this class of allocation rules with an appealing fairness property. Finally, we show that our results can be applied to a spare parts pooling situation.     

Finding saddle points on polyhedra: Solving certain continuous minimax problems

This article reviews procedures for computing saddle points of certain continuous concave-convex functions defined on polyhedra and investigates how certain parameters and payoff functions influence equilibrium solutions. The discussion centers on two widely studied applications: missile defense and market-share attraction games. In both settings, each player allocates a limited resource, called effort, among a finite number of alternatives. Equilibrium solutions to these two-person games are particularly easy to compute under a proportional effectiveness hypothesis, either in closed form or in a finite number of steps. One of the more interesting qualitative properties we establish is the identification of conditions under which the maximizing player can ignore the values of the alternatives in determining allocation decisions. © 1996 John Wiley & Sons, Inc.     

Some games of search on a lattice

In this article we shall deal with some two-person games on a lattice. These are games of search and ambush where the set of strategies of one of the players is determined by functions on the lattice. We give a general method to obtain a solution of these games and we apply it to three particular games. © 1993 John Wiley & Sons, Inc.     

Technical note: Characterization of binomial semivalues through delegation games

Semivalues are allocation rules for cooperative games that assign to each player in a given game a weighted sum of his marginal contributions to all coalitions he belongs to, where the weighting coefficients depend only on the coalition size. Binomial semivalues are a special class of semivalues whose weighting coefficients are obtained by means of a unique parameter. In particular, the Banzhaf value is a binomial semivalue. In this article, we provide an axiomatic characterization for each binomial semivalue. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

网络游戏赌博性质分析

网络游戏产业快速发展的同时,赌博现象混迹其中。网络游戏赌博与传统赌博只是形式上的不同,其实质就是一种赌博行为。只有从教育、法制、监督、自律四方面综合治理,才能使这个行业健康发展。     

On the isbell and marlow fire programming problem

A complete solution is derived to the Isbell and Marlow fire programming problem. The original work of Isbell and Marlow has been extended by determining the regions of the initial state space from which optimal paths lead to each of the terminal states of combat. The solution process has involved determining the domain of controllability for each of the terminal states of combat and the determination of dispersal surfaces. This solution process suggests a solution procedure applicable to a wider class of tactical allocation problems, terminal control attrition differential games. The structure of optimal target engagement policies in “fights to the finish” is discussed.     

不同游戏方式下的暴力网络游戏对大学生攻击性的影响

目的:探讨不同游戏方式下的暴力网络游戏对不同攻击性特质大学生攻击性的影响。方法:采用攻击性特质问卷、词汇决策任务和竞争反应时任务对60名大学生进行问卷和实验研究。结果:在不同游戏方式下,被试表现出的攻击性认知和行为存在显著差异(F(2,52)=4.41,P<0.05;F(1,52)=50.06,P<0.001)。高、低攻击性特质者在游戏后的攻击性认知和行为上存在显著差异(F(1,52)=15.25,P<0.001;F(1,52)=82.35,P<0.001)。结论:不同游戏方式下的暴力网络游戏对大学生的攻击性存在不同的影响,相比竞争游戏和单人游戏,合作游戏是一种较好的游戏方式,可以在一定程度减少大学生,特别是高攻击性特质大学生的攻击性认知和行为。此外,暴力网络游戏对大学生攻击性认知和攻击性行为的影响存在一致性。     

Simple stability of general n- person games

Herein are introduced noncooperative points of n-person games defined on compact and convex sets in a Euclidean space and continuous payoff functions, which are natural extensions of the respective concepts of maximin, minimax strategies and saddle points of two-person games. The conc:ept of equilibrium point appears as a special of one of those. As a particular case, we examine such points for the mixed extension of finite n-person games; finally, a related topic is illustrated. These results represent the first installment of a collection which will be continued in subsequent publications.     

Note: A geometrical method of solving certain games

One of the diagrammatic methods for solving two-person 2 × n matrix games can be extended to solve m × n games where each column of the matrix is a concave function of the row number. This gives a simple proof of a theorem of Benjamin and Goldman that such games have solutions involving no more than two consecutive strategies for the row player, and no more than two strategies for the column player. Two extensions are discussed. © 1994 John Wiley & Sons, Inc.     

Analytic solution for the nucleolus of a three‐player cooperative game

The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programing (LP) problems, or by solving a single, but very large‐scale, LP problem. This article proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed‐form) for a three‐player cooperative game in characteristic function form. We first consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with nonempty core and calculate the nucleolus solution analytically for five possible cases arising from the relationship among the value functions of different coalitions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010