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.     

正则对策的N-M稳定集及其唯一存在定理

研究了有非对称性和负传递性偏好的无限策略对策,提出了N-M稳定集和正则对策的概念,其中N-M稳定集是将合作对策中由Von Neumann 和Morgenstern给出的相应概念引入到策略对策中的.所谓正则对策是指其Nash均衡集中每条链关于一致偏好总有上界的无限策略对策.证明了每个正则对策都有唯一N-M稳定集. 此结果及其应用例子说明正则对策N-M稳定集的概念对于策略对策的纯Nash均衡的精炼起着重要作用.     

Patrolling a perimeter

In this paper we study the problem of patrolling a perimeter. The general situation considered here can correspond to different tactical problems and it is studied from the point of view of game theory. To put the ideas in a context we describe it as follows. An intruder seeks to carry out a sabotage on the perimeter of a protected zone. He has to perform the action along n consecutive days and has to position himself each day at one of m strategic points placed on this border. The first day he can take his place at any of the m points, but on successive days he can move only to adjacent points. Furthermore, the perimeter is protected by a patroller, who will select each day one of the m points to inspect. The strategic situation is modeled as a two-person zero-sum game, which is developed on a cyclic set of m points over n time units. We prove some interesting properties of the strategies, solve the game in closed form under certain constraints and obtain bounds for the value of the game in several non-solved cases.     

进化博弈决策机制设计综述

进化博弈论是一门交叉性强的综合性理论,在国内外已得到广泛研究和应用.本文系统论述了进化博弈的决策机制及其特点,指出了进化博弈研究的趋势,进化博弈论可作为中国科技工作者学习、研究和应用的有力工具.     

Optimal strategic reasoning with McNaughton functions

The aim of the paper is to explore strategic reasoning in strategic games of two players with an uncountably infinite space of strategies the payoff of which is given by McNaughton functions—functions on the unit interval which are piecewise linear with integer coefficients. McNaughton functions are of a special interest for approximate reasoning as they correspond to formulas of infinitely valued Lukasiewicz logic. The paper is focused on existence and structure of Nash equilibria and algorithms for their computation. Although the existence of mixed strategy equilibria follows from a general theorem (Glicksberg, 1952) [5], nothing is known about their structure neither the theorem provides any method for computing them. The central problem of the article is to characterize the class of strategic games with McNaughton payoffs which have a finitely supported Nash equilibrium. We give a sufficient condition for finite equilibria and we propose an algorithm for recovering the corresponding equilibrium strategies. Our result easily generalizes to n-player strategic games which don't need to be strictly competitive with a payoff functions represented by piecewise linear functions with real coefficients. Our conjecture is that every game with McNaughton payoff allows for finitely supported equilibrium strategies, however we leave proving/disproving of this conjecture for future investigations.     

无限阶段网络博弈中合作解的策略稳定性

合作博弈的经典合作解不满足时间一致性, 并缺乏策略稳定性. 本文研究无限阶段网络博弈合作解的策略稳定性理论. 首先建立时间一致的分配补偿程序实现合作解的动态分配, 然后建立针对联盟的惩罚策略, 给出合作解能够被强Nash均衡策略支撑的充分性条件, 最后证明了博弈中的惩罚策略局势是强Nash均衡, 从而保证了合作解的策略稳定性. 作为应用, 考察了重复囚徒困境网络博弈中Shapley值的策略稳定性.     

A differential game without a qualitative saddle point

Saddle points are defined for two-person differential games in which the players have opposing preference orderings over lotteries on a set of qualitative objectives, rather than numerical payoff functions. A simple example is then given of a game without such a qualitative saddle point.     

An evolutionary game theoretic perspective on e-collaboration: The collaboration effort and media relativeness

Studies of e-collaboration from a game-theoretical perspective are practically nonexistent. This article contributes to filling this gap by focusing on the strategic interaction between players as they decide whether and how much to collaborate with each other. We use evolutionary game theory to make predictions about a two-person e-collaboration game. More specifically, we extend the traditional Prisoners’ Dilemma and Snowdrift game theory notions to discrete-strategy e-collaboration games, by explicitly including social punishments into the players’ payoff functions. We also introduce continuous-strategy e-collaboration games with both complete and incomplete information. Finally, we provide two generic dynamic programming models for e-collaboration games with media selection.     

Axiomatizations of the core on the universal domain and other natural domains

We prove that the core on the set of all transferable utility games with players contained in a universe of at least five members can be axiomatized by the zero inessential game property, covariance under strategic equivalence, anonymity, boundedness, the weak reduced game property, the converse reduced game property, and the reconfirmation property. These properties also characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced games, and on the set of superadditive games. Suitable extensions of these properties yield an axiomatization of the core on sets of nontransferable utility games. Received September 1999/Final version December 2000     

“STRAGEDY” OF THE COMMONS

This paper computes open loop and subgame perfect Nash equilibria for an infinite horizon, common property resource model with congestion and stock externalities. The model permits the comparison of the game-theoretic approach and the traditional commons literature, which preceded the widespread recognition of the games, because the underlying assumptions are equivalent. With access to the commons restricted, the subgame perfect equilibrium captures the inefficiency associated with the strategic scramble to capture the resource reserves the open loop does not. Under sole ownership, the two equilibrium concepts coincide with the surplus maximizing extraction policy. In free access, the extraction strategies under both equilibrium concepts coincide with complete rent dissipation.     

Solutions for some bargaining games under the Harsanyi-Selten solution theory,part I: Theoretical preliminaries

Part I of this paper discusses the problem of how to model bargaining behavior, and outlines a few basic ideas of the Harsanyi-Selten solution theory. In particular, we discuss removal of imperfect equilibrium points from the game by using the uniformly perturbed game form. We also describe definition of the solution in terms of payoff-dominance and risk-dominance relations, and in terms of the net strategic distances, between the primitive equilibrium points. Part II of the paper will discuss the actual solutions our theory provides for some important classes of bargaining games.     

约束形式下广义最大元Nash均衡的存在性

运用广义最大元方法在非传递性偏好下给出了博弈均衡的存在性定理,推广了一些经典的博弈均衡存在性定理.在文中介绍策略式博弈的Nash均衡具有宽泛的条件,在微观经济理论中有广泛的应用.     

Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender–attacker game

Many models have been developed to study homeland security games between governments (defender) and terrorists (attacker, adversary, enemy), with the limiting assumption of the terrorists being rational or strategic. In this paper, we develop a novel hybrid model in which a centralized government allocates defensive resources among multiple potential targets to minimize total expected loss, in the face of a terrorist being either strategic or non-strategic. The attack probabilities of a strategic terrorist are endogenously determined in the model, while the attack probabilities of a non-strategic terrorist are exogenously provided. We study the robustness of defensive resource allocations by comparing the government’s total expected losses when: (a) the government knows the probability that the terrorist is strategic; (b) the government falsely believes that the terrorist is fully strategic, when the terrorist could be non-strategic; and (c) the government falsely believes that the terrorist is fully non-strategic, when the terrorist could be strategic. Besides providing six theorems to highlight the general results, we find that game models are generally preferred to non-game model even when the probability of a non-strategic terrorist is significantly greater than 50%. We conclude that defensive resource allocations based on game-theoretic models would not incur too much additional expected loss and thus more preferred, as compared to non-game-theoretic models.     

匹配对策模型的核心稳定性

本文研究匹配合作对策模型的核心稳定性。基于线性规划对偶理论和图论的相关知识，我们首先证明了匹配对策有稳定核心当且仅当其基础二部图有完美匹配。其次我们讨论了几个与核心稳定性密切相关的性质（核心的包容性、对策的精确性和可扩性）并证明了它们的等价性。基于这些结果，我们还讨论了相应问题的算法。     

Competition Among Conventions

A convention can be seen as a way of resolving a coordination problem. If different conventions exist in various geographical, social or other entities (called &;201C;groups&;201D;) and if there is some mobility between these groups, which conventions, if any, will emerge as the successful ones? A simple evolutionary process is suggested and it is shown that the process converges to a Nash equilibrium for all games satisfying weak acyclity. Further, if the process converges, it converges to an efficient convention for all games in which the Pareto optimal symmetric equilibria are strict. Hence, the paper presents an explanation for the endogenous evolution of efficiency. In contrast to most recent studies in evolutionary game theory, the conclusions do not rely on random &;201C;mutations&;201D;. Instead, the driving force is the tendency of players to have increased interaction with member of their own group (viscosity).     

On a New Class of Parallel Sequencing Situations and Related Games

This paper considers a special class of sequencing situations with two parallel machines in which each agent has precisely two jobs to be processed, one on each machine. The costs of an agent depend linearly on the final completion time of his jobs. We describe a procedure that provides an optimal processing order of the jobs for some particular classes. Furthermore, we study cooperative games arising from these sequencing situations. Our main result will be on the balancedness of these games.     

Job scheduling, cooperation, and control

This paper studies one machine job scheduling situations where clients can have more than one job to be processed and where a job can be of interest for different players. Corresponding cooperative games are introduced and a result on balancedness is provided.     

ON A LESS KNOWN NASH EQUILIBRIUM UNIQUENESS RESULT

We generalize a less known Nash equilibrium uniqueness result for games in strategic form. Its power is illustrated by applying it to a Public Goods Game, a Homogeneous Cournot Oligopoly Game and a Formal Transboundary Pollution Game.