Ordinal preference representations

Ordinal preferences have several advantages over the traditional cardinal expressions of preference. Three different representations of ordinal preferences useful in multi-participant modelling are presented, and their features compared. One approach is thepayoff representation that is based on an ordinal normal form game. A second representation of ordinal preferences is thepreference vector, based on the option form of the game. The option form consists of a list of players, with each player followed by the options under its control. The third representation of ordinal preferences is thepreference tree. A preference tree is an implied binary tree that captures the information of preference vector in a more compact manner by making use of its lexicographic structure. The preference tree offers considerable compactness and computational efficiency over the other two approaches.     

On the characterization of weighted simple games

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions.     

Game Trees For Decision Analysis

Game trees (or extensive-form games) were first defined by von Neumann and Morgenstern in 1944. In this paper we examine the use of game trees for representing Bayesian decision problems. We propose a method for solving game trees using local computation. This method is a special case of a method due to Wilson for computing equilibria in 2-person games. Game trees differ from decision trees in the representations of information constraints and uncertainty. We compare the game tree representation and solution technique with other techniques for decision analysis such as decision trees, influence diagrams, and valuation networks.     

A taxonomy of all ordinal 2 × 2 games

The 2 × 2 game is the simplest and most commonly employed representation of strategic conflict. The 78 strict ordinal 2 × 2 games have been used as conflict models extensively, and have been related in several different taxonomies. However, interest has recently focussed on the full set of 726 general ordinal games, in which one or both players may have equal preferences for two or more outcomes. This paper describes the development of a practical taxonomy of all 726 ordinal 2 × 2 games. The taxonomy provides for rapid identification of particular games, gives a convenient ordering, is as consistent as possible with previous work, and yet is not tied to any specific solution concepts. As well, definitions of several significant game properties are developed or extended to general ordinal games and applied in conjunction with the taxonomy.     

Expected utility theory under non-classical uncertainty

In this article, Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.     

Fitting in: Group effects and the evolution of fundamentalism

We provide an evolutionary model of conflict based on dyadic interactions within and between individuals drawn from a society containing fundamentalists and “others.” Thus, the paper presents an asymmetric game representation of group effects. Fundamentalist control of society is inversely related to the degree of social stratification, and fundamentalists’ intolerance of others. If, however, fundamentalism can be feigned (by displaying certain traits), then fundamentalists must balance their intolerance and insularity to take power. The model provides a novel means for distinguishing democratic versus open societies. This leads to a central result characterizing how fair and open societies can peacefully contravene fundamentalism.     

Values for rooted-tree and sink-tree digraph games and sharing a river

We introduce values for rooted-tree and sink-tree digraph games axiomatically and provide their explicit formula representation. These values may be considered as natural extensions of the lower equivalent and upper equivalent solutions for line-graph games studied in van den Brink et al. (Econ Theory 33:349–349, 2007). We study the distribution of Harsanyi dividends. We show that the problem of sharing a river with a delta or with multiple sources among different agents located at different levels along the riverbed can be embedded into the framework of a rooted-tree or sink-tree digraph game correspondingly.     

Coalitional Interval Games for Strategic Games in Which Players Cooperate

We propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. Associating with a strategic game a coalitional interval game we avoid having to take either a pessimistic or an optimistic approach to the problem. The paper makes two contributions to the literature: It provides a theoretical foundation for the study of coalitional interval games and it also provides, studies, and characterizes a natural method of associating coalitional interval games with strategic games.      

Group decision and negotiation support in evolving,nonshared information contexts

Based on evolutionary systems design (ESD), group decision and negotiation support in evolving, nonshared information contexts is discussed. A non-shared information context — one without full information sharing — is associated with what has been loosely called a noncooperative context in the group decision and negotiation support systems (GDNSS) literature. Without full information sharing, we have a game with incomplete information that, in general, is evolving. The paper discusses how the GDNSS, MEDIATOR, supports evolution of the group problem representation — a process of consensus seeking (through information sharing, here partial) subject to problem adaptation and restructuring within which compromise is possible.     

Hyperplane games,prize games and NTU values

The Shapley value is a well-known solution concept for TU games. The Maschler–Owen value and the NTU Shapley value are two well-known extensions of the Shapley value to NTU games. A hyperplane game is an NTU game in which the feasible set for each coalition is a hyperplane. On the domain of monotonic hyperplane games, the Maschler–Owen value is axiomatized (Hart Essays in game theory. Springer, 1994). Although the domain of hyperplane game is a very interesting class of games to study, unfortunately, on this domain, the NTU Shapley value is not well-defined, namely, it assigns an empty set to some hyperplane games. A prize game (Hart Essays in game theory. Springer, 1994) is an NTU game that can be obtained by “truncating” a hyperplane game. As such, a prize game describes essentially the same situation as the corresponding hyperplane game. It turns out that, on the domain of monotonic prize games, the NTU Shapley value is well-defined. Thus, one can define a value which is well-defined on the domain of monotonic hyperplane games as follows: given a monotonic hyperplane game, first, transform it into a prize game, and then apply the NTU Shapley value to it. We refer to the resulting value as the “generalized Shapley value” and compare the axiomatic properties of it with those of the Maschler–Owen value on the union of the class of monotonic hyperplane games and that of monotonic prize games. We also provide axiomatizations of the Maschler–Owen value and the generalized Shapley value on that domain.

     

作为偶缘性的游戏--伽达默尔游戏观解析

伽达默尔的游戏概念与偶缘性联系密切。偶缘性首先从文本阐释中表现出来 ,是对不同阐释境域的关注。游戏将偶缘性演化为一种客体性的边缘状态 ,抽除了游戏中的主体因素 ,从伽达默尔阐释学的游戏概念 ,可以演化到后现代主义无主体的观念。实际上 ,正是通过游戏概念 ,阐释学成为后现代主义的入口     

The chain store paradox

The chain store game is a simple game in extensive form which produces an inconsistency between game theoretical reasoning and plausible human behavior. Well-informed players must be expected to disobey game theoretical recommendations.The chain store paradox throws new light on the well-known difficulties arising in connection with finite repetitions of the prisoners dilemma game. Whereas these difficulties can be resolved by the assumption of secondary utilities arising in the course of playing the game, a similar approach to the chain store paradox is less satisfactory.It is argued that the explanation of the paradox requires a limited rationality view of human decision behavior. For this purpose a three-level theory of decision making is developed, where decisions can be made on different levels of rationality. This theory explains why insight into the rational solution of a decision problem does not necessarily mean that the corresponding course of action will be taken.     

Simultaneous moves multi-person continuous time concession game

The alternating offers strategic bargaining approach (Rubinstein, 1982) suggest a unique perfect equilibrium. In this equilibrium the bargaining ends immediately and the outcome is Pareto optimal. In this paper we consider a bargaining game in which players move simultaneously. Since we allow players only to lower their demands over time we denote this game as a concession game. We demonstrate that in this game there is a perfect equilibrium in which the bargaining lasts long enough so that the pie shrinks to zero. We show that we can generalize this game to a multi-player concession game in a straightforward manner and so avoiding the difficulties of generalizing the alternating offers game to the multi-player case.     

日本游戏批评思想地图——兼论游戏批评的向度

游戏批评包含不少向度,其中有两个向度常被运用,即指向文艺鉴赏的第一向度,与指向超越性问题意识的第二向度。日本的游戏批评起步于20世纪80年代,这些批评对当时流行的宇宙类游戏给予了高度关注,并从游戏文本中解读日本社会的深层构造。之后的游戏批评,把注意力转向游戏中普遍存在的故事性,批评的向度也由超越性的问题意识移向文艺鉴赏,逐渐成为市场机制的一部分。2000年以后,东浩纪与大冢英志的学术论争,催生了“游戏现实主义”,成就了日本游戏批评的最高峰,游戏批评逐渐被引回学术领域。如今,在日本政府与游戏业界的协助下,日本学界正在厘清已有的游戏研究成果,并着力于游戏批评史的建构。     

“囚徒困境”对于访谈研究初涉者的启示

从博弈的角度看，质的访谈是访谈者与被访者之间的博弈游戏，最佳策略是合作，以达成双赢。但对于访谈初涉者，在访谈过程中往往索取很多，给予却很少，结果被访者就成为受损方。不同于拔河游戏的“零和博弈”，一方的损带给另一方的是惠，在质的访谈中，这会成为两败俱伤的“负和博弈”。所以，作为一名访谈研究初涉者，务必走出访谈的“囚徒困境”，摆脱“零和博弈”与“负和博弈”，使访谈成为互惠互利的“正和博弈”。     

A Unified Approach To The Myerson Value And The Position Value

We reconsider the Myerson value and the position value for communication situations. In case the underlying game is a unanimity game, we show that each of these values can be computed using the inclusion--exclusion principle. Linearity of both values permits us to calculate them without needing the dividends of the induced games (graph-restricted game and link game). The expression of these dividends is only derived in the existing literature for special communication situations. Moreover, the associated inclusion--exclusion decomposability property depends on what we have called the graph allocation rule. This rule is the relative degree (relative indicator) for the position value (Myerson value).     

A note on the permutationally convex games

If marginal worth vector of a game for an ordering is in the core, the game does not have to be a p.c. game.     

The Lovász Extension of Market Games

The multilinear extension of a cooperative game was introduced by Owen in 1972. In this contribution we study the Lovász extension for cooperative games by using the marginal worth vectors and the dividends. First, we prove a formula for the marginal worth vectors with respect to compatible orderings. Next, we consider the direct market generated by a game. This model of utility function, proposed by Shapley and Shubik in 1969, is the concave biconjugate extension of the game. Then we obtain the following characterization: The utility function of a market game is the Lovász extension of the game if and only if the market game is supermodular. Finally, we present some preliminary problems about the relationship between cooperative games and combinatorial optimization.