结合案例分析游戏在儿童社会工作个案辅导中的运用

游戏是儿童表达想法和感受的重要媒介,在儿童的成长生活中占据着非常重要的地位。社会工作实务辅导有必要重视游戏对儿童的意义,将之融合进实务辅导之中。但目前我国社会工作专业领域中尚缺乏相关的理论和实践经验。本文结合自身实务经验,提出专业社工可在三个层面借鉴西方儿童游戏治疗理论的经验,指导个案辅导中的游戏运用,以期可以促进儿童个案社会工作实务的新发展。     

结合案例分析游戏在儿童社会工作个案辅导中的运用

游戏是儿童表达想法和感受的重要媒介,在儿童的成长生活中占据着非常重要的地位。社会工作实务辅导有必要重视游戏对儿童的意义,将之融合进实务辅导之中。但目前我国社会工作专业领域中尚缺乏相关的理论和实践经验。本文结合自身实务经验,提出专业社工可在三个层面借鉴西方儿童游戏治疗理论的经验,指导个案辅导中的游戏运用,以期可以促进儿童个案社会工作实务的新发展。     

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。     

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.      

Non-strict ordinal 2 × 2 games: A comprehensive computer-assisted analysis of the 726 possibilities

Game theory has provided many tools for the study of social conflict. The 2 × 2 game has been found to be a particularly useful model. This paper describes the enumeration and analysis of all 726 distinct 2 × 2 games. A computer is used to generate the complete set, and a wide variety of maximin, equilibrium and stability calculations is performed for each player for every outcome in every game. The resulting data set is of great value for both the modeling and analysis of social conflict.     

Folk theorems for the observable implications of repeated games

The fact that infinitely repeated games have many different equilibrium outcomes is known as the Folk Theorem. Previous versions of the Folk Theorem have characterized only the payoffs of the game. This paper shows that over a finite portion of an infinitely repeated game, the concept of perfect equilibrium imposes virtually no restrictions on observable behavior. The Prisoner's Dilemma is presented as an example and discussed in detail.I would like to thank an anonymous referee, Sushil Bikhchandani, David Hirshleifer, David Levine, Thomas Voss, and participants in the UCLA Game Theory Seminar for helpful comments.     

Domination structures and multicriteria problems in n-person games

Multiple criteria decision problems with one decision maker have been recognized and discussed in the recent literature in optimization theory, operations research and management science. The corresponding concept with n-decision makers, namely multicriteria n-person games, has not yet been extensively explored.In this paper we first demonstrate that existing solution concepts for single criterion n-person games in both normal form and characteristic function form induce domination structures (similar to those defined and studied by Yu [39] for multicriteria single decision maker problems) in various spaces, including the payoff space, the imputation space and the coalition space. This discussion provides an understanding of some underlying assumptions of the solution concepts and provides a basis for generalizing and generating new solution concepts not yet defined. Also we illustrate that domination structures may be regarded as a measure of power held by the players.We then illustrate that a multicriteria problem can naturally arise in decision situations involving (partial) conflict among n-persons. Using our discussion of solution concepts for single criterion games as a basis, various approaches for resolving both normal form and characteristic function form multicriteria n-person games are proposed. For multicriteria games in characteristic function form, we define a multicriteria core and show that there exists a single game point whose core is equal to the multicriteria core. If we reduce a multicriteria game to a single criterion game, domination structures which are more general than classical ones must be considered, otherwise some crucial information in the game may be lost. Finally, we discuss a parametrization process which, for a given multicriteria game, associates a single criterion game to each point in a parametric space. This parametrization provides a basis for the discussion of solution concepts in multicriteria n-person games.     

Differential marginality,van den Brink fairness,and the Shapley value

We revisit the characterization of the Shapley value by van den Brink (Int J Game Theory, 2001, 30:309–319) via efficiency, the Null player axiom, and some fairness axiom. In particular, we show that this characterization also works within certain classes of TU games, including the classes of superadditive and of convex games. Further, we advocate some differential version of the marginality axiom (Young, Int J Game Theory, 1985, 14: 65–72), which turns out to be equivalent to the van den Brink fairness axiom on large classes of games.     

Spatial externalities and risk in interdependent security games

Individuals regularly invest in self-protection to reduce the risk of an adverse event. The effectiveness of self-protection often depends on the actions of other economic agents and can be modeled as a stochastic coordination game with multiple Pareto-ranked equilibria. We use lab experiments to analyze tacit coordination in stochastic games with two kinds of interdependencies in payoffs: “non-spatial” in which every agent’s action has an impact on the risk faced by every other agent, and “spatial” in which agents only impact the risk faced by their immediate neighbors. We also compare behavior in the stochastic games to deterministic versions of the same games. We find that coordination on the payoff-dominant equilibrium is significantly easier in the deterministic games than in the stochastic games and that spatial interdependencies lead to greater levels of coordination in the deterministic game but not in the stochastic game. The difficulty with coordination observed in the stochastic games has important implications for many real-world examples of interdependent security and also illustrates the importance of not relying on data from deterministic experiments to analyze behavior in settings with risk.     

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.

     

Toward an understanding of the endogenous nature of group identification in games

It is commonly assumed that identification with a social group is constant throughout the play of a one-shot game in the absence of feedback. Our experiment provides evidence that challenges this assumption. Subjects play one of two versions of the prisoner's dilemma game. These versions are distinguished by the relative attractiveness of the uncooperative action. The version with a relatively attractive uncooperative action is referred to as the Easy Game and the other as the Difficult Game. Subjects who play the Difficult Game, exhibit a change in group identification which is related to their selected action. No such relationship exists within the Easy Game. Additionally, the change primarily occurs after the action is selected rather than upon inspection of the game.     

A Non-cooperative Axiomatization of the Core

We treat a class of multi-person bargaining mechanisms based on games in coalitional form. For this class of games we identify properties of non-cooperative solution concepts, which are necessary and sufficient for the equilibrium outcomes to coincide with the core of the underlying coalitional form game. We view this result as a non-cooperative axiomatization of the core. In contrast to most of the literature on multi-person bargaining we avoid a precise specification of the rules of the game. Alternatively, we impose properties of such games, which give rise to a large class of mechanisms, all of which are relevant for our axiomatization.     

Binary 2 × 2 games

The 2 × 2 game is the simplest interactive decision model that portrays concerned decision makers with genuine choices. There are two players, each of whom must choose one of two strategies, so that there are four possible outcomes. Binary 2 × 2 games are 2 × 2 games with no restrictions on the players' preference relations over the outcomes. They therefore generalize the strict ordinal 2 × 2 games and the ordinal 2 × 2 games, classes which have already been studied extensively. This paper enumerates the strategically distinct binary 2 × 2 games. It also identifies important subsets defined by the number of pure Nash equilibria and the occurrence of dominant strategies.     

Ellsberg games

In the standard formulation of game theory, agents use mixed strategies in the form of objective and probabilistically precise devices to conceal their actions. We introduce the larger set of probabilistically imprecise devices and study the consequences for the basic results on normal form games. While Nash equilibria remain equilibria in the extended game, there arise new Ellsberg equilibria with distinct outcomes, as we illustrate by negotiation games with three players. We characterize Ellsberg equilibria in two-person conflict and coordination games. These equilibria turn out to be related to experimental deviations from Nash equilibrium play.     

Granny Versus Game Theorist: Ambiguity in Experimental Games

We report on an experiment in which subjects choose actions in strategic games with either strategic complements or substitutes against a granny, a game theorist or other subjects. The games are selected in order to test predictions on the comparative statics of equilibrium with respect to changes in strategic ambiguity. We find that subjects face higher ambiguity while playing against the granny than playing against the game theorist if we assume that subjects are ambiguity averse. Moreover, under the same assumption, subjects choose more secure actions in games more prone to ambiguity which is in line with the predictions.      

Minimum cost spanning tree games and spillover stability

This article discusses interactive minimum cost spanning tree problems and argues that the standard approach of using a transferable utility game to come up with a fair allocation of the total costs has some flaws. A new model of spillover games is presented, in which each player??s decision whether or not to cooperate is properly taken into account.     

Marginality,differential marginality,and the Banzhaf value

We revisit the Nowak (Int J Game Theory 26:137–141, 1997) characterization of the Banzhaf value via 2-efficiency, the Dummy player axiom, symmetry, and marginality. In particular, we provide a brief proof that also works within the classes of superadditive games and of simple games. Within the intersection of these classes, one even can drop marginality. Further, we show that marginality and symmetry can be replaced by van den Brink fairness/differential marginality. For this axiomatization, 2-efficiency can be relaxed into superadditivity on the full domain of games.     

Arbitrage,rationality, and equilibrium

No-arbitrage is the fundamental principle of economic rationality which unifies normative decision theory, game theory, and market theory. In economic environments where money is available as a medium of measurement and exchange, no-arbitrage is synonymous with subjective expected utility maximization in personal decisions, competitive equilibria in capital markets and exchange economies, and correlated equilibria in noncooperative games. The arbitrage principle directly characterizes rationality at the market level; the appearance of deliberate optimization by individual agents is a consequence of their adaptation to the market. Concepts of equilibrium behavior in games and markets can thus be reconciled with the ideas that individual rationality is bounded, that agents use evolutionarily-shaped decision rules rather than numerical optimization algorithms, and that personal probabilities and utilities are inseparable and to some extent indeterminate. Risk-neutral probability distributions, interpretable as products of probabilities and marginal utilities, play a central role as observable quantities in economic systems.     

Outsourcing with identical suppliers and shortest-first policy: a laboratory experiment

We study experimentally in the laboratory two 2-player games that mimic a decentralized decision-making situation in which firms repeatedly outsource production orders to multiple identical suppliers. The first game has a unique (inefficient) equilibrium in mixed strategies, while the second game has two (efficient) equilibria in pure strategies and an infinite number of (inefficient) equilibria in mixed strategies. In both games, the optimal social costs can also be obtained via dominated strategies. We find that only in the second game subjects manage to reach an efficient outcome more often when matched in fixed pairs than when randomly rematched each round. Surprisingly, this is because subjects coordinate on dominated strategies (and not an efficient pure strategy equilibrium). We show theoretically that preferences for efficiency cannot explain our experimental results. Inequality aversion, on the other hand, cannot be rejected.     

Three-valued simple games

In this paper we study three-valued simple games as a natural extension of simple games. We analyze to which extent well-known results on the core and the Shapley value for simple games can be extended to this new setting. To describe the core of a three-valued simple game we introduce (primary and secondary) vital players, in analogy to veto players for simple games. Moreover, it is seen that the transfer property of Dubey (1975) can still be used to characterize the Shapley value for three-valued simple games. We illustrate three-valued simple games and the corresponding Shapley value in a parliamentary bicameral system.