Average Monotonic Cooperative Games

A subclass of monotonic transferable utility (T.U.) games is studied: average monotonic games. These games are totally balanced. We prove that the core coincides with both the bargaining set à la Davis and Maschler and the bargaining set à la Mas-Colell. To obtain this result a technique based on reduced games is used. Journal of Economic Literature Classification Number: C71     

Cooperative Outcomes through Noncooperative Games

This paper shows the equivalence between the stable solution set of any cooperative game in characteristic form (G1) and the subgame perfect Nash equilibria in pure strategies of a certain noncooperative game (G2). Players of G1 are named "agents." G2 is played by different players ("principals") who compete in wages to attract agents. The equivalence result holds when there are enough principals (if the game is superadditive, two principals suffice). Finally, another related cooperative game (G3) is constructed with both principals and agents as players. For G2 and G3 the same result is then proven, for any number of principals. Journal of Economic Literature Classification Numbers: C71 and C72.     

Balanced Contributions Axiom in the Solution of Cooperative Games

In a gamevin characteristic function form, suppose the Banzhaf value ψ is used to pay a coalitionSalready formed. Then coalitionSno longer receivesv(S); instead it receivesR^ψ(S) = ∑_{i ∈ S}ψ_i(v_s), wherev_Sdenotes the subgame of coalitionS. Surprisingly, the Shapley value of this new game Sh(N, R^ψ) is equal to the Banzhaf value ofv. In this paper we establish a similar result for all values satisfying balanced contributions axiom. Additionally, we introduce player's weights to obtain the corresponding result in the nonsymmetric case.Journal of Economic LiteratureClassification Number: C71     

不完全信息合作博弈的值：一个很有说服力的例子

一、导言合作博弈理论提出了各种模型来解释合作的收益如何在参与者之间分配。Shapley值在为可转移效用(TU)博弈定义的公平解组中起十分重要的作用。它给出了大量的公理的和非合作的证明。后来,为了把Shapley值扩展到非可转移效用博弈(NTU)中各种技术被开发出来了。比如Shapley     

Stochastic Cooperative Games: Superadditivity, Convexity, and Certainty Equivalents

This paper extends the notions of superadditivity and convexity to stochastic cooperative games. It is shown that convex games are superadditive and have nonempty cores, and that these results also hold in the context of NTU games. Furthermore, a subclass of stochastic cooperative games to which one can associate a deterministic cooperative game is considered. It is shown that such a stochastic cooperative game satisfies properties like nonemptiness of the core, superadditivity, and convexity if and only if the corresponding deterministic game satisfies these properties.Journal of Economic LiteratureClassification Number: C71.     

Comparable Axiomatizations of Two Allocation Rules for Cooperative Games with Transferable Utility and Their Subclass of Data Games

The axiom of balanced collective contributions is introduced as a collective variant of the axiom of balanced contributions proposed by Myerson. It requires the identical average impact of the withdrawal of any agent from a game on the remaining population. It turns out that the axiom of balanced collective contributions and the classical axiom of efficiency characterize the equal allocation of nonseparable costs, an allocation rule that is extensively used in cost allocation problems and in accounting. In particular, the equal allocation of nonseparable costs coincides with the nucleolus on the class of data games within the European REACH legislation. While our result does not hold on data games, extra axioms enable provision of comparable characterizations of the equal allocation of nonseparable costs and the Shapley value on this class of games.     

Common Pool Games are Convex Games

For the class of cooperative common pool games the paper focuses on the question of how, during the preplay negotiation process, the ability of coalitions to enforce their claims imposes externalities on the opposition by having an impact on the jointly produced resource. One of our main results is that common pool games are clear games. Based on this result we are able to derive sufficient conditions for the convexity of the characteristic function, which establishes the second main result in the paper, namely that cooperative common pool games are characterized by increasing returns with respect to the coalition size.     

Action-Graph Games

Representing and reasoning with games becomes difficult once they involve large numbers of actions and players, because the space requirement for utility functions can grow unmanageably. Action-Graph Games (AGGs) are a fully-expressive game representation that can compactly express utility functions with structure such as context-specific independence, anonymity, and additivity. We show that AGGs can be used to compactly represent all games that are compact when represented as graphical games, symmetric games, anonymous games, congestion games, and polymatrix games, as well as games that require exponential space under all of these existing representations. We give a polynomial-time algorithm for computing a player's expected utility under an arbitrary mixed-strategy profile, and show how to use this algorithm to achieve exponential speedups of existing methods for computing sample Nash equilibria. We present results of experiments showing that using AGGs leads to a dramatic increase in the size of games accessible to computational analysis.²     

Ambiguous Games

This paper introduces ambiguous games, a modification of the normal form that allows the presence of vagueness in players' beliefs over the opponents' choice of strategies. An appropriate notion of equilibrium is presented, and a general existence result is proved. Journal of Economic Literature Classification Numbers: C72, D81.     

Knowledge Games

The subject of epistemic logic is firmly entrenched in game theory, including the analysis of common knowledge and of public announcements, such as in 'hat problems'. How to analyse communications to sub groups of the public, and the effects of such common knowledge of a subgroup on the information state of a larger group, has only recently come into fruition. Knowledge games are introduced to provide a comfortably concrete vehicle for the study of such interactions. This paper introduces the concepts of knowledge game, deal of cards, knowledge game state, game action, and action execution. A deal of cards is a function from cards to players. A knowledge game state is represented by a pointed multiagent S5 model on the set of card deals where all players hold the same number of cards as in the actual deal. A game action combines a question with an answer, and is represented by a pointed multiagent S5 frame on the set of possible answers. The execution of a game action in a knowledge game state corresponds to the computation of a pointed multiagent S5 model that is a restriction of the direct product of the corresponding action frame and game model.     

Network Games

In contexts ranging from public goods provision to information collection, a player's well-being depends on his or her own action as well as on the actions taken by his or her neighbours. We provide a framework to analyse such strategic interactions when neighbourhood structure, modelled in terms of an underlying network of connections, affects payoffs. In our framework, individuals are partially informed about the structure of the social network. The introduction of incomplete information allows us to provide general results characterizing how the network structure, an individual's position within the network, the nature of games (strategic substitutes vs. complements and positive vs. negative externalities) and the level of information shape individual behaviour and payoffs.     

Simple Flow Games

This paper considers simple flow situations. We introduce the minimum cut solution and characterize it in terms of one-person efficiency, consistency, and converse consistency. Furthermore, we give several relations between the core of a simple flow game and four other solution concepts: the minimum cut solution, the least core, the kernel, and the bargaining set.Journal of Economic LiteratureClassification Numbers: C71.     

博弈论的新发展:行为博弈论

标准博弈论在"经济理性"假设下分析博弈参与者如何在追求各自最优目标的同时实现均衡。但是,由于现实行为人是"有限理性"的,标准博弈论对实践的解释和指导受到限制。为了延伸博弈论对现实活动的解释,行为博弈论将实验经济学与标准博弈论相融合,在博弈实验的基础上,考察和解释标准理论推断与实验结果之间的差异,引入行为因素改进标准博弈论的基本假定,重构博弈分析模型,以求达到准确解读有限理性的行为人在现实约束中如何行动的目的。     

Absorbing Team Games

A team is a group of people having the same motives but possibly different available actions. A team game is a game where two teams face each other. An absorbing game is a repeated game where some of the entries are absorbing, in the sense that once they are chosen the play terminates, and all future payoffs are equal to the payoff at the stage of termination. We prove that every absorbing team game has an equilibrium payoff and that there are -equilibrium profiles with cyclic structure. Journal of Economic Literature Classification Numbers: C72, C73.     

Games of Status

A status game is a cooperative game in which the outcomes are rank orderings of the players. They are a good model for certain situations in which players care about how their "status" compares with that of other players.
We present several formal models within this class. Included are authoritarian status games (where coalitions may assign positions in the rank ordering to nonmembers) and oligarchic status games (where they are unableto do so). We consider the issues of a value concept for authoritarian games and that of core existence for oligarchic games. We then add a transferable resource to the models, obtaining "games of wealth and status."
Finally, we consider an interesting variant, called a "secession game," where coalitions have the right to secede from the grand coalition and form their own smaller "subsocieties," each with its own hierarchy.     

Games of Fair Division

We consider the problem of fairly allocating an indivisible good to one of several agents equally entitled to it when monetary compensations to the others are possible. Our primary normative concept is no-envy. First, we show that there is no non-manipulable selection from the no-envy solution. Then we study the direct revelation games associated with subsolutions of the no-envy solution. The set of equilibrium allocations of any one of them coincides with the set of envy-free allocations for the true preferences. Journal of Economic Literature Classification Numbers: C72, D63, D7l, D82.     

Cournot and Bertrand Games

The author describes a series of matrix choice games illustrating monopoly, shared monopoly, Cournot, Bertrand, and Stackelberg behavior given either perfect complements or perfect substitutes. The games are created by using a spreadsheet to fill out a profit table given the choices of two players. One player selects the column, the other the row, and the table gives the profit of the row chooser. Because each player has a table, each thinks of him- or herself as the row chooser and the other as the column chooser. The games may be applied to international trade through the traditional Boeing v. Airbus story or, more currently, through foreign sales corporations. Addition of Bertrand competition allows discussion of price wars, and addition of perfect complements allows discussion of the proposed Microsoft breakup.