On the Rule of Chance Moves and Information in Two-Person Games

The value of information has been the subject of many studies in a strategic context.The central question in these studies is how valuable the information hidden in the chance moves of a game is for one or more of the players.Generally speaking, only the extra possibilities that are beneficial for the players have been considered so far.In this note we study the value of information for a special class of two-person games.For these games we also investigate how badly the players can do, both with and without knowing the result of the chance move. In this way one can determine to what extent the players are restricted in their possibilities by the fact that some information is hidden in the chance moves of the games.This allows for a comparison of the influence of the chance move to the control that the players have over the game result.information;games;control

Externalities and Compensation: Primeval Games and Solutions

The classical literature (Pigou (1920), Coase (1960), Arrow (1970)) and the relatively recent studies (cf.Varian (1994)) associate the externality problem with efficiency.This paper focuses explicitly on the compensation problem in the context of externalities.To capture the features of inter-individual externalities, this paper constructs a new game-theoretic framework: primeval games.These games are used to design normative compensation rules for the underlying compensation problems: the marginalistic rule, the concession rule, and the primeval rule.Characterizations of the marginalistic rule and the concession rule are provided and specific properties of the primeval rule are studied.externality;compensation;primeval games;marginalistic rule;concession rule;primeval rule

A note on games corresponding to sequencing situations with due dates

convex cooperative games;one-machine sequencing situations;due dates;ready times

A Non-cooperative Approach to the Compensation Rules for Primeval Games

AMS Classifications: 91A06; 91A10; 91A12externality;compensation;primeval games;marginalistic rule;concession rule;primeval rule;bidding mechanism;implementation

On Convexity for NTU-Games

For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept.Convexity can be defined in a number of ways, each having its own specific attractions.Basically, these definitions fall into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation.For games with non-transferable utility, however, the literature only offers two kinds of convexity, ordinal and cardinal convexity, which both extend the supermodular interpretation.In this paper, we introduce and analyse three new types of convexity for NTU-games that generalise the marginalistic interpretation of convexity.game theory

A Note on the Balancedness and the Concavity of Highway Games

A highway problem is determined by a connected graph which provides all potential entry and exit vertices and all possible edges that can be constructed between vertices, a cost function on the edges of the graph and a set of players, each in need of constructing a connection between a specific entry and exit vertex. Mosquera and Zarzuelo (2006) introduce highway problems and the corresponding cooperative cost games called high- way games to address the problem of fair allocation of the construction costs in case the underlying graph is a chain. In this note, we study the concavity and the balancedness of highway games on more general graphs. A graph G is called highway-game concave if for each highway problem in which G is the underlying graph the corresponding highway game is concave. The main result of our study is that a graph is highway-game concave if and only if it is weakly triangular. Moreover, we provide sufficient conditions on highway problems defined on cyclic graphs such that the corresponding highway games are balanced.cooperative games;highway games;cost sharing

On Three Shapley-Like Solutions for Cooperative Games with Random Payoffs

AMS classification: 90D12.cooperative games;random variables;Shapley values

The Structure of the Set of Equilibria for Two Person Multicriteria Games

In this paper the structure of the set of equilibria for two person multicriteria games is analysed. It turns out that the classical result for the set of equilibria for bimatrix games, that it is a finite union of polytopes, is only valid for multicriteria games if one of the players only has two pure strategies. A full polyhedral description of these polytopes can be derived when the player with an arbitrary number of pure strategies has one criterion.game theory;equilibrium theory