Multi-Issue Allocation Games

This paper introduces a new class of transferable-utility games, called multi-issue allocation games.These games arise from various allocation situations and are based on the concepts underlying the bankruptcy model, as introduced by O'Neill (1982).In this model, a perfectly divisible good (estate) has to be divided amongst a given set of agents, each of whom has some claim on the estate.Contrary to the standard bankruptcy model, the current model deals with situations in which the agents' claims are multi-dimensional, where the dimensions correspond to various issues.It is shown that the class of multi-issue allocation games coincides with the class of (nonnegative) exact games.The run-to-the-bank rule is introduced as a solution for multi-issue allocation situations and turns out to be Shapley value of the corresponding game.Finally, this run-to-the-bank rule is characterised by means of a consistency property.game theory;allocation games

Minimal exact balancedness

To verify whether a transferable utility game is exact, one has to check a linear inequalityfor each exact balanced collection of coalitions. This paper studies the structure andproperties of the class of exact balanced collections. Comparing the definition of exactbalanced collections with the definition of balanced collections, the weight vector of abalanced collection must be positive whereas the weight vector for an exact balancedcollection may contain one negative weight. We investigate minimal exact balanced collections, and show that only these collections are needed to obtain exactness. The relation between minimality of an exact balanced collection and uniqueness of the corresponding weight vector is analyzed. We show how the class of minimal exact balanced collections can be partitioned into three basic types each of which can be systematically generated.operations research and management science;

Compromise Solutions Based on Bankruptcy

In this paper we introduce a new family of compromise solutions for the class of compromise admissible games.These solutions extend bankruptcy rules.In particular, we show that the compromise extension of the run-to-the-bank rule coincides with the barycentre of the core cover and characterise this rule by consistency.We also provide a characterisation of the TAL-family of rules.bankruptcy;games

Job Scheduling, Cooperation and Control

This paper considers one machine job scheduling situations or sequencing problems, where clients can have more than a single job to be processed in order to get a final output.Moreover, a job can be of interest for different players. This means that one of the main assumptions in classic sequencing problems is dropped: the one to one correspondence between clients and jobs.It is shown that the corresponding cooperative games are balanced for specific types of cost criteria.scheduling;cooperation;game theory;cooperative games

Sequencing Games with Repeated Players

Two classes of one machine sequencing situations are considered in which each job corresponds to exactly one player but a player may have more than one job to be processed, so called RP(repeated player) sequencing situations.In max-RP sequencing situations it is assumed that each player's cost function is linear with respect to the maximum completion time of his jobs, whereas in min-RP sequencing situations the cost functions are linear with respect to the minimum completion times.For both classes, following explicit procedures to go from the initial processing order to an optimal order for the coalition of all players, equal gain splitting rules are defined.It is shown that these rules lead to core elements of the associated RP sequencing games.Moreover, it is seen that min-RP sequencing games are convex.cooperative game theory;sequencing;equal gain splitting;core;convexity

Measuring Skill in More-Person Games with Applications to Poker

In several jurisdictions, commercially exploiting a game of chance (rather than skill) is subject to a licensing regime. It is obvious that roulette is a game of chance and chess a game of skill, but the law does not provide a precise description of where the boundary between the two classes is drawn. We build upon the framework of Borm and Van der Genugten (2001) and Dreef et al. (2004) and propose a modification of the skill concept for more-person games. We apply our new skill measure to a simplified version of poker called Straight Poker and conclude that this game should be classified as a game of skill.games of chance;games of skill;poker

Multi-Issue Allocation Games

This paper introduces a new class of transferable-utility games, called multi-issue allocation games.These games arise from various allocation situations and are based on the concepts underlying the bankruptcy model, as introduced by O'Neill (1982).In this model, a perfectly divisible good (estate) has to be divided amongst a given set of agents, each of whom has some claim on the estate.Contrary to the standard bankruptcy model, the current model deals with situations in which the agents' claims are multi-dimensional, where the dimensions correspond to various issues.It is shown that the class of multi-issue allocation games coincides with the class of (nonnegative) exact games.The run-to-the-bank rule is introduced as a solution for multi-issue allocation situations and turns out to be Shapley value of the corresponding game.Finally, this run-to-the-bank rule is characterised by means of a consistency property.