A characterization of the proportional rule in multi-issue allocation situations

In multi-issue allocation situations, we have to divide a resource among a group of agents. The claim of each agent is a vector specifying the amount claimed by each agent on each issue. We present an axiomatic characterization of the proportional rule.     

On a New Class of Parallel Sequencing Situations and Related Games

This paper considers a special class of sequencing situations with two parallel machines in which each agent has precisely two jobs to be processed, one on each machine. The costs of an agent depend linearly on the final completion time of his jobs. We describe a procedure that provides an optimal processing order of the jobs for some particular classes. Furthermore, we study cooperative games arising from these sequencing situations. Our main result will be on the balancedness of these games.     

Observable graphs

An edge-colored directed graph is observable if an agent that moves along its edges from node to node is able to determine his position in the graph after a sufficiently long observation of the edge colors, and without accessing any information about the traversed nodes. When the agent is able to determine his position only from time to time, the graph is said to be partly observable. Observability in graphs is desirable in situations where autonomous agents are moving on a network and they want to localize themselves with limited information. In this paper, we completely characterize observable and partly observable graphs and show how these concepts relate to other concepts in the literature. Based on these characterizations, we provide polynomial time algorithms to decide observability, to decide partial observability, and to compute the minimal number of observations necessary for finding the position of an agent. In particular we prove that in the worst case this minimal number of observations increases quadratically with the number of nodes in the graph. We then consider the more difficult question of assigning colors to a graph so as to make it observable and we prove that two different versions of this problem are NP-complete.     

John disks,the Apollonian metric,and min-max properties

The main results of this paper are characterizations of John disks-the simply connected proper subdomains of the complex plane that satisfy a twisted double cone connectivity property. One of the characterizations of John disks is an analog of a result due to Gehring and Hag who found such a characterization for quasidisks. In both situations the geometric condition is an estimate for the domain’s hyperbolic metric in terms of its Apollonian metric. The other characterization is in terms of an arc min-max property.     

On solutions of Bayesian games

The theory of Bayesian games, as developped by W. Böge, is axiomatically treated. A direct access to the system of complete reflections is shown. Solutions for these games are defined and characterizations for their existence are given. Concrete situations are investigated for the case of (2,2)-games.     

Decision principles derived from risk measures

In this paper, we argue that a distinction exists between risk measures and decision principles. Though both are functionals assigning a real number to a random variable, we think there is a hierarchy between the two concepts. Risk measures operate on the first “level”, quantifying the risk in the situation under consideration, while decision principles operate on the second “level”, often being derived from the risk measure. We illustrate this distinction with several canonical examples of economic situations encountered in insurance and finance.Special attention is paid to the role of axiomatic characterizations in determining risk measures and decision principles. Some new axiomatic characterizations of families of risk measures and decision principles are also presented.     

Allocation rules for hypergraph communication situations

This paper considers hypergraph communication situations, where for a group of agents the economic possibilities are described by a coalitional game and the communication possibilities are described by a hypergraph in which the nodes are the agents and the edges are the subgroups of agents who can effect communication. Axiomatic characterizations are provided for two allocation rules, the Myerson value and the position value.     

Subgroup additivity in the queueing problem

Subgroup additivity requires that a rule assigns the same expected ‘relative’ utility to each agent whether an agent’s expected relative utility is calculated from the problem involving all agents or from its sub-problems with a smaller number of agents. In this paper, we investigate its implications for the queueing problem. As a result, we present characterizations of five important rules: the minimal transfer rule, the maximal transfer rule, the pivotal rule, the reward based pivotal rule, and the symmetrically balanced VCG rule. In addition to some basic axioms and subgroup additivity, the characterization results can be obtained by additionally imposing either a strategic axiom or an equity axiom.     

Multi-choice clan games and their core

In this paper, we consider market situations with two corners. One corner consists of a group of powerful agents with yes-or-no choices and clan behavior. The other corner consists of non-powerful agents with multi-choices regarding the extent at which cooperation with the clan can be achieved. Multi-choice clan games arise from such market situations. The focus is on the analysis of the core of multi-choice clan games. Several characterizations of multi-choice clan games by the shape of the core are given, and the connection between the convexity of a multi-choice clan game and the stability of its core is studied.      

Sharing costs in highways: A game theoretic approach

This paper introduces a new class of games, highway games, which arise from situations where there is a common resource that agents will jointly use. That resource is an ordered set of several indivisible sections, where each section has an associated fixed cost and each agent requires some consecutive sections. We present an easy formula to calculate the Shapley value, and we present an efficient procedure to calculate the nucleolus for this class of games.     

Tangent segments and orthogonality types in normed planes

The following characterizations of the Euclidean plane are obtained: the two tangent segments of the unit circle of a normed plane from each point of a disc centered at the origin with sufficiently large diameter have equal lengths; the lengths of the tangent segments from each point of a fixed circle centered at the origin are determined only by the radius of this circle. Three further characterizations of the Euclidean plane are obtained by considering properties of certain points related to an exterior point of the unit disc and the two tangent segments corresponding to it. To obtain one of these characterizations, the notion of arc-length orthogonality is introduced, and the Euclidean plane is also characterized via a relation between arc-length orthogonality and Birkhoff orthogonality.     

Convex games with an infinite number of players and sequencing situations

In this paper we study convex games with an infinite countable set of agents and provide characterizations of this class of games. To do so, and in order to overcome some shortcomings related to the difficulty of dealing with infinite orderings, we need to use a continuity property. Infinite sequencing situations where the number of jobs is infinite countable can be related to convex cooperative TU games. It is shown that some allocations turn out to be extreme points of the core of an infinite sequencing game.     

Optimal risk transfer for agents with germs

We introduce a new class of risk measures called generalized entropic risk measures (GERMS) that allow economic agents to have different attitudes towards different sources of risk. We formulate the problem of optimal risk transfer in terms of these risk measures and characterize the optimal transfer contract. The optimal contract involves what we call intertemporal source-dependent quotient sharing, where agents linearly share changes in the aggregate risk reserve that occur in response to shocks to the system over time, with scaling coefficients that depend on the attitudes of each agent towards the source of risk causing the shock. Generalized entropic risk measures are not dilations of a common base risk measure, so our results extend the class of risk measures for which explicit characterizations of the optimal transfer contract can be found.     

A note for tightening 0–1 models

We describe two approaches for 0–1 program model tightening that are based on the coefficient increasing and reduction methods proposed in Dietrich, Escudero and Chance (1993). We present some characterizations for the new formulations to be tighter than the original model. It can be shown that tighter models can be obtained even when applying any of both approaches to a redundant constraint; see Escudero and Muñoz (1998). We also present some situations where these approaches cannot be applied.     

Dynamic pricing and scheduling in a multi-class single-server queueing system

This paper investigates an optimal sequencing and dynamic pricing problem for a two-class queueing system. Using a Markov Decision Process based model, we obtain structural characterizations of optimal policies. In particular, it is shown that the optimal pricing policy depends on the entire queue length vector but some monotonicity results prevail as the composition of this vector changes. A numerical study finds that static pricing policies may have significant suboptimality but simple dynamic pricing policies perform well in most situations.     

General proportional mean residual life model

By considering a covariate random variable in the ordinary proportional mean residual life (PMRL) model, we introduce and study a general model, taking more situations into account with respect to the ordinary PMRL model. We investigate how stochastic structures of the proposed model are affected by the stochastic properties of the baseline and the mixing variables in the model. Several characterizations and preservation properties of the new model under different stochastic orders and aging classes are provided. In addition, to illustrate different properties of the model, some examples are presented.     

The Myerson Value and Superfluous Supports in Union Stable Systems

In this paper, the set of feasible coalitions in a cooperative game is given by a union stable system. Well-known examples of such systems are communication situations and permission structures. Two games associated with a game on a union stable system are the restricted game (on the set of players in the game) and the conference game (on the set of supports of the system). We define two types of superfluous support property through these two games and provide new characterizations for the Myerson value. Finally, we analyze inheritance of properties between the restricted game and the conference game.     

A probabilistic position value

In this article, we generalize the position value, defined by Meessen (Master??s thesis, 1988) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations (Gómez et al. in European Journal of Operational Research 190:539?C556, 2008). We provide two characterizations of this new allocation rule. Following in Slikker??s (International Journal of Game Theory 33:505?C514, 2005a) footsteps, we characterize the probabilistic position value using probabilistic versions of component efficiency and balanced link contributions. Then we generalize the notion of link potential, defined by Slikker (International Game Theory Review 7:473?C489, 2005b) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule.     

Four-point characterizations of real inner product spaces

Generalized euclidean spaces have been characterized among metric spaces by the requirement that each member of certain classes of quadruples of points of the metric space be congruent to a quadruple of points of a euclidean space. The present paper strengthens earlier characterizations which only require the embedding of certain classes of quadruples which contain a linear triple and in which some three of the six distances between pairs of points are equal. These results generalize some similar characterizations of euclidean spaces among normed linear spaces. Received 4 January 1999; revised 12 August 2002.     

Player splitting in extensive form games

By a player splitting we mean a mechanism that distributes the information sets of a player among so-called agents. A player splitting is called independent if each path in the game tree contains at most one agent of every player. Following Mertens (1989), a solution is said to have the player splitting property if, roughly speaking, the solution of an extensive form game does not change by applying independent player splittings. We show that Nash equilibria, perfect equilibria, Kohlberg-Mertens stable sets and Mertens stable sets have the player splitting property. An example is given to show that the proper equilibrium concept does not satisfy the player splitting property. Next, we give a definition of invariance under (general) player splittings which is an extension of the player splitting property to the situation where we also allow for dependent player splittings. We come to the conclusion that, for any given dependent player splitting, each of the above solutions is not invariant under this player splitting. The results are used to give several characterizations of the class of independent player splittings and the class of single appearance structures by means of invariance of solution concepts under player splittings. Received: December 1996/Revised Version: January 2000