Cases in Cooperation and Cutting the Cake

Cooperative game;sharing problem

- A PROCEDURE FOR SHARING RECYCLING COSTS

This paper examines a situation in which the production activities of different agents, in a common geographical location, create waste products that are either of a similar biological or chemical composition or offer commercially compatible combinations. What we propose here, therefore, is a cost-sharing model for the of recycling of their waste products. We concentrate, however, on the specific case in which the agents' activities are heterogeneous. We first examine, from a normative point of view, the cost-sharing rule, which we shall call the multi-commodity serial (MCS) rule. We introduce a property, that we call Cost-Based Equal Treatment, and we demonstrate that the unique rule verifying the Serial Principle and this property is the MCS rule. We then deal with the analysis of the agents' strategic behavior when they are allowed to select their own production levels, in which case the total cost is then split, in accordance with the MCS rule. We show that there is only one Nash equilibrium, which is obtained from an interactive elimination of dominated strategies.Cost Sharing Rules, Serial Cost Sharing, Dominance Solvability.

Semifuzzy games

A new type of decomposition of static games is defined in order to describe cases where overt behavior only is cooperative to a degree. The basic idea is to split the original game into a set of subgames defined by sets of decisions made by the players. In each subgame, different coalitions may form (e.g., two chain stores can cooperate in one city and not in another). To motivate the concept we give an example where such schizophrenic behaviour naturally arise between two firms competing on advertising and quantity. The new type of games are then compared to Aubin's fuzzy games and it is demonstrated that the core of these games with or without side-payments is identical to the core of the original games. We finally show how this type of games degenerates to fuzzy games under certain conditions. The concept of semifuzzy games therefore offers us a new way to think about fuzzy games, which allows us to avoid the interpretational difficulties associated with other approaches.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26171/1/0000250.pd

An Application of Game Theory: Cost Allocation

The allocation of operating costs among the lines of an insurance company is one'of the toughest problems of accounting; it is first shown that most of the methods used by the accountants fail to satisfy some natural requirements. Next it is proved that a cost allocation problem is identical to the determination of the value of a cooperative game with transferable utilities, and 4 new accounting methods that originate from game theory are proposed. One of those methods, the proportional nucleus, is recommended, due to its properties. Several practical examples are discussed throughout the paper. © 1984, International Actuarial Association. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Marginalism and the Shapley value

We survey axiomatic results concerning the Shapley value (Shapley (1953)). This marginalist allocation rule results from an axiomatic study of the class of coalitional games. Shapley (1953) specifies a list of desirable properties of solutions for this class of games, and he shows that the combination of these properties determines a unique allocation rule, now called the Shapley value. Several authors have enriched Shapley’s axiomatic study and have provided new characterizations of this allocation rule. The aim of this article is to put into perspective these characterizations. We highlight the logical relations between the axioms. Moreover, we show how the marginalist criterion, which was not explicitely present in Shapley’s characterisation, is progressively introduced into the axiomatic.Shapley value - axiomatic study - marginalismShapley value - axiomatic study - marginalism

Internal Telephone Billing Rates: A Novel Application of Non-Atomic Game Theory

Internal Telephone Billing Rates: A Novel Application of Non-Atomic Game Theor

Axiomatic Cost and Surplis-Sharing

The equitable division of a joint cost (or a jointly produced output) among agents with different shares or types of output (or input) commodities, is a central theme of the theory of cooperative games with transferable utility. Ever since Shapley's seminal contribution in 1953, this question has generated some of the deepest axiomatic results of modern microeconomic theory.More recently, the simpler problem of rationing a single commodity according to a profile of claims (reflecting individual needs, or demands, or liabilities) has been another fertile ground for axiomatic analysis. This rationing model is often called the bankruptcy problem in the literature.This chapter reviews the normative literature on these two models, and emphasizes their deep structural link via the Additivity axiom for cost sharing: individual cost shares depend additively upon the cost function. Loosely speaking, an additive cost-sharing method can be written as the integral of a rationing method, and this representation defines a linear isomorphism between additive cost-sharing methods and rationing methods.The simple proportionality rule in rationing thus corresponds to average cost pricing and to the Aumann-Shapley pricing method (respectively for homogeneous or heterogeneous output commodities). The uniform rationing rule, equalizing individual shares subject to the claim being an upper bound, corresponds to serial cost sharing. And random priority rationing corresponds to the Shapley-Shubik method, applying the Shapley formula to the Stand Alone costs.Several open problems are included. The axiomatic discussion of non-additive methods to share joint costs appears to be a promising direction for future research.