Allocation of fixed costs: characterization of the (dual) weighted Shapley value.

The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since then several axiomatizations have been proposed including one by Shapley in 1981 specifically addressed to cost allocation, a context in which weights appear naturally. It was at the occasion of a comment in which he only stated the axioms. The present paper offers a proof of Shapley's statement as well as an alternative set of axioms. It is shown that the value is the unique rule that allocates additional fixed costs fairly: only the players who are concerned contribute to the fixed cost and they contribute in proportion to their weights. A particular attention is given to the case where some players are assigned a zero weight.cost allocation, Shapley value, fixed cost.

Cooperative provision of indivisible public goods.

A community faces the obligation of providing an indivisible public good. Each member is capable of providing it at a certain cost and the solution is to rely on the player who can do it at the lowest cost. It is then natural that he or she be compensated by the other players. The question is to know how much they should each contribute. We model this compensation problem as a cost sharing game to which standard allocation rules are applied and related to the solution resulting from the auction procedures proposed by Kleindorfer and Sertel (1994).public goods, cost sharing, core, nucleolus, Shapley value.

Shapley compensation scheme

We study a particular class of cost sharing games – "data games" – covering situations wheresome players own data which are useful for a project pursued by the set of all players. Theproblem is to set up compensations between players. Data games are subadditive butgenerally not concave, and have a nonempty core. We characterize the core and compute thecompensation scheme derived from the Shapley value. We then compare it to the nucleolus.Although we use the term "data" our analysis actually applies to any good characterized bynon rivalry and excludability.cost sharing, Shapley value, nucleolus

Cooperative provision of indivisible public goods

A community faces the obligation of providing an indivisible public good. Each member is capable of providing it at a certain cost and the solution is to rely on the player who can do it at the lowest cost. It is then natural that he or she be compensated by the other players. The question is to know how much they should each contribute. We model this compensation problem as a cost sharing game to which standard allocation rules are applied and related to the solution resulting from the auction procedures proposed by Kleindorfer and Sertel (1994).public goods, cost sharing, core, nucleolus, Shapley value

Allocation of fixed costs and the weighted Shapley value

The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since then several approximations have been proposed including one by Shapley in 1981 specifically addressed to cost allocation, a context in which weights appear naturally. It was at the occasion of a comment in which he only stated the axioms. The present paper offers a proof of Shapley's statement as well as an alternative set of axioms. It is shown that the value is the unique rule that allocates additional fixed costs fairly: only the players who are concerned contribute to the fixed cost and they contribute in proportion to their weights. A particular attention is given to the case where some players are assigned a zero weight.cost allocation, Shapley value, fixed cost

Fixed costs and the axiomatization of Shapley’s sharing rule

The cost sharing rule derived from the Shapley value is the unique sharing rule which allocates fixed costs uniformlyCost sharing, Value, Fixed cost

Data games. Sharing public goods with exclusion

A group of agents considers collaborating on a project which requires putting together elements owned by some of them. These elements are pure public goods with exclusion i.e. nonrival but excludable goods like for instance knowledge, data or information, patents or copyrights. The present paper addresses the question of how should agents be compensated for the goods they own. It is shown that this problem can be framed as a cost sharing game - called ‘data game’ - to which standard cost sharing rules like the Shapley value or the nucleolus can then be applied and compared.Cost sharing, compensation, Shapley value

Data games: Sharing public goods with exclusion.

A group of firms decides to cooperate on a project that requires a combination of inputs held by some of them. These inputs are non-rival but excludable goods i.e. public goods with exclusion such as knowledge, data or information, patents or copyrights. We address the question of how firms should be compensated for the inputs they contribute. We show that this problem can be framed within a cost sharing game whose Shapley comes out as a natural solution. The main result concerns the regular structure of the core that enables a simple characterization of the nucleolus. However, compared to the Shapley value, the nucleolus defines compensations that appear to be less appropriate in the context of data sharing. Our analysis is inspired by the problem faced by the European chemical firms within the regulation program REACH that requires submission by 2018 of a detailed analysis of the substances they produce, import or use.cost sharing, Shapley value, core, nucleolus.

Data games. Sharing public goods with exclusion.

A group of agents considers collaborating on a project which requires putting together elements owned by some of them. These elements are pure public goods with exclusion i.e. nonrival but excludable goods like for instance knowledge, data or information, patents or copyrights. The present paper addresses the question of how should agents be compensated for the goods they own. It is shown that this problem can be framed as a cost sharing game – called "data game" – to which standard cost sharing rules like the Shapley value or the nucleolus can then be applied and compared.cost sharing, compensation, Shapley value.

Imperfect competition à la Negishi also with fixed costs

The paper studies equilibria for economies with imperfect competition and non-convex technologies. Following Negishi firms maximise profits under downward-sloping perceived demand functions. Negishi's assumptions, in particular the assumption of a single monopolistic competitor in each market, are relaxed. Existence of equilibria is obtained, under otherwise standard assumptions, for production sets defined in each firm by the union of a convex technology and a technology subjected to fixed costs. In the light of a counterexample it is assumed that fixed factors are distinct from variable factors. Technically the proof rests on pricing rules.imperfect competition, fixed costs, general equilibrium, perceived demands, pricing rules