The Rights-Egalitarian Solution for NTU Sharing Problems

The purpose of this paper is to extend the Rights Egalitarian solution (Herrero, Maschler & Villar, 1999) to the context of non-transferable utility sharing problems. Such an extension is not unique. Depending on the kind of properties we want to preserve we obtain two different generalizations. One is the "proportional solution", that corresponds to the Kalai-Smorodinsky solution for surplus sharing problems and the solution in Herrero (1998) for rationing problems. The other is the "Nash solution” that corresponds to the standard Nash bargaining solution for surplus sharing problems and the Nash rationing solution (Mariotti & Villar (2005) for the case of rationing problems.Sharing problems, rights egalitarian solution, NTU problems.

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.

Noncooperative Bargaining in Apex Games and the Kernel

This paper studies non-cooperative bargaining with random proposers in apex games. Two di¤erent protocols are considered: the egalitarian propocol, which selects each player to be the proposer with the same probability, and the proportional protocol, which selects each player with a probability proportional to his number of votes. Expected equilibrium payo¤s coincide with the kernel for the grand coalition regardless of the protocol. Expected payo¤s conditional on a coalition may depend on the protocol: given a coalition of the apex player with a minor player, an egalitarian protocol yields a nearly equal split whereas a proportional protocol leads to a proportional split.noncooperative bargaining;apex games;kernel;random proposers

Formulas for fair, reasonable and non-discriminatory royalty determination

This paper takes an axiomatic approach to determining “Fair, Reasonable, and Non-Discriminatory” (“FRAND”) royalties for intellectual property (“IP”) rights. Drawing on the extensive game theory literature on “surplus sharing/cost sharing” problems, I describe specific formulas for determining license fees that can be derived from basic fairness principles. In particular, I describe the Shapley Value, the Proportional Sharing Rule and the Nucleolus. The Proportional Sharing Rule has the advantage that it is the only rule that is invariant to mergers and splitting of the IP owners. I also explain why, at times, there may be no acceptable to solution. Further, I contrast these rules with the Efficient Component Pricing Rule (“ECPR”) suggested by Baumol and Swanson. Unlike, the ECPR, the rules identified in this paper can uniquely determine license fees when there is more than one owner of essential IP, and also incorporate various notions of fairness and equity.FRAND, Royalty Rates, Intellectual Property

Dividends and Weighted Values in Games with Externalities

We consider cooperative environments with externalities (games in partition function form) and provide a recursive definition of dividends for each coalition and any partition of the players it belongs to. We show that with this definition and equal sharing of these dividends the averaged sum of dividends for each player, over all the coalitions that contain the player, coincides with the corresponding average value of the player. We then construct weighted Shapley values by departing from equal division of dividends and finally, for each such value, provide a bidding mechanism implementing it.

A non-cooperative foundation for the continuous Raiffa solution

This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl–Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player’s opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes