The axiomatic approach to three values in games with coalition structure

We study three values for transferable utility games with coalition structure, including the Owen coalitional value and two weighted versions with weights given by the size of the coalitions. We provide three axiomatic characterizations using the properties of Efficiency, Linearity, Independence of Null Coalitions, and Coordination, with two versions of Balanced Contributions inside a Coalition and Weighted Sharing in Unanimity Games, respectively.coalition structure; coalitional value

Cooperative game theory and its application to natural, environmental, and water resource issues : 1. basic theory

Game theory provides useful insights into the way parties that share a scarce resource may plan their use of the resource under different situations. This review provides a brief and self-contained introduction to the theory of cooperative games. It can be used to get acquainted with the basics of cooperative games. Its goal is also to provide a basic introduction to this theory, in connection with a couple of surveys that analyze its use in the context of environmental problems and models. The main models (bargaining games, transfer utility, and non-transfer utility games) and issues and solutions are considered: bargaining solutions, single-value solutions like the Shapley value and the nucleolus, and multi-value solutions such as the core. The cooperative game theory (CGT) models that are reviewed in this paper favor solutions that include all possible players and ignore the strategic stages leading to coalition building. They focus on the possible results of the cooperation by answering questions such as: Which coalitions can be formed? And how can the coalitional gains be divided to secure a sustainable agreement? An important aspect associated with the solution concepts of CGT is the equitable and fair sharing of the cooperation gains.Environmental Economics&Policies,Economic Theory&Research,Livestock&Animal Husbandry,Education for the Knowledge Economy,Education for Development (superceded)

Steady Marginality: A Uniform Approach to Shapley Value for Games with Externalities

The Shapley value is one of the most important solution concepts in cooperative game theory. In coalitional games without externalities, it allows to compute a unique payoff division that meets certain desirable fairness axioms. However, in many realistic applications where externalities are present, Shapley's axioms fail to indicate such a unique division. Consequently, there are many extensions of Shapley value to the environment with externalities proposed in the literature built upon additional axioms. Two important such extensions are "externality-free" value by Pham Do and Norde and value that "absorbed all externalities" by McQuillin. They are good reference points in a space of potential payoff divisions for coalitional games with externalities as they limit the space at two opposite extremes. In a recent, important publication, De Clippel and Serrano presented a marginality-based axiomatization of the value by Pham Do Norde. In this paper, we propose a dual approach to marginality which allows us to derive the value of McQuillin. Thus, we close the picture outlined by De Clippel and Serrano

Coalition Formation in Political Games

We study the formation of a ruling coalition in political environments. Each individual is endowed with a level of political power. The ruling coalition consists of a subset of the individuals in the society and decides the distribution of resources. A ruling coalition needs to contain enough powerful members to win against any alternative coalition that may challenge it, and it needs to be self-enforcing, in the sense that none of its sub-coalitions should be able to secede and become the new ruling coalition. We first present an axiomatic approach that captures these notions and determines a (generically) unique ruling coalition. We then construct a simple dynamic game that encompasses these ideas and prove that the sequentially weakly dominant equilibria (and the Markovian trembling hand perfect equilibria) of this game coincide with the set of ruling coalitions of the axiomatic approach. We also show the equivalence of these notions to the core of a related non-transferable utility cooperative game. In all cases, the nature of the ruling coalition is determined by the power constraint, which requires that the ruling coalition be powerful enough, and by the enforcement constraint, which imposes that no sub-coalition of the ruling coalition that commands a majority is self-enforcing. The key insight that emerges from this characterization is that the coalition is made self-enforcing precisely by the failure of its winning sub-coalitions to be self-enforcing. This is most simply illustrated by the following simple finding: with a simple majority rule, while three-person (or larger) coalitions can be self-enforcing, two-person coalitions are generically not self-enforcing. Therefore, the reasoning in this paper suggests that three-person juntas or councils should be more common than two-person ones. In addition, we provide conditions under which the grand coalition will be the ruling coalition and conditions under which the most powerful individuals will not be included in the ruling coalition. We also use this framework to discuss endogenous party formation.

Coalition Formation in Political Games

We study the formation of a ruling coalition in political environments. Each individual is endowed with a level of political power. The ruling coalition consists of a subset of the individuals in the society and decides the distribution of resources. A ruling coalition needs to contain enough powerful members to win against any alternative coalition that may challenge it, and it needs to be self-enforcing, in the sense that none of its subcoalitions should be able to secede and become the new ruling coalition. We first present an axiomatic approach that captures these notions and determines a (generically) unique ruling coalition. We then construct a simple dynamic game that encompasses these ideas and prove that the sequentially weakly dominant equilibria (and the Markovian trembling hand perfect equilibria) of this game coincide with the set of ruling coalitions of the axiomatic approach. We also show the equivalence of these notions to the core of a related non-transferable utility cooperative game. In all cases, the nature of the ruling coalition is determined by the power constraint, which requires that the ruling coalition be powerful enough, and by the enforcement constraint, which imposes that no subcoalition of the ruling coalition that commands a majority is self-enforcing. The key insight that emerges from this characterization is that the coalition is made self-enforcing precisely by the failure of its winning subcoalitions to be self-enforcing. This is most simply illustrated by the following simple finding: with simple majority rule, while three-person (or larger) coalitions can be self-enforcing, two-person coalitions are generically not self-enforcing. Therefore, the reasoning in this paper suggests that three-person juntas or councils should be more common than two-person ones. In addition, we provide conditions under which the grand coalition will be the ruling coalition and conditions under which the most powerful individuals will not be included in the ruling coalition. We also use this framework to discuss endogenous party formation.Coalition Formation, Collective Choice, Cooperative Game Theory, Political Economy,Self-Enforcing Coalitions, Stability

The Harsanyi paradox and the 'right to talk' in bargaining among coalitions

We introduce a non-cooperative model of bargaining when players are divided into coalitions. The model is a modification of the mechanism in Vidal-Puga (Economic Theory, 2005) so that all the players have the same chances to make proposals. This means that players maintain their own 'right to talk' when joining a coalition. We apply this model to an intriguing example presented by Krasa, Tamimi and Yannelis (Journal of Mathematical Economics, 2003) and show that the Harsanyi paradox (forming a coalition may be disadvantageous) disappears.cooperative games bargaining coalition structure Harsanyi paradox

Pure bargaining problems with a coalition structure

The final publication is available at Springer via http://dx.doi.org/10.1007/s41412-016-0007-2We consider here pure bargaining problems endowed with a coalition structure such that each union is given its own utility. In this context we use the Shapley rule in order to assess the main options available to the agents: individual behavior, cooperative behavior, isolated unions behavior, and bargaining unions behavior. The latter two respectively recall the treatment given by Aumann–Drèze and Owen to cooperative games with a coalition structure. A numerical example illustrates the procedure. We provide criteria to compare any pair of behaviors for each agent, introduce and axiomatically characterize a modified Shapley rule, and determine its natural domain, that is, the set of problems where the bargaining unions behavior is the best option for all agents.Peer ReviewedPostprint (author's final draft

A Focal-Point Solution for Bargaining Problems with Coalition Structure

In this paper we study the restriction, to the class of bargaining problems with coalition structure, of several values which have been proposed on the class of non-transferable utility games with coalition structure. We prove that all of them coincide with the solution independently studied in Chae and Heidhues (2004) and Vidal-Puga (2005a). Several axiomatic characterizations and two noncooperative mechanisms are proposed.coalition structure bargaining values

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