Stable Representations of Constitutions published last year by Springer. A central interpretation of an effectivity function is that it models a constitution. Several well-known examples are analyzed in the light of our framework. Strategical and descriptive concepts of veto and effectivity functions are extended to the model. Such a model is called a bargaining game, and a prescription assigning an alternative to each bargaining game is called a bargaining solution. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function. Written for researchers and students in the field, this volume focuses on social choice functions that admit strong Nash equilibrium.
We fully characterize the representations for three kinds of equilibrium: Nash equilibrium; acceptable equilibrium Pareto optimal Nash equilibrium ; and strong Nash equilibrium. . Loosely speaking this index measures the difficulty of the emergence of configurations that produce a deadlock. The effectivity functions of a strongly Nash implementable social choice correspondence. The solution to the problem of mass elections is fully characterised. In the particular case of simple games, the stability index is closely related to the Nakamura Number.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Rebekah McClure. I can highly recommend the book by Bezalel Peleg and Hans Peters: a real pleasure for scholars working on effectivity functions and social choice functions, and a great learning opportunity for those who are not that familiar with the topics in question. Games in characteristic function form are used to model an allocation of decision power among individuals involved in a voting situation. Structural properties of the system like maximality, regularity, superadditivity and exactness are defined and used to determine the type of instability that may affect the system. Effectivity functions with convex feasible sets.
A common objection to the method of majority decision is that it is illiberal. Configurations that produce instability are called cycles. Using the foregoing definition we investigate game forms that faithfully represent the distribution of power in the society, and allow the members of the society to exercise their rights simultaneously. Further results concern Pareto optimality of Nash equilibrium outcomes. A veto theory is constructed for a finite committee and a measure space of alternatives. Implementation in strong Nash equilibrium.
Several well-known examples are analyzed in the light of our framework. We give a new definition of constitution which consists of three components: the set of rights, the assignment of rights to groups of members of the society, and the distribution of power in the society as a function of the distribution of rights. Equilibria of type 2 and 3. It is a binary relation that says for each coalition T and each subset of outcomes B whether or not T can force the final outcome within B. The latter means that there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions satisfying the minimal requirement of respecting first order stochastic dominance among lotteries.
Abstract The concept of an effectivity function is adopted as a formal model,of a constitution. Economics Version of Record Voting problems with a continuum of voters and finitely many alternatives are considered. Effectivity functions for finitely many players and alternatives are considered. The problem of strong representation is to find a strategically acceptable social choice function that entails the allocation of power prescribed by a given game. You can help correct errors and omissions.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. An overview of the book. Written by two authors who have made outstanding contributions to the developed theory, the book will be very useful for game and social choice experts, lecturers, and master's and Ph. In the noncooperative approach, solutions are derived as equilibria of strategic models describing an underlying bargaining procedure. Abstract Many sincere compliments should be addressed to Bezalel Peleg and Hans Peters, the authors of the book Strategic Social Choice. Cooperative equilibria of type 1. A first main,result of the paper is a characterization of all effectivity functions that have,a Nash consistent representation for the case without,special structure on the set of alternatives social states.
Finally, we find a connection between Sen's minimal liberalism and Maskin's result on implementation by Nash equilibria. It also allows you to accept potential citations to this item that we are uncertain about. Series Title: Responsibility: by Bezalel Peleg, Hans Peters. A representation of an effectivity function is a game form with the same power structure as that speci? Jerusalem Bezalel Peleg Maastricht Hans Peters April 2010 v Contents Preview to this book. It is an excellent contribution, bringing together a lot of material in a single manuscript in a coherent way.
In Section 4 we deal with representations of constitutions by game forms. He then constructs, for all possible committees, well-behaved representative voting procedures which are not distorted by strategic voting, giving complete solutions for certain important classes of committees. In particular, we establish an upper bound on the stability index of maximal interaction forms. Written by two authors who have made outstanding contributions to the developed theory, the book will be very useful for game and social choice experts, lecturers, and master's and Ph. We prove that the stability index for maximal effectivity functions and for maximal local effectivity functions is either 2 or 3. We characterize completely the family of regular binary effectivity rules.
We apply this result to Peleg's problem of strong representation of simple games. Aleskerov, Mathematical Reviews, Issue 2012 b Hans Peters ist Klinischer Psychologe, Sonder- und Heilpädagoge und war über 30 Jahre in einer großen Einrichtung für geistig behinderte Menschen tätig, zuletzt als Leiter der Abteilung Intensivbehandlung. Each definition is followed by a simple but nontrivial example. It presents an overview of the main results in this area during the past four decades. A social choice rule is binary if it is rationalized by an acyclic binary relation.