A note on manipulability of large voting schemes

A voting system is a rule which assigns to every possible combination of votes (by any number of individuals) an alternative. We define the notion of asymptotic nonmanipulability for voting systems, and prove that every representable positionalist voting system is asymptotically nonmanipulable. Various aspects of manipulation of large voting schemes and several examples are also discussed.     

Consistent voting systems with a continuum of voters

Voting problems with a continuum of voters and finitely many alternatives are considered. Since the Gibbard–Satterthwaite theorem persists in this model, we relax the non-manipulability requirement as follows: are there social choice functions (SCFs) such that for every profile of preferences there exists a strong Nash equilibrium resulting in the alternative assigned by the SCF? Such SCFs are called exactly and strongly consistent. The paper extends the work of Peleg (Econometrica 46:153–161, 1978a) and others. Specifically, a class of anonymous SCFs with the required property is characterized through blocking coefficients of alternatives and through associated effectivity functions.     

Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization

The concept of coalition proof Nash equilibrium was introduced by Bernheim et al. [5]. In the present paper, we consider the representation problem for coalition proof Nash equilibrium: For a given effectivity function, describing the power structure or the system of rights of coalitions in society, it is investigated whether there is a game form which gives rise to this effectivity function and which is such that for any preference assignment, there is a coalition proof Nash equilibrium.  It is shown that the effectivity functions which can be represented in coalition proof Nash equilibrium are exactly those which satisfy the well-known properties of maximality and superadditivity. As a corollary of the result, we obtain necessary conditions for implementation of a social choice correspondence in coalition proof Nash equilibrium which can be formulated in terms of the associated effectivity function. Received: 24 June 1999/Accepted: 20 September 2000     

Dynamic Policies for Optimal LEO Satellite Launches

Low‐earth orbit satellite (LEO) systems continue to provide mobile communication services. The issue of cost containment in system maintenance is a critical factor for continued operation. Satellite finite life‐times follow a stochastic process, and since satellite replenishment cost is the most significant on‐going cost of operation, finding optimal launch policies is of paramount importance. This paper formulates the satellite launch problem as a Markovian decision model that can be solved using dynamic programming. The policy space of the system is enormous and traditional action space dominance rules do not apply. In order to solve the dynamic program for realistic problem sizes, a novel procedure for limiting the state space considered in the dynamic program is developed. The viability of the proposed solution procedure is demonstrated in example problems using realistic system data. The policies derived by the proposed solution procedure are superior to those currently considered by LEO system operators, and result in substantial annual cost savings.     

Extending the Condorcet Jury Theorem to a general dependent jury

We investigate necessary and sufficient conditions for the existence of Bayesian-Nash equilibria that satisfy the Condorcet Jury Theorem (CJT). In the Bayesian game G _n among n jurors, we allow for arbitrary distribution on the types of jurors. In particular, any kind of dependency is possible. If each juror i has a ??constant strategy??, ?? ⁱ (that is, a strategy that is independent of the size n ?? i of the jury), such that ?? = (?? ¹, ?? ², . . . , ?? ⁿ . . .) satisfies the CJT, then by McLennan (Am Political Sci Rev 92:413?C419, 1998) there exists a Bayesian-Nash equilibrium that also satisfies the CJT. We translate the CJT condition on sequences of constant strategies into the following problem:

(**) For a given sequence of binary random variables X?=?(X ¹, X ², . . . , X ⁿ , . . .) with joint distribution P, does the distribution P satisfy the asymptotic part of the CJT?

We provide sufficient conditions and two general (distinct) necessary conditions for (**). We give a complete solution to this problem when X is a sequence of exchangeable binary random variables.     

Axiomatic characterizations of solutions for Bayesian games

Bayesian equilibria are characterized by means of consistency and one-person rationality in combination with non-emptiness or converse consistency. Moreover, strong and coalition-proof Bayesian equilibria of extended Bayesian games are introduced and it is seen that these notions can be characterized by means of consistency, one-person rationality, a version of Pareto optimality and a modification of converse consistency. It is shown that, in case of the strong Bayesian equilibrium correspondence, converse consistency can be replaced by non-emptiness. As examples we treat Bayesian potential games and Bayesian congestion games.     

Nucleoli as maximizers of collective satisfaction functions

Two preimputations of a given TU game can be compared via the Lorenz order applied to the vectors of satisfactions. One preimputation is `socially more desirable' than the other, if its corresponding vector of satisfactions Lorenz dominates the satisfaction vector with respect to the second preimputation. It is shown that the prenucleolus, the anti-prenucleolus, and the modified nucleolus are maximal in this Lorenz order. Here the modified nucleolus is the unique preimputation which lexicographically minimizes the envies between the coalitions, i.e. the differences of excesses. Recently Sudh?lter developed this solution concept. Properties of the set of all undominated preimputations, the maximal satisfaction solution, are discussed. A function on the set of preimputations is called collective satisfaction function if it respects the Lorenz order. We prove that both classical nucleoli are unique minimizers of certain `weighted Gini inequality indices', which are derived from some collective satisfaction functions. For the (pre)nucleolus the function proposed by Kohlberg, who characterized the nucleolus as a solution of a single minimization problem, can be chosen. Finally, a collective satisfaction function is defined such that the modified nucleolus is its unique maximizer. Received: 18 October 1996 / Accepted: 31 January 1997     

Effectivity functions, game forms, games, and rights

 In this paper we offer an axiomatic approach for the investigation of rights by means of game forms. 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). 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. Several well-known examples are analyzed in the light of our framework. Finally, we find a connection between Sen’s minimal liberalism and Maskin’s result on implementation by Nash equilibria. Received: 25 November 1994/Accepted: 28 June 1996