共查询到20条相似文献,搜索用时 31 毫秒
1.
Sylvain Béal 《Theory and Decision》2010,69(2):183-204
We study the finitely repeated prisoner’s dilemma in which the players are restricted to choosing strategies which are implementable
by a machine with a bound on its complexity. One player has to use a finite automaton while the other player has to use a
finite perceptron. Some examples illustrate that the sets of strategies which are induced by these two types of machines are
different and not ordered by set inclusion. Repeated game payoffs are evaluated according to the limit of means. The main
result establishes that a cooperation at almost all stages of the game is an equilibrium outcome if the complexity of the
machines the players may use is limited enough and if the length T of the repeated game is sufficiently large. This result persists when more than T states are allowed in the player’s automaton. We further consider a variant of the model in which the two players are restricted
to choosing strategies which are implementable by perceptrons and prove that the players can cooperate at most of the stages
provided that the complexity of their perceptrons is sufficiently reduced. 相似文献
2.
Özgür Kıbrıs 《Theory and Decision》2012,72(4):509-523
We interpret solution rules on a class of simple allocation problems as data on the choices of a policy maker. We analyze
conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii) representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical
function on the allocation space. Our main results are as follows: (i) a well-known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction independent and other-c monotonic rule is transitive-rational; and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function. 相似文献
3.
We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic
comparison method, and show that these methods are, respectively, related to the copula T
M
(the minimum operator) and the Ł ukasiewicz copula T
L
used to join marginal cumulative distribution functions into bivariate cumulative distribution functions. Given a collection
of ordered lists of the same length, we generate by means of T
M
and T
L
two probabilistic relations Q
M
and Q
L
and identify their type of transitivity. Finally, it is shown that any probabilistic relation with rational elements on a
3-dimensional space of alternatives which possesses one of these types of transitivity, can be generated by three ordered
lists and at least one of the two extreme comparison methods. 相似文献
4.
We consider the problem of choosing the location of a public facility either (a) on a tree network or (b) in a Euclidean space. (a) (1996) characterize the class of target rules on a tree network by Pareto efficiency and population-monotonicity. Using Vohra's (1999) characterization of rules that satisfy Pareto efficiency and replacement-domination, we give a short proof of the previous characterization and show that it also holds on the domain of symmetric preferences. (b) The result obtained for model (a) proves to be crucial for the analysis of the problem of choosing the location of a public facility in a Euclidean space. Our main result is the characterization of the class of coordinatewise target rules by unanimity, strategy-proofness, and either replacement-domination or population-monotonicity. 相似文献
5.
In this paper, we compare the attitude towards current risk of two expected-utility-maximizing investors who are identical except that the first investor will live longer than the second one. It is often suggested that the young investor should take more risks than the old investor. We consider as a benchmark the case of complete markets with a zero risk-free rate. We show that a necessary and sufficient condition to assure that younger is riskier is that the Arrow-Pratt index of absolute tolerance (T) be convex. If we allow for a positive risk-free rate, the necessary and sufficient condition is T convex, plus T(0) = 0. It extends the well-known result that rational investors can behave myopically if and only if the utility function exhibits constant relative risk aversion. 相似文献
6.
Raymond H. Burros 《Theory and Decision》1975,6(2):177-183
After defining the complementary relation R of a binary relation R on a set X, this paper constructs the binary relation C (is a complementary property of) on the set P of nine well known elementary properties that R might possess. It deduces some theorems about C; especially that symmetry is the only one of these possible properties of R on X that is possessed by C on P. The set P may be enlarged to contain other elementary properties of R on X without changing the truth of these theorems, when the symbols of sets are properly modified. Finally, the paper discusses the desirability of a general theory of elementary properties of binary relations for the further development of statistical decision theory. 相似文献
7.
In the division problem with single-peaked preferences, an allocation rule is strategy-proof for same tops if no one can gain by reporting a false preference relation having the true peak. This new condition is so weak that it is
implied by strategy-proofness and tops-only. We show that the uniform rule is the only rule satisfying this mild property under efficiency and envy-freeness. We then analyze how largely the preference domain can be extended with admitting a rule satisfying the three axioms, and
show that the single-plateaued domain is the unique such maximal domain. 相似文献
8.
McGarvey (Econometrica, 21(4), 608–610, 1953) has shown that any irreflexive and anti-symmetric relation can be obtained as
a relation induced by majority rule. We address the analogous issue for dominance relations of finite cooperative games with
non-transferable utility (coalitional NTU games). We find any irreflexive relation over a finite set can be obtained as the dominance relation of some finite coalitional NTU game. We also show that any such dominance relation
is induced by a non-cooperative game through β-effectivity. Dominance relations obtainable through α-effectivity, however, have to comply with a more restrictive condition, which we refer to as the edge-mapping property. 相似文献
9.
Ranking finite subsets of a given set X of elements is the formal object of analysis in this article. This problem has found a wide range of economic interpretations
in the literature. The focus of the article is on the family of rankings that are additively representable. Existing characterizations
are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn (1996), Journal of Mathematical Psychology
40, 64–77 showed that the number of sufficient and necessary conditions that are needed to characterize such a family has
no upper bound as the cardinality of X increases. In turn, this article proposes a way to overcome these difficulties and allows for the characterization of a meaningful
(sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu’s (1990), Recherches
Economiques de Louvain 56, 383–390) characterization of the cardinality-based rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized
in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of “focal” elements is
not given ex-ante; but brought out by the axioms.
相似文献
10.
M. Carmen Sánchez 《Theory and Decision》1998,45(1):1-17
The rationalization of a choice function, in terms of assumptions that involve expansion or contraction properties of the feasible set, over non-finite sets is analyzed. Schwartz's results (1976), stated in the finite case, are extended to this more general framework. Moreover, a characterization result when continuity conditions are imposed on the choice function, as well as on the binary relation that rationalizes it, is presented. 相似文献
11.
We study the existence of a group of individuals which has some decisive power for social choice correspondences that satisfy a monotonicity property which we call modified monotonicity. And we examine the relation between modified monotonicity and strategy-proofness of social choice correspondences according to the definition by Duggan and Schwartz (2000). We will show mainly the following two results. (1) Modified monotonicity implies the existence of an oligarchy. An oligarchy is a group of individuals such that it has some decisive power (semi-decisiveness), and at least one of the most preferred alternatives of every its member is always chosen by any social choice correspondence. (2) Strategy-proofness of social choice correspondences is equivalent to modified monotonicity. 相似文献
12.
A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In this paper we consider TU-games in which the players are organized into a coalition structure being a finite partition of the set of players. The Shapley value has been generalized by Owen to TU-games in coalition structure. We redefine this value function as a share function and show that this solution satisfies the multiplication property that the share of a player in some coalition is equal to the product of the Shapley share of the coalition in a game between the coalitions and the Shapley share of the player in a game between the players within the coalition. Analogously we introduce a Banzhaf coalition structure share function. Application of these share functions to simple majority games show some appealing properties. 相似文献
13.
We consider domains with a natural property called top-circularity. We show that if such a domain satisfies either the maximal conflict property or the weak conflict property, then it is dictatorial. We obtain the result in Sato (Rev Econ Des 14(3):331–342, 2010) as a corollary. Furthermore, it follows from our results that the union of a single-peaked domain and a single-dipped domain (with respect to a given ordering over the alternatives) is dictatorial. 相似文献
14.
Luisa Carpente Balbina Casas-Méndez Ignacio García-Jurado Anne van den Nouweland 《Theory and Decision》2008,65(3):253-269
We propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and
upper values of finite two-person zero-sum games. Associating with a strategic game a coalitional interval game we avoid having to take either a pessimistic or an optimistic approach to the problem. The paper makes two contributions
to the literature: It provides a theoretical foundation for the study of coalitional interval games and it also provides,
studies, and characterizes a natural method of associating coalitional interval games with strategic games.
相似文献
15.
A bargaining solution is a social compromise if it is metrically rationalizable, i.e., if it has an optimum (depending on the situation, smallest or largest) distance from some reference point. We explore the workability and the limits of metric rationalization in bargaining theory where compromising is a core issue. We demonstrate that many well-known bargaining solutions are social compromises with respect to reasonable metrics. In the metric approach, bargaining solutions can be grounded in axioms on how society measures differences between utility allocations. Using this approach, we provide an axiomatic characterization for the class of social compromises that are based on p-norms and for the attending bargaining solutions. We further show that bargaining solutions which satisfy Pareto Optimality and Individual Rationality can always be metrically rationalized. 相似文献
16.
An efficient method of value assessment of a set of exchangeable alternatives A = {a
1,a
2, ,a
n} is presented. It particularly applies to situations where certain preferences may be easily evaluated or are already known, while other binary comparisons may not at once be available. Further applications are to ranking partial tournaments and the emergence and the characterisation of organisational hierarchy. By sequentially performing transitively efficient assessments of uncompared pairs, an initial weakly acyclical preference structure in A is transformed into an ordering of A in echelons. We call these nicely surveyable preference structures echelon orders. Theoretical properties of echelon orders are investigated, including a characterisation and a numerical representation. 相似文献
17.
Susanne Fuchs-Seliger 《Theory and Decision》2012,72(4):431-444
This article is concerned with extensions of a continuous ordering R on a set X to a subset P(X) of the power set of X. The underlying topology will be the Hausdorff metric topology. We will see that continuous extensions of R do not require that P(X) contain every nonempty finite subset of X. Therefore, the analysis can be applied to consumer theory and inverse choice functions. In analogy to these functions budget
correspondences are established which relate alternatives x with certain subsets of X, according to the extended ordering. 相似文献
18.
Jan Heufer 《Theory and Decision》2011,71(4):575-592
This article explores rationalizability issues for finite sets of observations of stochastic choice in the framework introduced
by Bandyopadhyay et al. (Journal of Economic Theory, 84(1), 95–110, 1999). It is argued that a useful approach is to consider indirect preferences on budgets instead of direct preferences on commodity
bundles. A new rationalizability condition for stochastic choices, “rationalizable in terms of stochastic orderings on the
normalized price space” (rsop), is defined. rsop is satisfied if and only if there exists a solution to a linear feasibility problem. The existence of a solution also implies
rationalizability in terms of stochastic orderings on the commodity space. Furthermore it is shown that the problem of finding
sufficiency conditions for binary choice probabilities to be rationalizable bears similarities to the problem considered here. 相似文献
19.
The budget-voting paradox states that, when social alternatives are proper subsets of a finite set of decisions, choosing
decision-wise according to the majority rule may select an alternative that is covered in the majority tournament among alternatives.
Individual preferences are defined on single decisions, and are extended to preferences over the alternative set by means
of a preference extension rule. We prove the existence of the paradox for any rank-based, monotone, and independent extension
rule.
相似文献
20.
Chen Idson Lorraine Krantz David H. Osherson Daniel Bonini Nicolao 《Journal of Risk and Uncertainty》2001,22(3):227-249
We propose a theory that relates perceived evidence to numerical probability judgment. The most successful prior account of this relation is Support Theory, advanced in Tversky and Koehler (1994). Support Theory, however, implies additive probability estimates for binary partitions. In contrast, superadditivity has been documented in Macchi, Osherson, and Krantz (1999), and both sub- and superadditivity appear in the experiments reported here. Nonadditivity suggests asymmetry in the processing of focal and nonfocal hypotheses, even within binary partitions. We extend Support Theory by revising its basic equation to allow such asymmetry, and compare the two equations' ability to predict numerical assessments of probability from scaled estimates of evidence for and against a given proposition. Both between- and within-subject experimental designs are employed for this purpose. We find that the revised equation is more accurate than the original Support Theory equation. The implications of asymmetric processing on qualitative assessments of chance are also briefly discussed. 相似文献