Bayesian learning in repeated games of incomplete information

In Nachbar [20] and, more definitively, Nachbar [22], I argued that, for a large class of discounted infinitely repeated games of complete information (i.e. stage game payoff functions are common knowledge), it is impossible to construct a Bayesian learning theory in which player beliefs are simultaneously weakly cautious, symmetric, and consistent. The present paper establishes a similar impossibility theorem for repeated games of incomplete information, that is, for repeated games in which stage game payoff functions are private information. Received: 15 October 1997/Accepted: 17 March 1999     

Double implementation in Nash and strong Nash equilibria

 We deal with the implementation problem where agents in some groups can cooperate (or form coalitions) and in some others cannot. We consider a situation where the planner does not know whether agents in a group can cooperate or not. We provide a necessary and sufficient condition for a correspondence to be implementable in such a situation. Received: 28 February 1995/Accepted: 13 March 1996     

Nash Implementation with Lottery Mechanisms

Consider the problem of exact Nash Implementation of social choice correspondences. Define a lottery mechanism as a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. When preferences over alternatives are strict, we show that Maskin monotonicity (Maskin in Rev Econ stud 66: 23–38, 1999) is both necessary and sufficient for a social choice correspondence to be Nash implementable. We discuss how to relax the assumption of strict preferences. Next, we examine social choice correspondences with private components. Finally, we apply our method to the issue of voluntary implementation (Jackon and Palfrey in J Econ Theory 98: 1–25, 2001).I thank Toyo Sakai for his comments on a previous draft. I also thank two anonymous referees and an editor of this journal for helpful comments that improved this paper. A previous version circulated as “A note on Maskin monotonicity”. After the results presented here were obtained, I became aware of a new unpublished paper by Benoit and Ok (2004). The result of Theorem 2 and the discussion that follows is partially similar to their Theorem 1.     

Estimating the reliability and validity of personal support measures: full information ML estimation with planned incomplete data

Egocentered networks are common in social science research. Here, the unit of analysis is a respondent (ego) together with his/her personal network (alters). Usually, several variables are used to describe the relationship between egos and alters.In this paper, the aim is to estimate the reliability and validity of the averages of these measures by the multitrait–multimethod (MTMM) approach. This approach usually requires at least three repeated measurements (methods) of the same variable (trait) for model identification. This places a considerable burden on the respondent and increases the cost of data collection.In this paper, we use a split ballot MTMM experimental design, proposed by Saris (1999), in which separate groups of respondents get different combinations of just two methods. The design can also be regarded as having a planned missing data structure. The maximum likelihood estimation is used in the manner suggested by Allison (1987) of a confirmatory factor analysis model for MTMM-designs specified in Saris and Andrews (1991). This procedure is applied to social support data collected in the city of Ljubljana (Slovenia) in the year 2000.     

Games with capacity manipulation: incentives and Nash equilibria

Studying the interactions between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and sufficient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal and intern-optimal stable rules. We then introduce generalized games of manipulation in which hospitals move first and state their capacities, and interns are subsequently assigned to hospitals using a sequential mechanism. In this setting, we first consider stable revelation mechanisms and introduce conditions guaranteeing the stability of the outcome. Next, we prove that every stable non-revelation mechanism leads to unstable allocations, unless restrictions on the preferences of the agents are introduced.     

Nash implementation and the bargaining problem

We study Nash implementation of the bargaining solutions in a cake sharing set up. We argue that the minimal Pareto optimal, symmetric and Nash implementable SBS is the one inducing all Pareto optimal and midpoint-dominating utility vectors in each state.     

Maximal symmetry and the Nash solution

The Nash Bargaining Solution is characterised by using the new axiom of Maximal Symmetry in place of Nash's Independence of Irrelevant Alternatives and Symmetry. This axiom expresses the idea that a fair arbitrator should treat symmetric alternatives in the same way, subject to the feasibility constraint. An advantage of the proposed characterisations is that they are valid on a wide set of domains, in particular domains including, or consisting of, non-convex problems. Received: 16 March 1998/Accepted: 13 October 1998     

Nash implementation of Lindahl allocations

We define a class of Nash based mechanisms that implement Lindahl allocations in standard public good economies. As those that first proved Nash implementation of Lindahl allocations, defined by Hurwicz (1979) and Walker (1981), the mechanisms provided here are continuous, feasible, and independent of agents' characteristics. In economies with two agents (e.g., bilateral monopolies, duopolies, principal-agent models), our mechanisms are also applicable, in contrast to the well-behaved mechanisms in the literature, and they satisfy favourable stability properties.     

Distributive justice and the Nash bargaining solution

Suppes-Sen dominance or SS-proofness (SSP) is a commonly accepted criterion of impartiality in distributive justice. Mariotti (Review of Economic Studies, 66, 733–741, 1999) characterized the Nash bargaining solution using Nash’s (Econometrica, 18, 155–162, 1950) scale invariance (SI) axiom and SSP. In this article, we introduce equity dominance (E-dominance). Using the intersection of SS-dominance and E-dominance requirements, we obtain a weaker version of SSP (WSSP). In addition, we consider α ? SSP, where α measures the degree of minimum acceptable inequity aversion; α ? SSP is weaker than weak Pareto optimality (WPO) when α = 1. We then show that it is still possible to characterize the Nash solution using WSSP and SI only or using α -SSP, SI, and individual rationality (IR) only for any \({\alpha \in [0,1)}\). Using the union of SS-dominance and E-dominance requirements, we obtain a stronger version of SSP (SSSP). It turns out that there is no bargaining solution that satisfies SSSP and SI, but the Egalitarian solution turns out to be the unique solution satisfying SSSP.     

纳什均衡与社团管理困境——基于博弈论的高校学生社团管理分析

我国高校学生社团管理上存在的一些问题,正影响和制约着社团新功能的发挥和可持续发展。本文试从博弈视角对之进行重新考量,通过建立、分析博弈模型,求出纳什均衡解,并以此为理论依据,结合具体实践,探讨解决问题的可行途径。     

对等理论与进口商标的翻译

好的商标翻译不仅可以为企业带来好的第一印象,而且可以对产品的销售起到很大的推动作用。尤金奈达的对等翻译理论在进口商标的翻译中有可应用性及可操作性。在该理论指导下翻译进口商标时应采取不同的策略。不仅要达到语言功能上的对等,也要具有对等的经济效益。     

Weakest collective rationality and the Nash bargaining solution

We propose a new axiom, weakest collective rationality (WCR) which is weaker than both weak Pareto optimality (WPO) in Nash’s (Econometrica 18:155–162, 1950) original characterization and strong individual rationality (SIR) in Roth’s (Math Oper Res 2:64–65, 1977) characterization of the Nash bargaining solution. We then characterize the Nash solution by symmetry (SYM), scale invariance (SI), independence of irrelevant alternatives (IIA) and our weakest collective rationality (WCR) axiom.     

An axiomatization of the Nash bargaining solution

I prove that ‘Disagreement Point Convexity’ and ‘Midpoint Domination’ characterize the Nash bargaining solution on the class of two-player bargaining problems and on the class of smooth bargaining problems. I propose an example to show that these two axioms do not characterize the Nash bargaining solution on the class of bargaining problems with more than two players. I prove that the other solutions that satisfy these two properties are not lower hemi-continuous. These different results refine the analysis of Chun (Econ Lett 34:311–316, 1990). I also highlight a rather unexpected link with the result of Dagan et al. (Soc Choice Welfare 19:811–823, 2002).     

A characterization of the Nash bargaining solution

We characterize the Nash bargaining solution replacing the axiom of Independence of Irrelevant Alternatives with three independent axioms: Independence of Non-Individually Rational Alternatives, Twisting, and Disagreement Point Convexity. We give a non-cooperative bargaining interpretation to this last axiom. Received: 4 September 2000/Accepted: 6 September 2001     

On the necessary and sufficient conditions for Nash implementation

The purpose of this paper is to provide a constructive way of checking whether or not a social choice correspondence can be implemented in Nash equilibria. The results apply when there are two or more players. The usefulness of this constructive approach is illustrated for the case of single-peaked preferences over , a two-person public good economy with monotonic preferences, and a two-person exchange economy with monotonic preferences.I am grateful to Rajeev Bhattacharya, William Thomson, Takehiko Yamato, and an anonymous referee, for helpful comments. This research was supported by grants from the Bank of Sweden Tercentenary Foundation and the Royal Swedish Academy of Sciences.     

On continuity of incomplete preferences

A weak (strict) preference relation is continuous if it has a closed (open) graph; it is hemicontinuous if its upper and lower contour sets are closed (open). If preferences are complete these four conditions are equivalent. Without completeness continuity in each case is stronger than hemicontinuity. This paper provides general characterizations of continuity in terms of hemicontinuity for weak preferences that are modeled as (possibly incomplete) preorders and for strict preferences that are modeled as strict partial orders. Some behavioral implications associated with the two approaches are also discussed.     

Risky social choice with incomplete or noisy interpersonal comparisons of well-being

In this study, we develop a model of social choice over lotteries, where people’s psychological characteristics are mutable, their preferences may be incomplete, and incomplete or noisy interpersonal comparisons of well-being are possible. Formally, we suppose individual preferences are described by a von Neumann-Morgenstern (vNM) preference order on a space of lotteries over psychophysical states; the social planner must construct a vNM preference order on lotteries over social states. First, we consider a model where the individual vNM preference order is incomplete (so not all interpersonal comparisons are possible). Then, we consider a model where the individual vNM preference order is complete, but unknown to the planner, and thus modelled by a random variable. In both cases, we obtain characterizations of a utilitarian social welfare function.     

Establishing Derived Equivalence Relations of Basic Geography Skills in Children with Autism

The Analysis of Verbal Behavior - The present study evaluated the efficacy of a stimulus-equivalence training procedure in teaching basic geography skills to two children with autism. The...     

Modeling large electorates with Fourier series, with applications to Nash equilibria in proximity and directional models of spatial competition

 In this paper we introduce harmonic analysis (Fourier series) as a tool for characterizing the existence of Nash equilibria in two-dimensional spatial majority rule voting games with large electorates. We apply our methods both to traditional proximity models and to directional models. In the latter voters exhibit preferences over directions rather than over alternatives, per se. A directional equilibrium can be characterized as a Condorcet direction, in analogy to the Condorcet (majority) winner in the usual voting models, i.e., a direction which is preferred by a majority to (or at least is not beaten by) any other direction. We provide a parallel treatment of the total median condition for equilibrium under proximity voting and equilibrium conditions for directional voting that shows that the former result is in terms of a strict equality (a knife-edge result very unlikely to hold) while the latter is in terms of an inequality which is relatively easy to satisfy. For the Matthews [3] directional model and a variant of the Rabinowitz and Macdonald [7] directional model, we present a sufficiency condition for the existence of a Condorcet directional vector in terms of the odd-numbered components of the Fourier series representing the density distribution of the voter points. We interpret our theoretical results by looking at real-world voter distributions and direction fields among voter points derived from U.S. and Norwegian survey data. Received: 7 July 1995 / Accepted: 14 May 1996     

Equivalence Relations and Behavior: An Introductory Tutorial

With an emphasis on procedural fundamentals, the original behavior-analytic equivalence experiments and the equivalence paradigm are described briefly. A few of the subsequent developments and implications are noted, with special reference to the possible significance of the findings with respect to language and cognition.