Lottery Decisions and Probability Weighting Function

This article analyzes the implications of basic lottery tests for the probability weighting function w(p). We first show that the w(p) function with one argument cannot accommodate three basic tests of lottery choice. We also discuss in detail the links between the w(p) function with one argument and the preference reversal paradox. In the last section we propose an evaluation function that accommodates the restrictions imposed by the tests and we provide an example of such function.     

Finite Alternating-Move Arbitration Schemes and the Equal Area Solution

We start by considering the Alternate Strike (AS) scheme, a real-life arbitration scheme where two parties select an arbitrator by alternately crossing off at each round one name from a given panel of arbitrators. We find out that the AS scheme is not invariant to “bad” alternatives. We then consider another alternating-move scheme, the Voting by Alternating Offers and Vetoes (VAOV) scheme, which is invariant to bad alternatives. We fully characterize the subgame perfect equilibrium outcome sets of these above two schemes in terms of the rankings of the parties over the alternatives only. We also identify some of the typical equilibria of these above two schemes. We then analyze two additional alternating-move schemes in which players’ current proposals have to either honor or enhance their previous proposals. We show that the first scheme’s equilibrium outcome set coincides with that of the AS scheme, and the equilibrium outcome set of the second scheme coincides with that of the VAOV scheme. Finally, it turns out that all schemes’ equilibrium outcome sets converge to the Equal Area solution’s outcome of cooperative bargaining problem, if the alternatives are distributed uniformly over the comprehensive utility possibility set and as the number of alternatives tends to infinity. Journal of Economic Literature Classification Number: C72.     

Entry rates and the risks of misalignment in the EU8

New member states will join the EMU in the coming years. Setting the central parity at which they will join has been and will be a challenging task, as there is a considerable amount of uncertainty, both from a theoretical and an empirical perspective, surrounding the determination of the optimal exchange rate. Given the probable difficulty in evaluating the equilibrium rate it is thus advisable to focus on the effects of a misalignment of the entry rate for the economy, as it has implications for countries’ real and nominal convergence. An overvalued exchange rate would have an adverse impact on a country's competitiveness and its growth, while an undervalued currency would contribute to an overheating of the economy and an excessive inflation. The objective of this paper is to better understand the role of the entry rates for short run inflation and GDP developments and their implications for the inflation criterion and the real convergence process. Having estimated equilibrium exchange rates for eight out of ten countries that entered the EU in May 2004: Czech Republic, Estonia, Hungary, Lithuania, Latvia, Poland, Slovenia and Slovakia we conduct simulations showing what their adjustments to equilibrium would be if their entry rates deviated from the optimal ones.     

Implementation without rationality assumptions

Hurwicz (Social Choice and public decision making. Essays in honor of Kenneth J. Arrow, Cambridge University Press, Cambridge, 1986) was the first to study an approach to implementation theory based on choice functions instead of preference relations. We argue that the solution concept used by him, the generalized Nash equilibrium, is not really compatible with the idea that individual behavior is describable by a choice function. A new solution concept that better fits the choice function framework is then introduced. Using this, we investigate what behavioral assumptions are needed for the full characterizations of Nash implementable social choice correspondences to still hold. We will show that a condition known as Property α is central.     

On the emptiness of the stability set of order d

We know from Li's theorem (1993) that the stability set of order d may be empty for some preference profiles. However, one may wonder whether such situations are just rare oddities or not. In this paper, we partially answer this question by considering the restrictive case where the number of alternatives is the smallest compatible with an empty stability set. More precisely, we provide an upper bound on the probability for having an empty stability set of order d for the majority game under the Impartial Weak Ordering Culture assumption. This upper bound is already extremely low for small population and tends to zero as the number of individuals goes to infinity.     

Testing a “Push–Pull” theory of work commitment among organizational professionals

Writers have suggested that the current trend toward decreased job security requires employees to commit more strongly to newly “professionalized” occupations to compensate for social and resource support no longer received from their employers. And it has sometimes been implied that such a shift toward increased professional commitment will arise naturally as organizational commitment is whittled away by perceived job insecurity. We propose that job insecurity does not automatically push the employee toward professional commitment, but rather that such commitment stems from the pull of perceived occupational professionalization. We construct a nonrecursive model proposing relationships between job insecurity, perceived professionalization, and both organizational and professional commitment. This model is supported (using structural equation modeling) in a study of 622 employees in 3 occupations: corporate law, human resource management, and computer programming, all of which can be considered professions or semiprofessions. Finally, we suggest how occupations can be fashioned better to support employees when faced with job insecurity and job loss.     

Strategy-proofness,tops-only,and the uniform rule

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.     

Dynamic focal points in N-person coordination games

To understand how groups coordinate, we study infinitely repeated N-player coordination games in the context of strategic uncertainty. In a situation where players share no common language or culture, ambiguity is always present. However, finding an adequate principle for a common language is not easy: a tradeoff between simplicity and efficiency has to be made. All these points are illustrated on repeated N-player coordination games on m loci. In particular, we demonstrate how a common principle can accelerate coordination. We present very simple rules that are optimal in the space of all languages for m (number of coordination loci) from 2 to 5 and for all N, the number of players. We also show that when more memory is used in the language (strategies), players may not coordinate, whereas this is never the case when players remember only the previous period.     

Endogenous correlated equilibria in noncooperative games

Most of the results of modern game theory presuppose that the choices rational agents make in noncooperative games are probabilistically independent. In this paper I argue that there is noa priori reason for rational agents to assume probabilistic independence. I introduce a solution concept for noncooperative games called anendogenous correlated equilibrium, which generalizes the Nash equilibrium concept by dropping probabilistic independence. I contrast the endogenous correlated equilibrium with the correlated equilibrium defined by Aumann (1974, 1987). I conclude that in general the endogenous correlated equilibrium concept is a more appropriate solution concept for noncooperative game theory than the less general Nash equilibrium concept. I close by discussing the relationship between endogenous correlated equilibrium and the game solution concept calledrationalizability introduced by Bernheim (1984) and Pearce (1984).     

Piaget's Social Psychology

Piaget's social psychology is not widely discussed among psychologists, partly because much of it is still contained in untranslated French works. In this article I summarize the main lines of Piaget's social psychology and briefly indicate its relation to current theories in social psychology. Rejecting both Durkheim's sociological holism and Tarde's individualism, Piaget advances a sociological relativism (relationalism) in which all social facts are reducible to social relations and these, in turn, are reducible to rules, values and signs. Piaget's theory of social values takes the form of a social exchange theory characterized in an abstract logical way. Piaget claims social exchange requires normative principles of reciprocity and that individual social development results in such an equilibrium because rationality itself is social and based upon social cooperation. These views, in turn, derive from Piaget's orthogenetic views concerning the course of evolution: development can be characterized as an increase in equilibrium manifested both in individual action and in social interaction.     

An incompleteness problem in Harsanyi's general theory of games and certain related theories of non-cooperative games

The theory of games recently proposed by John C. Harsanyi in A General Theory of Rational Behavior in Game Situations, (Econometrica, Vol. 34, No. 3) has one anomalous feature, viz., that it generates for a special class of non-cooperative games solutions which are not equilibrium points. It is argued that this feature of the theory turns on an argument concerning the instability of weak equilibrium points, and that this argument, in turn, involves appeal to an unrestricted version of a postulate subsequently included in the theory in restricted form. It is then shown that if this line of reasoning is permitted, then one must, by parity of reasoning, permit another instability argument. But, if both of these instability arguments are permitted in the construction of the theory, the resultant theory must be incomplete, in the sense that there will be simple non-cooperative games for which such a theory cannot yield solutions. This result is then generalized and shown to be endemic to all theories which have made the equilibrium condition central to the treatment of non-cooperative games. Some suggestions are then offered concerning how this incompleteness problem can be resolved, and what one might expect concerning the postulate structure and implications of a theory of games which embodies the revisions necessitated by a resolution of this problem.This research was supported by a grant to the author from the City University of New York Faculty Research Award Program.     

Correcting misconceptions about the development of social work in China: a response to Cunfu Jia

In this brief debate article we respond to Cunfu Jia's criticism of our article ‘Defining the Profession?’ (International Journal of Social Work 16: 382–389). We address the issue of ‘evidence’ and the issue of the applicability to China of the global definition of social work. We suggest that although debate articles by their very nature risk generating false dichotomies, they provide an important and welcome opportunity to explore commonality and difference and to develop our knowledge and thinking as a result of an international exchange of views.     

Portfolio stock adjustment and the real exchange rate: The Dollar-Mark (DM) and Mark-Sterling

The advent of “freely floating” exchange rates in the 1970's coincided with the emergence of what is known as “monetary” or “asset” models of exchange rate behavior where exchange ratesmove to equilibrate demand for stocks of monies. The fundamental monetary model assumes purchasing power parity holds in the long-run, and therefore exchange rates are determined by the same factors that determine relative prices, to wit, money stocks, real incomes, and nominal interest rates. Though early proponents of the monetary view clearly emphasized its long-run nature, empirical testing has by and large neglected this caveat. Thus a model developed for long-run equilibrium exchange rates has instead been tested many times over on short-run equilibrium rates. The latter require a distinct model of their own. This paper develops a short-run equilibrium exchange rate model based on deviations of the short-run exchange rate from its long-run equilibrium. The model differs in that all variables are cast in real terms. It also differs in that the monetary and current account exchange rate versions are shown to be subsets of the more general wealth/portfolio framework used here. The present model considers, in addition to stocks of monies, stocks of foreign assets, and stocks of domestic wealth.     

A Simple Model of Secure Public Communication

Public communication is secure if a hostile third-party cannot decode the messages exchanged by the communicating parties. In Nash equilibrium, communication by computationally unbounded players cannot be secure. We assume complexity averse players, and show that a simple, secure, and costless communication protocol becomes available as the marginal complexity cost tends to zero.      

Not so cheap talk: costly and discrete communication

We model an interaction between an informed sender and an uninformed receiver. As in the classic cheap talk setup, the informed player sends a message to an uninformed receiver who is to take an action which affects the payoffs of both players. However, in our model, the sender can communicate only through the use of discrete messages which are ordered by the cost incurred by the sender. We characterize the resulting equilibria without refining out-of-equilibrium beliefs. Subsequently, we apply an adapted version of the no incentive to separate (NITS) condition to our model. We show that if the sender and receiver have aligned preferences regarding the action of the receiver, then NITS only admits the equilibrium with the largest possible number of induced actions. When the preferences between players are not aligned, we show that NITS does not guarantee uniqueness, and we provide an example where an increase in communication costs can improve communication. As we show, this improvement can occur to such an extent that the equilibrium outperforms the Goltsman et al. (J Econ Theory 144:1397–1420, 2009) upper bound for receiver’s payoffs in mediated communication.     

Can good news lead to a more pessimistic choice of action?

Adapting a definition introduced by Milgrom (1981) we say that a signal about the environment is good news relative to some initial beliefs if the posterior beliefs dominate the initial beliefs in the sense of first-order stochastic dominance (the assumption being that higher values of the parameter representing the environment mean better environments). We give an example where good news leads to the adoption of a more pessimistic course of action (we say that action a ₁, reveals greater pessimism than action a ₂, if it gives higher payoff in bad environments and lower payoff in good environments). We then give sufficient conditions for a signal not to induce a more pessimistic choice of action.A first version of this paper was written when the author was Heyworth Research Fellow at Nuffield College, Oxford, and presented at the Second Annual Congress of the European Economic Association (Copenhagen, August 1987). The author is grateful to an anonymous referee for helpful comments.     

Oligarchy for Social Choice Correspondences and Strategy-Proofness

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.     

Another impossibility result for normal form games

It is shown that the axioms Cubitt and Sugden (1994; Economic J. 104: 798) impose on a theory of rationally justifiable play (TRJP) do not prevent the possibility that two players necessarily disagree concerning the probability they ascribe to the choice of a third player. This appears to indicate that those axioms are not sufficient for defining a `reasonable' TRJP. In addition, for the case in which a player's beliefs are statistically independent, conditions for a TRJP are suggested under which the existence of a quasi-strict equilibrium is sufficient, but the existence of a consistent n-pair is not, for defining a TRJP meeting those requirements.     

A note on the two person exchange game

The two person exchange game is analysed using core theory, the Nash solution and the competitive equilibrium. It is shown for specific utility functions that relative to the other trader, the less wealthy trader does better under the Nash solution than he would under the competitive solution. Conversely, the trader with the lower initial utility level does better under the competitive solution than he would under the Nash solution. If traders have disparate initial endowments, it is argued that outcomes should be restricted to a reduced core containing the Nash and competitive solutions as endpoints.     

Rational beliefs in extensive games

Given an extensive game, with every node x and every player i a subset k _i (x) of the set of terminal nodes is associated, and is given the interpretation of player i's knowledge (or information) at node x. A belief of player i is a function that associates with every node x an element of the set K _i (x). A belief system is an n-tuple of beliefs, one for each player. A belief system is rational if it satisfies some natural consistency properties. The main result of the paper is that the notion of rational belief system gives rise to a refinement of the notion of subgame-perfect equilibrium.