Valuing Others’ Information under Imperfect Expectations

Sometimes we believe that others receive harmful information. However, Marschak’s value of information framework always assigns non-negative value under expected utility: it starts from the decision maker’s beliefs – and one can never anticipate information’s harmfulness for oneself. The impact of decision makers’ capabilities to process information and of their expectations remains hidden behind the individual and subjective perspective Marschak’s framework assumes. By introducing a second decision maker as a point of reference, this paper introduces a way for evaluating others’ information from a cross-individual, imperfect expectations perspective for agents maximising expected utility. We define the cross-value of information that can become negative – then the information is “harmful” from a cross-individual perspective – and we define (mutual) cost of limited information processing capabilities and imperfect expectations as an opportunity cost from this same point of reference. The simple relationship between these two expected utility-based concepts and Marschak’s framework is shown, and we discuss evaluating short-term reactions of stock market prices to new information as an important domain of valuing others’ information.      

Strategic behavior under partial cooperation

We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash’s best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both types of equilibria. We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return.     

Competence effects for choices involving gains and losses

We investigate how choices for uncertain gain and loss prospects are affected by the decision maker’s perceived level of knowledge about the underlying domain of uncertainty. Specifically, we test whether Heath and Tversky’s (J Risk Uncertain 4:5–28, 1991) competence hypothesis extends from gains to losses. We predict that the commonly-observed preference for high knowledge over low knowledge prospects for gains reverses for losses. We employ an empirical setup in which participants make hypothetical choices between gain or loss prospects in which the outcome depends on whether a high or low knowledge event occurs. We infer decision weighting functions for high and low knowledge events from choices using a representative agent preference model. For gains, we replicate the results of Kilka and Weber (Manage Sci 47:1712–1726, 2001), finding that decision makers are more attracted to choices that they feel more knowledgeable about. However, for losses, we find limited support for our extension of the competence effect.     

An experimental study of the generosity game

We study ultimatum and dictator variants of the generosity game. In this game, the first mover chooses the amount of money to be distributed between the players within a given interval, knowing that her own share is fixed. Thus, the first mover is not confronted with the typical trade-off between her own and the other’s payoff. For each variant of the game, we study three treatments that vary the range of potential pie sizes so as to assess the influence of these changes on the first movers’ generosity. We find that removing the trade-off inspires significant generosity, which is not always affected by the second mover’s veto power. Moreover, the manipulation of the choice set indicates that choices are influenced by the available alternatives.     

Strategic games with security and potential level players

This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420, 1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, Proceedings of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica, 52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players.      

What are the minimal requirements of rational choice? Arguments from the sequential-decision setting

There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and rationality, 1988b; Theory Decis 25:25–78, 1988c) ‘consequentialist’ argument for the SEU preference axioms, but go on to formulate a related diachronic-Dutch-book-style’ argument that better achieves Hammond’s aims. Some deny the importance of Dutch-book sure losses, however, in which case, Seidenfeld’s (Econ Philos 4:267–290, 1988a) argument that distinguishes between theories that relax independence and those that relax ordering is relevant. I unravel Seidenfeld’s argument in light of the various criticisms of it and show that the crux of the argument is somewhat different and much more persuasive than what others have taken it to be; the critical issue is the modelling of future choices between ‘indifferent’ decision-tree branches in the sequential setting. Finally, I consider how Seidenfeld’s conclusions might nonetheless be resisted.     

Great Expectations. Part I: On the Customizability of Generalized Expected Utility

We propose a generalization of expected utility that we call generalized EU (GEU), where a decision maker’s beliefs are represented by plausibility measures and the decision maker’s tastes are represented by general (i.e., not necessarily real-valued) utility functions. We show that every agent, “rational” or not, can be modeled as a GEU maximizer. We then show that we can customize GEU by selectively imposing just the constraints we want. In particular, we show how each of Savage’s postulates corresponds to constraints on GEU.     

On Decomposing Net Final Values: Eva,Sva and Shadow Project

A decomposition model of Net Final Values (NFV), named Systemic Value Added (SVA), is proposed for decision-making purposes, based on a systemic approach introduced in Magni [Magni, C. A. (2003), Bulletin of Economic Research 55(2), 149–176; Magni, C. A. (2004) Economic Modelling 21, 595–617]. The model translates the notion of excess profit giving formal expression to a counterfactual alternative available to the decision maker. Relations with other decomposition models are studied, among which Stewart’s [Stewart, G.B. (1991), The Quest for Value: The EVA™ Management Guide, Harper Collins, Publishers Inc]. The index here introduced differs from Stewart’s Economic Value Added (EVA) in that it rests on a different interpretation of the notion of excess profit and is formally connected with the EVA model by means of a shadow project. The SVA is formally and conceptually threefold, in that it is economic, financial, accounting-flavoured. Some results are offered, providing sufficient and necessary conditions for decomposing NFV. Relations between a project’s SVA and its shadow project’s EVA are shown, all results of Pressacco and Stucchi [Pressacco, F. and Stucchi, P. (1997), Rivista di Matematica per le Scienze Economiche e Sociali 20, 165–185] are proved by making use of the systemic approach and the shadow counterparts of those results are also shown.     

Perceptron versus automaton in the finitely repeated prisoner’s dilemma

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.     

Portfolio Inertia and Epsilon-Contaminations

This article analyzes investors’ portfolio selection problems in a two-period dynamic model of Knightian uncertainty. We account for the existence of portfolio inertia in this two-period framework. Furthermore, by incorporating investors’ updating behavior, we analyze how observing new information in the first period will affect investors’ behavior. By this analysis, we show that observing new information in the first period will expand portfolio inertia in the second period compared with the case in which observing new information has not been gained in the first period if the degree of Knightian uncertainty is sufficiently large.     

A Note On Impossibility Theorems and Seniority Rules

We characterize seniority rules, also known as lexical dictatorships, under weak consistency constraints on the groups choice function. These constraints are base triple-acyclicity in the case of binary choices and rationalizability (although not rationality) in the case of choices between an arbitrary number of alternatives. Existing results on these weakened constraints remain silent on the treatment of the groups most junior individuals and therefore do not yield a complete characterization of seniority rules. We also impose a universal domain, binary strict Pareto optimality, binary Pareto indifference, binary independence of irrelevant alternatives, and the newly introduced condition of conflict resolution. The latter condition requires a social choice rules not to remain indecisive between alternatives for which individuals have conflicting preferences.JEL CLASSIFICATIONS: D63, D71This revised version was published online in May 2005 with a corrected article title.     

The Evolution of Coding in Signaling Games

Signaling games with reinforcement learning have been used to model the evolution of term languages (Lewis 1969, Convention. Cambridge, MA: Harvard University Press; Skyrms 2006, “Signals” Presidential Address. Philosophy of Science Association for PSA). In this article, syntactic games, extensions of David Lewis’s original sender–receiver game, are used to illustrate how a language that exploits available syntactic structure might evolve to code for states of the world. The evolution of a language occurs in the context of available vocabulary and syntax—the role played by each component is compared in the context of simple reinforcement learning.     

Elementary proof that mean–variance implies quadratic utility

An extensive literature overlapping economics, statistical decision theory and finance, contrasts expected utility [EU] with the more recent framework of mean–variance (MV). A basic proposition is that MV follows from EU under the assumption of quadratic utility. A less recognized proposition, first raised by Markowitz, is that MV is fully justified under EU, if and only if utility is quadratic. The existing proof of this proposition relies on an assumption from EU, described here as “Buridan’s axiom” after the French philosopher’s fable of the ass that starved out of indifference between two bales of hay. To satisfy this axiom, MV must represent not only “pure” strategies, but also their probability mixtures, as points in the (σ, μ) plane. Markowitz and others have argued that probability mixtures are represented sufficiently by (σ, μ) only under quadratic utility, and hence that MV, interpreted as a mathematical re-expression of EU, implies quadratic utility. We prove a stronger form of this theorem, not involving or contradicting Buridan’s axiom, nor any more fundamental axiom of utility theory.     

Is the Disposition of Constrained Maximization Chosen Rationally?

One of the most important issues in moral philosophy is whether morality can be justified by rationality. The purpose of this study is to examine Gauthier’s moral theory, focusing on the disposition of constrained maximization, which is the main thrust of his project to justify morality rationally. First of all, I shall investigate Gauthier’s assumption and condition for the rationality of the disposition of constrained maximization so as to disclose that the disposition of constrained maximization is not necessarily chosen by rational agents. Then I shall explore his other arguments including ones for the reinterpretation of rationality and the self-critical reflection of rational beings, which can be considered as his further efforts to make the disposition of constrained maximization a rational choice. By exploring them, I shall attempt to indicate that those arguments are not valid so long as he clings to the maximizing conception of rationality and thereby this conception of rationality itself is not enough to provide morality with a basis.     

What Hindu Sati can teach us about the sociocultural and social psychological dynamics of suicide

By leveraging the case of Hindu sati, this paper elucidates the ways in which structure and culture condition suicidal behavior by way of social psychological and emotional dynamics. Conventionally, sati falls under Durkheim's discussion of altruistic suicides, or the self‐sacrifice of underindividuated or excessively integrated peoples like widows in traditional societies. In light of the fact that Durkheim's interpretation was based on uneven data, nineteenth century Eurocentric beliefs, and a theoretical framework that can no longer resist modification and elaboration, by reconsidering sati it is possible to sketch a new model that strengthens Durkheim's theory by making it more robust and generalizable. The following model is built on five principles. First, integration and regulation are not distinct causal forces, but overlapping contextual conditions. Second, to better explain the variation in suicidality across time and space, we must also pay attention to culture as it provides the underlying meanings of suicide that can increase the odds a person or class of persons become suicidal or are protected against suicidality. Third, structure still matters, but in many cases, the role power and power‐differentials play must be considered. Fourth, understanding why and how people choose suicide depends on incorporating identity and status processes. Fifth, because the expression of social emotions like shame are patterned by structural and cultural conditions, to understand how suicidality is socioculturally patterned we must further explore the link between identity/status, social emotions, and structure and culture.     

Measures of Powerlessness in Simple Games

Consider a simple game with n players. Let ψ_i be the Shapley–Shubik power index for player i. Then 1-ψ_i measures his powerlessness. We break down this powerlessness into two components – a `quixote index' Q <sub>i</sub> (which measures how much of a `quixote' i is), and a `follower index' F <sub>i</sub> (which measures how much of a `follower' he is). Formulae, properties, and axiomatizations for Q and F are given. Examples are also supplied. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the Robustness of the Winner’s Curse Phenomenon

We set out to find ways to help decision makers overcome the “winner’s curse,” a phenomenon commonly observed in asymmetric information bargaining situations, and instead found strong support for its robustness. In a series of manipulations of the “Acquiring a Company Task,” we tried to enhance decision makers’ cognitive understanding of the task. We did so by presenting them with different parameters of the task, having them compare and contrast these different parameters, giving them full feedback on their history of choices and resulting outcomes, and allowing them to interact with a human opponent instead of a computer program. Much to our surprise, none of these manipulations led to a better understanding of the task. Our results demonstrate and emphasize the robustness of the winner’s curse phenomenon.      

A revealed preference analysis of solutions to simple allocation problems

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.     

Dynamic consistency in extensive form decision problems

In a stimulating paper, Piccione and Rubinstein (1997) argued how a decision maker could undertake dynamically inconsistent choices when, in an extensive form decision problem, she has a particular type of imperfect recall named absentmindedness. Such memory limitation obtains whenever information sets include decision histories along the same decision path. Starting from work focusing on the absentminded driver example, and independently developed by Segal (2000) and Dimitri (1999), the main theorem of this article provides a general result of dynamically consistent choices, valid for a large class of finite extensive form decision problems without nature.