Farsightedly stable networks

A set of networks G is pairwise farsightedly stable (i) if all possible farsighted pairwise deviations from any network g G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying conditions (i) and (ii). A non-empty pairwise farsightedly stable set always exists. We provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominant network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest pairwise consistent set and the von Neumann–Morgenstern pairwise farsightedly stable set.     

Strong Belief and Forward Induction Reasoning

We provide a unified epistemic analysis of some forward-induction solution concepts in games with complete and incomplete information. We suggest that forward induction reasoning may be usefully interpreted as a set of assumptions governing the players' belief revision processes, and define a notion of strong belief to formalize these assumptions. Building on the notion of strong belief, we provide an epistemic characterization of extensive-form rationalizability and the intuitive criterion, as well as sufficient epistemic conditions for the backward induction outcome in generic games with perfect information. Journal of Economic Literature Classification Numbers: C72, D82.     

Epistemic equivalence of extended belief hierarchies

In this paper, we introduce a notion of epistemic equivalence between hierarchies of conditional beliefs and hierarchies of lexicographic beliefs, thus extending the standard equivalence results of Halpern (2010) and Brandenburger et al. (2007) to an interactive setting, and we show that there is a Borel surjective function, mapping each conditional belief hierarchy to its epistemically equivalent lexicographic belief hierarchy. Then, using our equivalence result we construct a terminal type space model for lexicographic belief hierarchies. Finally, we show that whenever we restrict attention to full-support beliefs, epistemic equivalence between a lexicographic belief hierarchy and a conditional belief hierarchy implies that an arbitrary Borel event is commonly assumed under the lexicographic belief hierarchy if and only if it is commonly strongly believed under the conditional belief hierarchy. This is the first result in the literature directly linking common assumption in rationality (Brandenburger et al., 2008) with common strong belief in rationality (Battigalli and Siniscalchi, 2002).     

Correlated Nash equilibrium

We modify the epistemic conditions for Nash equilibrium only to accommodate Gilboa and Schmeidler's [I. Gilboa, D. Schmeidler, Maxmin expected utility with nonunique prior, J. Math. Econ. 18 (1989) 141-153] maxmin expected utility preferences, and identify the equilibrium concept in n-player strategic games that characterizes the modified epistemic conditions. The epistemic characterization supports the equilibrium concept as a minimal generalization of Nash equilibrium, in the sense that it deviates from Nash equilibrium only in terms of players' attitude towards ambiguity. Consequently, comparing it with Nash equilibrium constitutes a ceteris paribus study of the effects of ambiguity on how a game is played. For example, with ambiguity, (beliefs about) action choices are in general correlated.     

Equilibrium in a decentralized market with adverse selection

Summary. This paper deals with trade volume and distribution of surplus in markets subject to adverse selection. In a model where two qualities of a good exist, I show that if trade is decentralized (i.e. conducted via random pairwise meetings of agents), then all units of the good are traded, and all agents have positive ex-ante expected payoffs. This feature is present regardless of the quality distribution, and persists in the limit as discounting is made negligible. This offers a sharp contrast to models of centralized trade with adverse selection (Akerlof, Wilson). Received: April 2, 2001; revised version: March 29, 2002 RID="*" ID="*" This research was funded by a grant from UQAM. I wish to thank Roberto Serrano and seminar participants at UQAM, Queen's University at Kingston, the 2001 CEME General Equilibrium Conference (Brown University), and the 2001 North American Summer Meeting of the Econometric Society (University of Maryland) for comments.     

A Logic for Suspicious Players: Epistemic Actions and Belief–Updates in Games

This paper introduces a notion of 'epistemic action' to describe changes in the information states of the players in a game. For this, ideas are developed from earlier contributions. The ideas are enriched to cover not just purely epistemic actions, but also fact–changing actions ('real moves', e.g. choosing a card, exchanging cards etc.) and nondeterministic actions and strategies (conditional actions having knowledge tests as conditions). The author considers natural operations with epistemic actions and uses them to describe significant aspects of the interaction between beliefs and actions in a game. A logic is used that combines in a specific way a multiagent epistemic logic with a dynamic logic of 'epistemic actions'. The author presents a complete and decidable proof system for this logic. As an application, the author analyses a specific example of a dialogue game (a version of the Muddy Children Puzzle, in which some of the children can 'cheat' by engaging in secret communication moves, while others may be punished for their credulity). Also presented is a sketch of a 'rule–based' approach to games with imperfect information (allowing 'sneaky' possibilities, such as cheating, being deceived and suspecting the others to be cheating).     

The probability of violating Arrow’s conditions

Arrow’s impossibility theorem shows that all preference aggregation rules (PARs) must violate a specific set of normative conditions (transitivity, Pareto, IIA, nondictatorship) over an unrestricted domain of preference profiles. However, the theorem does not address which PARs are more likely to violate those conditions across preference profiles. We compare the probabilities that thirteen PARs (anti-plurality, Hare, Nanson, plurality, plurality runoff, Simpson–Kramer, Baldwin, Borda, Coombs, Copeland, Dowdall, pairwise majority, and ranked pairs) violate Arrow’s conditions. We prove that Baldwin, Borda, Coombs, Copeland, Dowdall, and ranked pairs are less likely to violate IIA than the first six PARs, and they are less likely to violate Arrow’s conditions jointly. In contrast, pairwise majority never violates IIA but can violate transitivity. Simulations with three alternatives reveal that among the PARs studied, pairwise majority is the most likely to satisfy Arrow’s conditions jointly. Our results suggest pairwise majority violates transitivity with a small probability, while the other PARs violate IIA with much larger probabilities.     

Farsightedly stable networks

A set of networks G is pairwise farsightedly stable (i) if all possible farsighted pairwise deviations from any network g∈ G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying conditions (i) and (ii). A non-empty pairwise farsightedly stable set always exists. We provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominant network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest pairwise consistent set and the von Neumann–Morgenstern pairwise farsightedly stable set.     

The local best response criterion: An epistemic approach to equilibrium refinement

The standard refinement criteria for extensive form games, including subgame perfect, perfect, perfect Bayesian, sequential, and proper, reject important classes of reasonable Nash equilibria and accept many unreasonable Nash equilibria. This paper develops a new refinement criterion, based on epistemic game theory, that captures the concept of a Nash equilibrium that is plausible when players are rational. I call this the local best response (LBR) criterion. This criterion is conceptually simpler than the standard refinement criteria because it does not depend on out-of-equilibrium, counterfactual, or passage to the limit arguments. The LBR is also informationally richer because it clarifies the epistemic conditions that render a Nash equilibrium reasonable. The LBR criterion appears to render the traditional refinement criteria superfluous.     

Beyond choice: investigating the sensitivity and validity of measures of strength of preference

Many experiments investigating different decision theories have relied heavily on pairwise choices between lotteries. These are easy to incentivise, but often yield only limited dichotomous information. This paper considers whether respondents’ judgments about their strength of preference (SoP) for one alternative over another can usefully supplement standard choice data. We report extensive evidence that such judgments show sensitivity to variations in question format and parameter values in the directions we should expect, not only within-subject but also between-sample. We illustrate how such judgments can usefully supplement standard pairwise choice data and enrich our understanding of observed behaviour.     

Aggregation and pairwise aggregation of demand when the distribution of income is fixed

This paper derives necessary and sufficient conditions for “pairwise aggregation” of the demand functions of a group of consumers (conditions under which the mean demand for each pair of consumers satisfies the Slutsky restrictions) when the distribution of income is fixed. The sufficient conditions imply existence of a “representative” competitive consumer whose demand is the mean demand of the group. The necessary conditions imply that such a representative consumer exists for every fixed income distribution only if the consumers have homothetic preferences or, alternatively, if for each price vector, all the consumers' income expansion paths lie in the same plane.     

Belief and higher-order belief in the centipede games: An experimental investigation

This paper experimentally explores the epistemic conditions behind people's non-equilibrium behaviour in the centipede games. We propose a novel design of laboratory experiment to elicit people's first- and second-order beliefs regarding their opponents' choices and beliefs. The measured beliefs, together with the choice data, help us to estimate people's level of rationality, belief of rationality and second-order belief of rationality. To examine how these epistemic variables are affected by the social-efficiency property of the classic increasing-sum centipede game, we revisit the constant-sum centipede and compare the measured epistemic conditions from the constant-sum with those from the classic centipede. We find that people's non-backward induction behaviour may be attributed to the diffusion of beliefs and higher-order beliefs in the increasing-sum centipede. We consider a behavioural model in which people's preferences for social efficiency are incorporated into the extended utility maximization problem. Our analytical and estimation results indicate that the presence of efficiency-oriented players and people's belief towards the uncertain portion of such type of players may play a part in the non-backward-induction outcomes in experimental centipede games.     

Codification,Abstraction, and Firm Differences: A Cognitive Information-based Perspective

Synopsis The resource-based view shares with population ecology, organizational systematics, organizational cladistics, and institutional theory a concern with why firms differ and with what keeps them different. These two questions only have meaning if – as has been the case in the eoclassical theory of the firm – similarities between firms are taken as the default assumption. This paper distinguishes between ontological heterogeneity – differences in the world – and epistemic heterogeneity – differences in the way that the world is construed. Focusing on the latter, it puts forward an argument for taking epistemic heterogeneity between firms as the default assumption. It starts with a general analysis of how living systems make sense of the world. It then goes on to identify the cognitive activities of codification and abstraction as key sources of epistemic heterogeneity. The findings are applied to those systems called firms where a dominant logic allows epistemic heterogeneity to persist. In some case this leads to competitive advantage, in others to a debilitating inertia. The implications for a knowledge-based theory of the firm are briefly explored.     

Problems of Emergency Arbitration

This paper explores ethical burdens facing the economics profession which are associated with epistemic features of economic practice. Economists exert power over those they purport to serve by virtue of epistemic asymmetry between themselves and others, i.e., the intellectual monopoly they enjoy over a vitally important body of knowledge. But they also face the problem of epistemic insufficiency, which implies that they may do substantial harm as they try to do good. The paper explores the ethical entailments of the epistemic features of economics, and argues that managing the ethical challenges requires a new field of inquiry, the field of professional economic ethics, and not just a code of conduct.     

Belief consistency and trade consistency

Interpersonal consistency can be described in epistemic terms as a property of beliefs, or in economic terms as the impossibility of certain trades. The existence of a common prior from which all agentsʼ beliefs are derived is of the first kind. The non-existence of an agreeable bet, that is, a contingent zero-sum trade which is always favorable to all agents, is of the second kind. It is well established that these two notions of consistency are equivalent for finite type spaces but not for countable ones. We present three equivalences of epistemic consistency and economic consistency conditions for countable type spaces, defining in this way three levels of consistency of type spaces: weak consistency, consistency, and strong consistency. These three levels coincide in the finite case. We fully analyze the level of consistency of type spaces based on the knowledge structure of Rubinsteinʼs email game. The new notion of belief consistency introduced here helps to justify the requirement of boundedness of payoff functions in countable type spaces by showing that in a large class of spaces there exists an agreeable unbounded bet even when a common prior exists.     

Consistency of beliefs and epistemic conditions for Nash and correlated equilibria

A consistency condition (action-consistency) on the interim beliefs of players in a game is introduced. Action-consistency is weaker than common priors and, unlike common priors, is characterized by a “no-bets” condition on verifiable events. Using action-consistency, we provide epistemic conditions to Nash and correlated equilibria weakening the common knowledge restrictions in Aumann and Brandenburger [Aumann, R., Brandenburger, A., 1995. Epistemic conditions for Nash equilibrium. Econometrica 63, 1161–1180] and Aumann [Aumann, R., 1987. Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55, 1–18].     

Common knowledge and quantification

Summary. The paper consists of two parts. The first one is a concise introduction to epistemic (both propositional and predicate) logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with at most one free variable. We provide the monodic fragments of the most important common knowledge predicate logics with finite Hilbert-style axiomatizations, prove their completeness, and single out a number of decidable subfragments. On the other hand, we show that the addition of equality to the monodic fragment makes it not recursively enumerable. Received: March 7, 2001; revised version: April 4, 2001     

The Case For Strategic Realism: A Response To Lawson

Tony Lawson makes a compelling case that it is only naive realism that feminist social scientists and philosophers need to avoid, not any and all realist arguments. However, he leaves mysterious, on the one hand, why so many feminists have preferred epistemological to ontological arguments and, on the other hand, why naive realism, which is indeed problematic, can appear to be a good scientific/epistemic strategy. The essay below tries to demystify these phenomena, notes a possible misleading aspect of his use of the term "epistemological relativism", and argues for a somewhat more limited value of the ontological argument he proposes for standpoint epistemologies.     

An overlapping-generations model with search

Search is embedded in an overlapping-generations model. The young participate in a centralized market, and then are matched in pairs in a decentralized market. The old only participate in the centralized market. If the buyer's bargaining power in pairwise trade is close to unity and if the old are risk averse, then the golden-rule rate of money transfer is positive. Such risk aversion, the pairwise meetings, and dependence of the young's saving on the rate of return are necessary for this result.     

Endogenous market segmentation with heterogeneous agents

Summary. An explanation is provided for the evolution of segmented marketplaces in a pairwise exchange economy. Large traders operating in a pairwise exchange market prefer to meet other similar traders, because this enables them to trade their endowments in a smaller number of encounters. Large and small traders, however, cannot be distinguished a priori, and the existence of the small traders imposes a negative externality on the large traders. We show that, under conditions which are not very restrictive, establishing a separate market (perhaps with an entry fee) designated for the large traders induces the two types of traders to segment themselves. However, this segmentation is not necessarily welfare improving. Received: January 12, 2001; revised version: July 17, 2002 RID="*" ID="*" I wish to thank the participants in the Friday Theory Workshop at the University of Sydney, and the participants at the 17th Australian Theory Workshop at the University of Melbourne for comments and discussion. John Hillas and Stephen King pointed out an omission in an earlier version, and Catherine de Fontenay and Hodaka Morita made extensive comments on earlier drafts. This work was initiated while I was a short-term visitor at the University of Southern California.