Synchronic information,knowledge and common knowledge in extensive games

Restricting attention to the class of extensive games defined by von Neumann and Morgenstern (1944) with the added assumption of perfect recall, we specify the information of each player at each node of the game-tree in a way which is coherent with the original information structure of the extensive form. We show that this approach provides a framework for a formal and rigorous treatment of questions of knowledge and common knowledge at every node of the tree. We construct a particular information partition for each player and show that it captures the notion of maximum information in the sense that it is the finest within the class of information partitions that satisfy four natural properties. Using this notion of “maximum information” we are able to provide an alternative characterization of the meet of the information partitions.     

Information,trade and common knowledge

In any voluntary trading process, if agents have rational expectations, then it is common knowledge among them that the equilibrium trade is feasible and individually rational. This condition is used to show that when risk-averse traders begin at a Pareto optimal allocation (relative to their prior beliefs) and then receive private information (which disturbs the marginal conditions), they can still never agree to any non-null trade. On markets, information is revealed by price changes. An equilibrium with fully revealing price changes always exists, and even at other equilibria the information revealed by price changes “swamps” each trader's private information.     

Coordination,timing and common knowledge

There is tight link between coordination and common knowledge. The role of higher order beliefs in static incomplete information games has been widely studied. In particular, information frictions break down common knowledge. A large body of literature in economics examine dynamic coordination problems when there are timing frictions, in the sense that players do not all move at once. Timing frictions in dynamic coordination games play a role that is closely analogous to information frictions in static coordination games.This paper makes explicit the role of higher order beliefs about timing in dynamic coordination games with timing frictions. An event is said to be effectively known if a player knew the event when he last had an option to change his behavior. The lack of effective common knowledge of the time drives results of dynamic coordination games.     

Search, common knowledge, and competition

This paper analyzes the effects of buyer search costs and seller private and common knowledge on seller competition. It shows that lack of common knowledge results in the equilibrium price continuously decreasing to the perfectly competitive one as buyer search costs for price decrease from positive for all buyers to zero for all buyers, even if each market agent's uncertainty (in the private knowledge) is small. At the same time, if the uncertainty of each seller about buyer valuations is small, the effects of a small change in the search costs or of information structure on pricing may be large (but continuous).     

Consensus and common knowledge of an aggregate of decisions

McKelvey and Page [McKelvey, R., Page, T., 1986. Common knowledge, consensus and aggregate information. Econometrica 54, 109–127] generalized Aumann's [Aumann, R.J., 1976. Agreeing to disagree. Ann. Statist. 4, 1236–1239] agreement theorem to the case where agents have common knowledge of a statistic of their posterior probabilities of some event. They showed that if individuals have the same prior, and if the statistic satisfies a stochastic regularity condition, then common knowledge of it implies equality of all posteriors. We show a similar result in a more general setting where agents have common knowledge of a statistic of their individual decisions. Decisions can be posteriors as well as discrete actions such as buy or sell. We show that if the decision rule followed by individuals is balanced union consistent, and if the statistic of individual decisions is exhaustive, then common knowledge of it implies equality of all decisions. We give an example showing that neither Cave's [Cave, J., 1983. Learning to agree. Econ. Letters 12, 147–152] union consistency condition nor Parikh and Krasucki's [Parikh, R., Krasucki, P., 1990. Communication, consensus and knowledge. J. Econ. Theory 52, 178–189] convexity condition is sufficient to guarantee the result.     

Imperfect common knowledge and the information value of prices

Summary. When economic agents have diverse private information on the fundamentals of the economy, prices may serve as a poor aggregator of this private information. We examine the information value of prices in a monopolistic competition setting that has become standard in the New Keynesian macroeconomics literature. We show that public information has a disproportionate effect on agents’ decisions, crowds out private information, and thereby has the potential to degrade the information value of prices. This effect is strongest in an economy with keen price competition. Monetary policy must rely on less informative signals of the underlying cost conditions.Received: 6 November 2003, Revised: 19 November 2004 JEL Classification Numbers: E31, E32, E58.This paper supersedes the discussion in the first half of our longer paper that circulated under the title “Public and Private Information in Monetary Policy Models”. We thank Andy Filardo, Marvin Goodfriend, Nobu Kiyotaki, John Moore, Stephen Morris and Lars Svensson for advice and comments at various stages of the project, and to Herakles Polemarchakis, Roko Aliprantis and an anonymous referee for their helpful comments and guidance. The views are those of the authors and do not necessarily represent those of the BIS. The second author acknowledges support from the U.K. ESRC under grant RES 000220450. Correspondence to: H.S. Shin     

The Nash-threats folk theorem with communication and approximate common knowledge in two player games

We show that the use of communications to coordinate equilibria generates a Nash-threats folk theorem in two-player games with “almost public” information. The results generalize to the n-person case. However, the two-person case is more difficult because it is not possible to sustain equilibria by comparing the reports of different players, and using these “third parties” to effectively enforce contracts.     

The enduring allure of objective probability

Probability measures are properly considered subjective, if only as a result of the knowledge limitations of human experience. Even if objective probability can be demonstrated as an unambiguously verifiable property of the physical world, our necessarily imperfect access to such aspects of reality would necessitate the construction of subjective probability measures for examinations of human behavior. This paper will explore the distinction between subjective and purportedly objective probability in principle, and demonstrate that actual probabilities can only be subjective, at least ex ante. The paper will next examine the persistent efforts of philosophers, mathematicians, and particularly quantitatively-inclined social scientists, to construct and employ mistaken conceptions of purportedly objective probability. The neo-indeterminist interpretation of sub-atomic particle physics is addressed next, with its attempt to construct an objective-probabilistic account of reality based on the Heisenberg uncertainty principle. An explanation is suggested for the persistent allure of objective probability in the social sciences, which purports to offer a more economical and parsimonious basis for human behavior and the formation of expectations. The view that there are ontologically privileged, objectively-verifiable probabilities and expectations, will be examined and criticized. It appears to be one source of the discredited, though nonetheless widespread and persistent, belief in the efficacy and feasibility of central economic planning.     

The knowledge multiplier

The paper develops a formal model of external knowledge and identifies the role of knowledge multipliers. Social interactions and knowledge multipliers play a crucial role in determining the rate of technological change. The analytical identification of the knowledge multiplier expression constitutes a key step in the appreciation of the crucial role of knowledge interactions. First, social considerations endogenously change the knowledge production function of each firm. The knowledge multiplier is the specific mechanism by means of which external knowledge contributes to enhance the innovative capacity of each firm. The production function of knowledge shows that the larger the knowledge multiplier is the stronger are the cumulative positive effects of external knowledge on the generation of new knowledge. Second, social considerations explain the long-run dynamics of innovation. Social reinforcement and the knowledge multiplier determine the rise or fall in the rate of accumulation of technological knowledge.     

Existence of nontrivial equilibria in repeated games with imperfect private monitoring

We consider finitely repeated games with imperfect private monitoring, and provide several sufficient conditions for such a game to have an equilibrium whose outcome is different from repetition of Nash equilibria of the stage game. Surprisingly, the conditions are consistent with uniqueness of the stage game equilibrium. A class of repeated chicken is shown to satisfy the condition.     

The expected probability of Condorcet's paradox

Let P(n,p) be the probability that there is a Condorcet winner on three alternatives for n (odd) voters. The vector p defines the probability that a randomly selected voter will have any of the six linear rankings on three alternatives as his or her preference ranking. It is shown that if all p vectors are equally likely, the expected value of P(n,p) is given by 15(n+3)²/[16(n+2)(n+4)].     

The probability approach to general equilibrium with production

We develop an alternative approach to the general equilibrium analysis of a stochastic production economy when firms’ choices of investment influence the probability distributions of their output. Using a normative approach we derive the criterion that a firm should maximize to obtain a Pareto optimal equilibrium: the criterion expresses the firm’s contribution to the expected social utility of output, and is not the linear criterion of market value. If firms do not know agents utility functions, and are restricted to using the information conveyed by prices then they can construct an approximate criterion which leads to a second-best choice of investment which, in examples, is found to be close to the first best. We are grateful to participants in the 2006 Public Economic Theory Conference, Hanoi, the 2007 CARESS/COWLES workshop on General Equilibrium at Yale University, the 2007 SAET Conference at Kos, Greece, the NSF/NBER 2007 Conference on General Equilibrium at Northwestern University, and seminars at Rice University, the University of Southern California, Indiana University, and U.C. Davis for helpful comments. We particularly thank Jacques Drèze and David Cass for stimulating discussions, and a referee for helpful suggestions for improving the paper.     

The use of knowledge about society

Selection of efficient institutions or policies in politics requires constituents to estimate the net benefits of political reforms. Political competition fails to inform constituents of the costs of forgone political alternatives. Ignorance of ‘political opportunity costs’ prevents the adoption of welfare enhancing reforms of public institutions and policies. The empirical record supports this contention.     

The role of tacit knowledge in connecting knowledge exchange and combination with innovation

Using the Resource-Based View, this paper aims to provide a better understanding of the effect of knowledge on innovation. With this general aim in mind, we relate knowledge’s nature (tacit vs. explicit) and process (e.g. knowledge exchange and combination) to innovation. Using a sample of 105 innovative firms, we find a positive linear effect of tacit knowledge on innovation and a curvilinear relationship between knowledge exchange and combination and innovation. We also find a moderating effect of tacit knowledge on the curvilinear relationship between knowledge exchange and combination and innovation. We speculate on our findings and connect them to previous theory.     

The common pool of transitional profits

Transitional profits are above-normal profits that can be earned by firms as a result of changes in market conditions or entrepreneurial innovations of the firm. They are a common pool and are competed away by firms that enter profitable markets or imitate the innovations of profitable firms. The economics literature provides two conflicting views on transitional profits. One is that above-normal profit is a sign of economic inefficiency and is the result of either monopoly power or disequilibrium. The other is that economic profit is necessary for economic efficiency because profit is the lure that pushes entrepreneurs to allocate resources more efficiently. Both views are considered, along with an analysis of whether this common pool resource is competed away too rapidly, as the theory of common pool resources would suggest.     

The source of some paradoxes from social choice and probability

An elementary argument is developed to explain and unite several paradoxes coming from probability and from social choice. This geometric approach is illustrated with new results about the intransitivities of election rankings over subsets of alternatives, agenda manipulation, conditional probability, and waiting times.     

On the dynamics of generation and utilisation of knowledge: The local character of knowledge

In this paper a theoretical framework for the analysis of knowledge suitable to study processes of knowledge generation and utilisation in advanced post-industrial societies is presented. This framework is based on two fundamental properties of knowledge, that of being a co-relational structure and that of being a retrieval/interpretative structure. The paper shows that a third property, the local character of knowledge, can be derived from the two fundamental ones. Furthermore, it is shown that the production of knowledge can be analysed by means of concepts currently used in economics, such as the division of labour, coordination, specialization, competition and so on. Finally, the paper shows that the framework proposed here is compatible with a number of epistemological concepts and theories and applicable to the empirical analysis of processes of knowledge generation and utilization in firms.     

知识员工的激励效用分析

目前企业激励方式存在着两大误区，一是重视经营者激励而忽视了对员工的激励，二是将一般员工激励与知识员工激励等同。忽视前者的结果是导致了非X效率；忽视了后者的结果是员工激励效用的非最大化。一般员工激励主要是一种结果激励，激励效用最大化主要是通过经济报酬激励实现的，而知识员工的激励主要是一种过程激励，激励效用最大化主要是通过复合激励实现的，进而为知识员工激励提供相应的激励制度安排。     

The effectiveness of international knowledge spillover channels

Using panel data from 16 Organization for Economic Cooperation and Development (OECD) countries for the period 1981–2000, we examine the significance of international knowledge spillovers through inward and outward foreign direct investment (FDI), intermediate goods imports, and a disembodied direct channel. Knowledge spillovers through the disembodied direct channel are approximated by using a measure of technological proximity and patent citations between countries. Using estimation models that reflect recent developments in non-stationary panel data econometrics, we show that international knowledge spillovers through inward FDI and the disembodied direct channel are significant and robust. In contrast, outward FDI and imports of intermediate goods are not conducive to international knowledge spillovers.