Information structures with unawareness

I construct a state space model with unawareness following [R.J. Aumann, Agreeing to disagree, Ann. Stat. 76 (1976) 1236-1239]. Dekel et al. [E. Dekel, B.L. Lipman, A. Rustichini, Standard state-space models preclude unawareness, Econometrica 66 (1998) 159-173] show that standard state space models are incapable of representing unawareness. The model circumvents the impossibility result by endowing the agent with a subjective state space that differs from the full state space when he has the unawareness problem. Information is modeled as a pair, consisting of both factual information and awareness information. The model preserves the central properties of the standard information partition model.     

Bayesian games with unawareness and unawareness perfection

Applying unawareness belief structures introduced in Heifetz et al. (Games Econ Behav 77:100–121, 2013a), we develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower awareness levels. We apply Bayesian games with unawareness to investigate the robustness of equilibria to uncertainty about opponents’ awareness of actions. We show that a Nash equilibrium of a strategic game is robust to unawareness of actions if and only if it is not weakly dominated. Finally, we discuss the relationship between standard Bayesian games and Bayesian games with unawareness.     

Inductive reasoning about unawareness

We develop a model of games with awareness that allows for differential levels of awareness. We show that, for the standard modal-logical interpretations of belief and awareness, a player cannot believe there exist propositions of which he is unaware. Nevertheless, we argue that a boundedly rational individual may regard the possibility that there exist propositions of which she is unaware as being supported by inductive reasoning, based on past experience and consideration of the limited awareness of others. In this paper, we provide a formal representation of inductive reasoning in the context of a dynamic game with differential awareness. We show that, given differential awareness over time and between players, individuals can derive inductive support for propositions expressing their own unawareness. We consider the ecological rationality of heuristics to guide decisions in problems involving differential awareness.     

Substantive Rationality and Backward Induction

S. Modica and A. Rustichini (1994, Theory and Decision37, 107–124) provided a logic for reasoning about knowledge where agents may be unaware of certain propositions. However, their original approach had the unpleasant property that nontrivial unawareness was incompatible with partitional information structures. More recently, Modica and Rustichini (1999, Games Econ. Behav.27, 265–298) have provided an approach that allows for nontrivial unawareness in partitional information structures. Here it is shown that their approach can be viewed as a special case of a general approach to unawareness considered by R. Fagin and J. Y. Halpern (1988, Artificial Intelligence34, 39–76). Journal of Economic Literature Classification Numbers: D80, D83.     

Universal type structures with unawareness

Infinite hierarchies of awareness and beliefs arise in games with unawareness, similarly to belief hierarchies in standard games. A natural question is whether each hierarchy describes the playerʼs awareness of the hierarchies of other players and beliefs over these, or whether the reasoning can continue indefinitely. This paper constructs the universal type structure with unawareness where each type has an awareness level and a belief over types. Countable hierarchies are therefore sufficient to describe all uncertainty in games with unawareness.     

Unique Implementation of the Full Surplus Extraction Outcome in Auctions with Correlated Types

In auctions with correlated types it is possible to design mechanisms such that full surplus extraction can be obtained as the outcome of an equilibrium in which agents use (weakly) dominant strategies. However, it is not assured that the outcome is unique. We present an example in which no mechanism can yield the full surplus extraction outcome as the unique Bayesian equilibrium outcome. Next we show that in the standard auction model the multiplicity problem can be fully resolved using sequential mechanisms, i.e., we show that it is possible to obtain the full surplus extraction outcome as the unique perfect Bayesian equilibrium outcome.Journal of Economic LiteratureClassification Numbers: D44; D70.     

Interactive unawareness

The standard state-spaces of asymmetric information preclude non-trivial forms of unawareness (Modica and Rustichini (Theory Decision 37 (1994) 107–124); Dekel, Lipman and Rustichini (Econometrica 66 (1998) 159–173)). We introduce a generalized state-space model that allows for non-trivial unawareness among several individuals, and which satisfies strong properties of knowledge as well as all the desiderata on unawareness proposed this far in the literature.     

Multiplicity of Cournot Equilibria and Involuntary Unemployment

In an overlapping generations model with Cournot competition on the goods market it is shown that a continuum of stationary states and perfect foresight trajectories exists with unemployment at arbitrary low wages. Decisive for this is the influence that different forecast functions have on the objective demand curve, even though they are consistent with perfect foresight. With an example it is shown that simple adaptive and constant memory forecast rules generate such unemployment equilibria. The corresponding temporary equilibrium dynamics may display stable unemployment and unstable full employment equilibria.Journal of Economic LiteratureClassification Numbers: D43, D51, E24     

Competitive equilibrium with unawareness in economies with production

This paper investigates an extension of the GEI-unawareness framework by Modica et al. (Econ. Theory 12 (1998) 259) to economies with entrepreneurial production. Existence of equilibrium is guaranteed given decreasing returns to scale. Firm's value and investment decision in equilibrium are characterized. An example of commodity innovation shows that the effect of different degrees of awareness on investment decisions depend upon the degree of risk aversion. In the case of log preferences unawareness may not matter for commodity innovation, although this depends on other preference features.     

Incomplete Markets, Transitory Shocks, and Welfare

Although equilibrium allocations in models with incomplete markets are generally not Pareto-efficient, it is often argued that quantitative welfare losses from missing assets are small when time horizons are long and shocks are transitory. In this paper we use a computational analysis to show that even in the simplest infinite horizon model without aggregate uncertainty welfare losses can be substantial. Furthermore we show that in this model welfare losses from incomplete markets do not necessarily disappear when one considers calibrations of the model in which agents become very patient. We argue that when the economic model is calibrated to higher frequency data, the period persistence of negative income shocks must increase as well. In this case the welfare loss of incomplete markets remains constant even as agents' rate of time preference tends to one. Journal of Economic Literature Classification Numbers: D52, D58, D60.     

Credible Equilibria in Games with Utilities Changing during the Play

Whenever one deals with an interactive decision situation of long duration, one has to take into account that priorities of the participants may change during the conflict. In this paper we propose an extensive-form game model to handle such situations and suggest and study a solution concept, called credible equilibrium, which generalizes the concept of Nash equilibrium. We also discuss possible variants to this concept and applications of the model to other types of games. American Mathematical Society Classification Numbers: 90A06, 90A07, 90A43, 90A56, 90D06, 90D10, 90D35, 90D40, 90D80. Journal of Economic Literature Classification Numbers: C70, C72, D10, D11, D80, D83.     

On the Growth and Welfare Effects of Defense R&D

In the United States, defense R&D share of GDP has decreased significantly since 1960. To analyze the implications on growth and welfare, we develop an R&D‐based growth model that features the commonly discussed crowding‐out and spillover effects of defense R&D on civilian R&D. The model also captures the effects of defense technology on (a) national security resembling consumption‐type public goods and (b) aggregate productivity via the spin‐off effect resembling productive public goods. In this framework, economic growth is driven by market‐based civilian R&D as in standard R&D‐based growth models and government‐financed public goods (i.e., defense R&D) as in Barro (1990). We find that defense R&D has an inverted‐U effect on growth, and the growth‐maximizing level of defense R&D is increasing in the spillover and spin‐off effects. As for the welfare‐maximizing level of defense R&D, it is increasing in the security‐enhancing effect of defense technology, and there exists a critical degree of this security‐enhancing effect below (above) which the welfare‐maximizing level is below (above) the growth‐maximizing level.     

Estimation of R&D depreciation rates: a suggested methodology and preliminary application

Abstract The 2008 version of the SNA has recommended capitalization of R&D expenditures. To implement this recommendation, we need to determine the depreciation rate of R&D capital. In this paper, we develop a simple model, based on a production function method that allows for monopolistic competition, to estimate the annual depreciation rate of R&D capital. We treat R&D capital as a technology shifter instead of as an explicit input factor. Both the R&D stock and the time variable are used to capture technological progress. Estimated R&D depreciation rates and markup factors are presented for the U.S. manufacturing sector and four U.S. knowledge‐intensive industries.     

Endogenous cost asymmetry and insufficient entry in the absence of scale economies

The paper by Ghosh and Saha (Econ Theory 30:575–586, 2007) shows that entry can be socially excessive even if there are no scale economies. We show that exogenous cost asymmetry is responsible for this result. In a simple model with R&D investment by the more cost efficient firm, thus creating endogenous cost asymmetry, we show that entry is socially insufficient instead of excessive if the slope of the marginal cost of R&D is not very high.     

Optimal research and development and the cost of business cycles

While research and development (R&D) investment has been procyclical in the post-war period, recent literature suggests that the optimal path for R&D is countercyclical, and that the economy would be better off by subsidizing R&D in recessions. The objective of this paper is to analyze the welfare effects of distortions in the intertemporal allocation of R&D resources and to compare diverse policy interventions so as to improve social welfare. To this end, we introduce a calibrated dynamic stochastic general equilibrium model with Schumpeterian endogenous growth that is capable of explaining the observed procyclicality of R&D. Our results show that the cost of business cycles is lower in the decentralized economy with procyclical R&D than in the efficient allocation with countercyclical R&D. This is because the suboptimal propagation of shocks in the decentralized equilibrium offsets some of the existing steady-state distortions. In this second-best context, countercyclical R&D subsidies have no positive effect on welfare. In contrast, fiscal policies aimed at restoring the optimal steady-state produce large welfare gains.     

COOPERATIVE MANAGERIAL DELEGATION,R&D AND COLLUSION

Existing literature on managerial delegation indicates that collusive outcomes can be obtained in an oligopoly game through cooperative managerial delegation. In contrast, this paper shows that, if managers are delegated to choose R&D, in addition to choosing production levels, full‐collusive outcomes cannot be achieved through cooperative delegation. Moreover, (i) under cooperative delegation, semi‐collusion always yields lower profit, higher R&D, higher price and lower social welfare than that in the case of competition and (ii) cooperative delegation leads to a higher profit lower R&D, higher price and lower social welfare than the no delegation case, irrespective of product market conduct.     

Unawareness of theorems

This paper provides a set-theoretic model of knowledge and unawareness. A new property called Awareness Leads to Knowledge shows that unawareness of theorems not only constrains an agent’s knowledge, but also can impair his reasoning about what other agents know. For example, in contrast to Li (J Econ Theory 144:977–993, 2009), Heifetz et al. (J Econ Theory 130:78–94, 25 2006) and the standard model of knowledge, it is possible that two agents disagree on whether another agent knows a particular event. The model follows Aumann (Ann Stat 4:1236–1239, 1976) in defining common knowledge and characterizing it in terms of a self-evident event, but departs in showing that no-trade theorems do not hold.     

Biotechnology as a Technological Paradigm in the Global Knowledge Structure

The aim of this study is to analyse whether the receipt of public R&D funding determines firm's R&D strategy selection. This issue is crucial, as previous studies have shown that each R&D strategy is associated to a higher, or lower, innovation performance. We consider three R&D strategies – make, buy, make–buy – and three different sources of public funding – regional, state and other (such as EU). The model estimation is performed through a multinomial logit model with random effects with a sample of 457 large firms for the period 1992–2005, taken from the Spanish Survey of Business Strategies. The main finding is that the source of the funding influences whether firms select the make, buy or make–buy strategy. Additionally, because of the panel structure of the sample, we observe that the effect of public funding on the R&D strategy selection lasts longer for state and regional funds than for other funds.     

New market creation through transformation

Is new market creation a search and selectionprocess within the theoretical space of all possible markets? Or is it the outcome of a process of transformation of extant realities into new possibilities? In this article we consider new market creation as a process involving a new network of stakeholders. The network is initiated through an effectual commitment that sets in motion two concurrent cycles of expanding resources and convergingconstraints that result in the new market. The dynamic model was induced from two empirical investigations, a cognitive science-based investigation of entrepreneurial expertise, and a real time history of the RFID industry. JEL Classification: M13, M31, D4, D52, D71, D72, L1, L2, P42 We would like to thank the Batten Institute at the Darden Graduate School of Business Administration, University of Virginia, for supporting this research. We would also like to thank the following on specific contributions to our thesis: Anil Menon for his relentless insistence on more precise formulations of effectual reasoning; Jim March for his conversation and for inspiring us to dig into Type I and Type II errors; Rob Wiltbank for firming up the section on opportunity costs; and Stuart Read for helping us clarify our writing. Correspondence to: S.D. Sarasvathy