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.     

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.     

Subjective states: A more robust model

We study the demand for flexibility and what it reveals about subjective uncertainty. As in Kreps [D. Kreps, 1979. A representation theorem for ‘preference for flexibility’. Econometrica 47, 565–577], Nehring [K. Nehring, 1996. Preference for flexibility and freedom of choice in a Savage framework. UC Davis Working Paper; K. Nehring, 1999. Preference for flexibility in a Savage framework. Econometrica 67, 101–119] and Dekel et al. [E. Dekel, B. Lipman, A. Rustichini, 2001. Representing preferences with a unique subjective state space. Econometrica 69, 891–934], the latter is represented by a subjective state space consisting of possible future preferences over actions to be chosen ex post. One contribution is to provide axiomatic foundations for a range of alternative hypotheses about the nature of these ex post preferences. Secondly, we establish a sense in which the subjective state space is uniquely pinned down by the ex ante ranking of (random) menus. Finally, we demonstrate the tractability of our representation by showing that it can model the two comparative notions “2 desires more flexibility than 1” and “2 is more averse to flexibility-risk than is 1.”     

Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents

We provide several different generalizations of Debreu’s social equilibrium theorem by allowing for asymmetric information and a continuum of agents. The results not only extend the ones in Kim and Yannelis (J Econ Theory 77:330–353, 1977), Yannelis and Rustichini (Stud Econ Theory 2:23–48, 1991), but also new theorems are obtained which allow for a convexifying effect on aggregation (non-concavity assumption on the utility functions) and non-convex strategy sets (pure strategies). This is achieved by imposing the assumption of “many more agents than strategies” (Rustichini and Yannelis in Stud Econ Theory 1:249–265, 1991; Tourky and Yannelis in J Econ Theory 101:189–221, 2001; Podczeck in Econ Theory 22:699–725, 2003). To the memory of Gerard Debreu. A preliminary draft was presented in Paris, in April of 2005. I have benefited from the discussion, comments and questions of Erik Balder, Jean-Marc Bonnisseu, Bernard Cornet and Filipe Martins Da-Rocha and Conny Podczeck. A careful and knowledgeable referee made several useful comments and rescued me from a mishap.     

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.     

Truthful mechanism design for multidimensional scheduling via cycle monotonicity

We consider the makespan-minimization problem on unrelated machines in the context of algorithmic mechanism design. No truthful mechanisms with non-trivial approximation guarantees are known for this multidimensional domain. We study a well-motivated special case (also a multidimensional domain), where the processing time of a job on each machine is either “low” or “high.” We give a general technique to convert any c-approximation algorithm (in a black-box fashion) to a 3c-approximation truthful-in-expectation mechanism. Our construction uses fractional truthful mechanisms as a building block, and builds upon a technique of Lavi and Swamy [Lavi, R., Swamy, C., 2005. Truthful and near-optimal mechanism design via linear programming. In: Proc. 46th FOCS, pp. 595–604]. When all jobs have identical low and high values, we devise a deterministic 2-approximation truthful mechanism. The chief novelty of our results is that we do not utilize explicit price definitions to prove truthfulness. Instead we design algorithms that satisfy cycle monotonicity [Rochet, J., 1987. A necessary and sufficient condition for rationalizability in a quasilinear context. J. Math. Econ. 16, 191–200], a necessary and sufficient condition for truthfulness in multidimensional settings; this is the first work that leverages this characterization.     

The cone condition,properness, and extremely desirable commodities

Summary This note links two conditions which have generated some interest in the literature and have an important role in proving the existence of an equilibrium, the second welfare theorem and the core equivalence theorem in infinite dimensional commodity spaces: These are thecone condition introduced in Chichilnisky and Kaiman (1980), and theproperness condition in Mas-Colell (1986a), which were studied also in Yannelis and Zame (1986), Aliprantis et al. (1987a, b) and (1989), Aliprantis and Burkinshaw (1988), Mas-Colell (1986b), Chichilnisky and Heal (1984, 1992), and Rustichini and Yannelis (1991) among others. I establish that these two conditions are the same. Indeed, the cone condition coincides also with the assumption of anextremely desirable commodity used in Yannelis and Zame (1986) and Rustichini and Yannelis (1991). The motivation for studying these conditions comes from the same economic application, showing the need to bring within the scope of equilibrium theory commodity spaces whose positive orthants have empty interior, a typical situation in infinite dimensional linear spaces.I thank the participants of several seminars and workshops, two anonymous referees, CD. Aliprantis, D. Brown, D. Cass, D. Foley, G. Heal, H-M. Wu, A. Khan, R. Radner, A. Rustichini and N. Yannelis, for their comments and suggestions. Hospitality and financial support from the Stanford Institute for Theoretical Economics during the summer of 1991 is gratefully acknowledged.     

Cournot–Nash equilibria in continuum games with non-ordered preferences

In the usual framework of continuum games with externalities, we substantially generalize Cournot–Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79–94; On the existence of Cournot–Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207–223; A unifying pair of Cournot–Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437–470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237–246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9–15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345–348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econ. 3 (1976) 313–316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233–245].     

The core of an economy with differential information

Summary We introduce a new core concept for an exchange economy with differential information which is contained in the coarse core concept of Wilson (1978). We prove the existence of: (i) a core allocation for an exchange economy with differential information and; (ii) an -core strategy for a game in normal form with differential information.On different occasions I have benefited from discussions, comments and suggestions by C.D. Aliprantis, Kim Border, Don Brown, Baskar Chacravorti, Mark Feldman, Leo Hurwicz, Charlie Kahn, John Ledyard, Andreu Mas-Colell, Flavio Menezes, Tom Palfrey, Ed Prescott, Aldo Rustichini, David Schmeidler and Sanjay Srivastava. Mark Feldman and Aldo Rustichini both independently brought to my attention the related work of Wilson (1978). My thanks are extended to all the above individuals as well as to a careful referee. Of course, I am responsible for any remaining shortcomings.     

An Econometric Estimation of Industrial Water Demand in France

This study investigates the structure of industrial water demand byestimating the derived demand for water on a sample of industrialestablishments located in the south-west of France. Productiontechnologies are represented by short-term variable cost functions andapproximated by a translog form. Industrial water use is modeled ashaving three components: the quantity of water bought to a waterutility, the quantity of autonomous water and the quantity of watertreated prior to use. We include in this framework water effluents,which are considered as a by-product of the production process, emittedby firms. Each of the three water components is treated as a separateinput and all are estimated as a system of simultaneous equations. Themodel is estimated on a sample of 51 industrial plants in the Girondedistrict observed from 1994 to 1996 using Seemingly Unrelated Regression(SUR) and Feasible Generalized Least Squares (FGLS). Results ofestimations show that industrial firms are sensitive to water priceinputs. Network water elasticity is estimated at –0.29. It variesfrom –0.10 to –0.79 according to the type of industryconsidered. Autonomous water price elasticity is not significant.Elasticity for treated water is evaluated at –1.42 at themean-sample and varies from –0.90 to –2.21 according to theindustry considered.     

Growth dynamics in a model of endogenous time preference

We incorporate endogenous time preference in a simple Diamond-type economy with production and analyze the resulting dynamics both for the competitive and command equilibrium. We assume an individual's rate of time preference is decreasing in consumption (decreasing marginal impatience) and show that this intuitively more appealing assumption is consistent with a stable, non-trivial competitive equilibrium. Analysis of the competitive equilibrium indicates that the observed ‘non-convergence’ of cross-country per capita income could partially be explained by cross-country differences in ‘innate patience’. Examination of the local dynamics around the ‘optimal’ solution suggests that this particular preference structure exhibiting diminishing marginal impatience may generate endogenous business cycle phenomenon.     

Why the poor do not expropriate the rich: an old argument in new garb

We consider a political economy with two partisan parties; each party represents a given constituency of voters. If one party (Labour) represents poor voters and the other (Christian Democrats) rich voters, if a redistributive tax policy is the only issue, and if there are no incentive considerations, then in equilibrium the party representing the poor will propose a tax rate of unity. If, however, there are two issues – tax policy and religion, for instance – then this is not generally the case. The analysis shows that, if a simple condition on the distribution of voter preferences holds, then, as the salience of the non-economic issue increases, the tax rate proposed by Labour in equilibrium will fall – possibly even to zero – even though a majority of the population may have an ideal tax rate of unity.     

General equilibrium in economies with adverse selection

We model economies of adverse selection as Arrow–Debreu economies. In the spirit of Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we identify the consumption set of the individuals with the set of lotteries over net transfers. Thus, prices are linear in lotteries, but they may be non linear in commodity bundles. First, we study a weak equilibrium notion by viewing the economy of adverse selection as a pure exchange economy. The weak equilibrium set is non empty, but some of the allocations may be inefficient, and the equilibria indeterminate. Second, following Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we introduce an intermediary (firm) supplying feasible and incentive compatible measures. Equilibria are constrained efficient, but the equilibrium set is empty for an open set of economies containing the Rothschild and Stiglitz insurance economies. The research of A. Rustichini was supported by the NSF grant NSF/SES-0136556.     

Nominal rigidities, skewness and inflation regimes

The menu-costs model developed by Ball and Mankiw (BM) [Ball, L., Mankiw, N.G., 1994. Asymmetric price adjustment and economic fluctuations. Economic Journal 104 (423), 247–261; Ball, L., Mankiw, N.G., 1995. Relative-Price Changes as Aggregate supply shocks. Quarterly Journal of Economics 110 (1), 161–193] predicts that inflation is positively related to the skewness of price changes distribution. We test this prediction in different inflationary contexts: Spain (1975–2002) and Argentina (1960–1989). We find a positive inflation–skewness relationship in both countries at low inflation, even though the mean annual inflation rates were very different: 2.2% for Spain and 23% for Argentina. Therefore, the threshold of low inflation under which the menu-costs model is suitable is determined endogenously, and it depends on the inflationary experience of each economy. In the higher inflation periods skewness is not significant. Finally, our results suggest that the menu-costs model is not suitable beyond certain threshold of inflation.     

The Lost Decades: Developing Countries' Stagnation in Spite of Policy Reform 1980–1998

I document in this paper a puzzle thathas not received previous attention in the literature. In 1980–98,median per capita income growth in developing countries was 0.0percent, as compared to 2.5 percent in 1960–79. Yet I documentin this paper that variables that are standard in growth regressions—policieslike financial depth and real overvaluation, and initial conditionslike health, education, fertility, and infrastructure generallyimproved from 1960–79 to 1980–98. Developing countrygrowth should have increased instead of decreased according tothe standard growth regression determinants of growth. The stagnationseems to represent a disappointing outcome to the movement towardsthe ``Washington Consensus' by developing countries. I speculatethat worldwide factors like the increase in world interest rates,the increased debt burden of developing countries, the growthslowdown in the industrial world, and skill-biased technicalchange may have contributed to the developing countries' stagnation,although I am not able to establish decisive evidence for thesehypotheses. I also document that many growth regressions aremis-specified in a way similar to the Jones (1995) critique thata stationary variable (growth) is being regressed on non-stationaryvariables like policies and initial conditions. It may be thatthe 1960–1979 period was the unusual period for LDC growth,and the 1980–98 stagnation of poor countries representsa return to the historical pattern of divergence between richand poor countries.     

Capital–skill complementarity and inequality: A sensitivity analysis

Krusell et al. in [Krusell, P., Ohanian, L., Ríos-Rull, J.V., Violante, G.L., 2000. Capital–skill complementarity and inequality: A macroeconomic analysis. Econometrica 68 (5), 1029–1053] analyzed the capital–skill complementarity hypothesis as an explanation for the behavior of the US skill premium. We refit Krusell et al.'s [Krusell, P., Ohanian, L., Ríos-Rull, J.V., Violante, G.L., 2000. Capital–skill complementarity and inequality: A macroeconomic analysis. Econometrica 68 (5), 1029–1053] model with two alternative capital equipment price series: One proposed by Greenwood et al. [Greenwood, J., Hercowitz, Z., Krusell, P., 1997. Long-run implications of investment-specific technological change. Amer. Econ. Rev. 87 (3), 342–362] and the official, revised National Income and Product Accounts (NIPA) data. We find that capital–skill complementarity is preserved, but other results were sensitive to the data used. Specifically, the fit of the model was similar to Krusell et al.'s [Krusell, P., Ohanian, L., Ríos-Rull, J.V., Violante, G.L., 2000. Capital–skill complementarity and inequality: A macroeconomic analysis. Econometrica 68 (5), 1029–1053] using the NIPA data, but not the Greenwood et al. [Greenwood, J., Hercowitz, Z., Krusell, P., 1997. Long-run implications of investment-specific technological change. Amer. Econ. Rev. 87 (3), 342–362] data. Also, both series produce estimates of the elasticity of substitution between unskilled labor and equipment that are substantially larger than Krusell et al.'s [Krusell, P., Ohanian, L., Ríos-Rull, J.V., Violante, G.L., 2000. Capital–skill complementarity and inequality: A macroeconomic analysis. Econometrica 68 (5), 1029–1053] estimates.     

On the existence of a stationary optimal stock for a multi-sector economy: A primal approach

Using a purely primal approach, we show the existence of a non-trivial stationary optimal stock for a multi-sector economy. Our result generalizes earlier work by dropping the δ-productivity assumption and by replacing the continuity hypothesis on the utility function by upper semicontinuity.