Remarks on the first welfare theorem with nonordered preferences

A strong convexity assumption is used to establish the first fundamental theorem of welfare economics using the strong definition of Pareto optimality without assuming that the weak preference relations are complete or transitive. An example demonstrates that Debreu's (Proc. Nat. Acad. Sci., 40 (1954), 588–592) nonsatiation and convexity assumptions are insufficient to establish the result in the absence of transitivity.     

A Unifying Pair of Cournot-Nash Equilibrium Existence Results

For games with a measure space of players a tandem pair, consisting of a mixed and a pure Cournot-Nash equilibrium existence result, is presented. Their generality causes them to be completely mutually equivalent. This provides a unifying pair of Cournot-Nash existence results that goes considerably beyond the central result of E. J. Balder (1995, Int. J. Game Theory24, 79-94, Theorem 2.1). The versatility of this pair is demonstrated by the following new applications: (i) unification and generalization of the two equilibrium distribution existence results by K. P. Rath (1996, J. Math. Econ.26, 305-324) for anonymous games, (ii) generalization of the equilibrium existence result of T. Kim and N. C. Yannelis (1997, J. Econ. Theory77, 330-353) for Bayesian differential information games, (iii) inclusion of the Bayesian Nash equilibrium existence results of P. R. Milgrom and R. J. Weber (1985, Math. Oper. Res.10, 619-632) and E. J. Balder (1988, Math. Operations Res.13, 265-276) for games with private information in the sense of J. C. Harsanyi (1967, Manage. Sci.14, 159-182). Journal of Economic Literature Classification Number: C72.     

On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

The present paper deals with the existence of equilibria in economies whose commodity space is L_∞(M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's (J. Econ. Theory4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.     

On equilibrium in Hart's securities exchange model

In this paper, we use a no unbounded arbitrage condition to give a very direct proof of the existence of equilibrium in Hart's unbounded securities exchange model (J. Econ. Theory, 9 (1974), 293–311). We also examine the relationship between the no unbounded arbitrage condition and the sufficiency conditions of Hart, ibid. and Hammond (J, Econ. Theory, 31 (1983), 170–175). We present an example to show that if traders are not sufficiently risk averse, then Hammond's overlapping expectations condition is not, in general, equivalent to the no unbounded arbitrage condition or Hart's sufficiency conditions, and therefore, is not sufficient to guarantee the existence of equilibrium. We also present an example to show that it is possible for the no unbounded arbitrage condition to hold without overlapping expectations, and therefore, it is possible for equilibrium to exist without overlapping expectations.     

Price Level Determinacy under a Pure Interest Rate Peg

In this article we reexamine a famous result by T. J. Sargent and N. Wallace (1975, Journal of Political Economy83, 241–254) according to which a “pure interest rate peg” leads to nominal price indeterminacy. We use P. Weil's (1991, International Economic Review32, 37–53) generalization of the Sidrauski–Brock model, where arrival of new “generations” of infinitely lived agents is allowed, and we obtain the following results: (i) Nominal indeterminacy holds in the traditional Sidrauski–Brock framework; (ii) This nominal indeterminacy disappears as soon as new generations arrive in time, via some rigorous version of Patinkin's “real balance effect”; (iii) A multiplicity of solutions may still remain, but full determinacy occurs in some cases, depending notably on fiscal policy or the distribution of endowments in time. Journal of Economic Literature Classification Numbers: E4, E5     

Super-modularity: Applications to convex games and to the greedy algorithm for LP

L. S. Shapley (Internat. J. Game Theory1 (1971), 11–26) showed that if a game is convex, then all the marginal worth vectors are members of the core. J. Edmonds (in “Combinatorial Structures and Their Applications” (R. Guy et al., Eds.), pp. 69–87, Gordon & Breach, New York, 1970) considered a class of linear programming problems for which the greedy algorithm works. The present paper unifies these studies, and establishes the converse of each theorem.     

How Communication Improves Efficiency in Bargaining Games

We study a double auction with two-sided private information and preplay communication, for which Myerson and Satterthwaite (1983, J. Econ. Theory28, 265–281) showed that all equilibria are inefficient and the Chatterjee–Samuleson linear equilibrium is most efficient. Like several others, we find that players use communication to surpass equilibrium levels of efficiency, especially when the communication is face-to-face. Our main contribution is an analysis of how communication helps the parties achieve such high levels of efficiency. We find that when preplay communication is allowed, efficiency above equilibrium levels is a result of what we call “dyadic” strategies that allow the parties to coordinate on a single price that reflects both parties' valuations. Journal of Economic Literature Classification Numbers: C78, D82.     

An empirical comparison of implied tree models for KOSPI 200 index options

This paper compares implied tree models for KOSPI 200 index options with regards to the pricing and hedging performance. With Cox, Ross, and Rubinstein's [Cox, J., Ross, S., & Rubinsteinm, M., 1979. Option pricing: A simplified approach. Journal of Financial Economics, 7, 229–263] standard binomial tree (SBT) model as a benchmark, we analyzed three models: Rubinstein's [Rubinstein, M., 1994. Implied binomial trees. Journal of Finance, 49, 771–818] implied binomial tree (IBT), Jackwerth's [Jackwerth, J. C., 1997. Generalized binomial trees. Journal of Derivatives, 5, 7–17] generalized binomial tree (GBT), and Derman and Kani's [Derman, E., & Kani, I., 1994. Riding on a smile. Risk, 7, 32–39] implied volatility tree (IVT) models. The SBT model, the simplest, shows the best performance. Moreover, the delta-hedged strategy in all of the binomial models generates, on average, negative gains. This finding, consistent with the findings by Bakshi and Kapadia [Bakshi, G., & Kapadia, N., 2003. Delta-hedged gains and the negative market volatility risk premium. Review of Financial Studies, 16, 527–566], indicates the existence of a negative market volatility risk premium.     

Generic 4 × 4 Two Person Games Have at Most 15 Nash Equilibria

The maximal generic number of Nash equilibria for two person games in which the two agents each have four pure strategies is shown to be 15. In contrast to Keiding (1997),Games Econ. Behav.21, 148–160, who arrives at this result by referring to the enumeration of Grünbaum and Sreedharan (1967),J. Combin. Theory2, 437–465, our argument is based on a collection of lemmas that constrain the set of equilibria. Several of these pertain to any common numberdof pure strategies for the two agents.Journal of Economic LiteratureClassification Number: C72.     

Rational Choice and the Condorcet Jury Theorem

In a recent paper, Austen-Smith and Banks (1996,Amer. Polit. Sci. Rev.90, 34–45), criticize the current literature on the Condorcet jury theorem as neglecting the behavioral underpinnings of decision-making. They leave open the question whether allowing mixed strategies would sustain the conclusions of the Condorcet jury theorem. In this paper, it is shown that these conclusions can hold in equilibrium. In other words, “a rational choice foundation for the claim that majorities invariably ‘do better’ than individuals” is derived. (Journal of Economic LiteratureClassification Number: D72.     

Essential aggregation procedures on restricted domains of preferences

The restricted domains of individuals' preferences that permit the construction of Arrow social welfare functions and nonmanipulable voting procedures in which each of n voters has some power are characterized. In this context a domain is the Cartesian product of n sets of strict preference orderings. Variants of this result are obtained under the additional requirement of neutrality and in the case when alternatives are vectors whose ith components affect only the ith voter. Kalai and Muller's analogous result (J. Econ. Theory16 (1977), 457–469) concerning nondictatorial procedures is discussed and proved as a corollary to the main theorem.     

Some extensions of a claim of Aumann in an axiomatic model of knowledge

The paper begins by presenting an axiomatic model of simple and iterated knowledge. A formal definition of the intuitive notion of common knowledge is given and shown equivalent to previous characterizations. It is shown that agents have information partitions. The second part generalizes Aumann's (Ann. Statist.4 (1976), 1236–1239) well-known propositions about common knowledge between two rational agents of each other's probability assignments. It is shown that: common knowledge of decisions—if these are rational—implies a common decision for like-minded agents; and that a “dialogue” in decisions leads to a common decision. A “no-trade” theorem is given which includes trade under complete uncertainty.     

Does Intrinsic Habit Formation Actually Resolve the Equity Premium Puzzle?

G. M. Constantinides (1990, Journal of Political Economy98, 519–543) describes a simple model of intrinsic habit formation that appears to resolve the “equity premium puzzle” of R. Mehra and E. C. Prescott (1985, Journal of Monetary Economics15, 145–161). This finding is particularly important, since it has motivated a broader consideration of the implications of habit formation preferences in dynamic equilibrium models. However, consumption growth actually behaves very differently pre- and post-1948, and the explanatory power of the habit formation model is driven by the pre-1948 data. Using data from 1949 to 2000, constructed in a manner comparable to R. Mehra and E. C. Prescott, I demonstrate that intrinsic habit cannot rationalize the unconditional moments of discrete consumption and real asset returns with values of the risk aversion coefficient that are less than four times larger than the values found by G. M. Constantinides for any feasible calibration of the model. Journal of Economic Literature Classification Numbers: E21, G12.     

Existence and fairness of value allocation without convex preferences

Shafer (Econometrica, 48 (1980), 467–476) proved that in a finite exchange economy value allocations exist, provided that each agent has convex, complete, transitive, compact and monotone preferences. However, if preferences are not convex, then value allocations may not exist. To remedy this difficulty we enlarge the set of value allocations by introducing the concept of approximate value allocations, and show that in a finite exchange economy approximate value allocations exist, even if preferences are not convex, or compact, or monotone. This value existence result can be used to provide a very general value existence theorem for a sequence of finite economies. Further, we show that value allocations may discriminate in favor of or against a coalition of agents.     

The impact of the two-tier plan/market system in chinese industry

There has been a great expansion in the role of the market mechanism in the distribution of industrial goods in China since the late 1970s. A two-tier system, whereby part of total production of each good is allocated by various kinds of directive plans, part by markets, has emerged. It is argued that the two-tier system has resulted in the demise of the direct role of mandatory planning in the allocation of industrial goods, and that the inherent dynamic tendencies of the system are leading to a continual increase in the share of the market over time. J. Comp. Econ., September 1987, 11(3), pp. 295–308. The World Bank, Washington, D.C. 20433.     

Marx,postmodernity, and transformation of the individual

Postmodernity raises for Marxism the question of what happens to the alienated subject's consciousness and purposeful action in the aftermath of its alienation. Arguing that some of Marx's own ideas can shed light on this question, I make a conceptual distinction between form of consciousness and mode of consciousness to capture what I take to be the kernel of his thinking on the transformation of the “average” individual and her/his consciousness in his Early Writings, and especially in the Grundrisse.     

Evolutionary Learning in Signalling Games

We study equilibrium selection by evolutionary learning in monotone two-type signalling games. The learning process we study extends that introduced by Young (1993, Econometrica61, 57–84) to deal with incomplete information and sequential moves; it thus involves stochastic trembles. For vanishing trembles the process gives rise to strong selection among sequential equilibria: if the game has separating equilibria, then in the long run only play according to the so-called Riley equilibrium will be observed frequently. Journal of Economic Literature Classification Number: C72.     

The Role of Absolute Continuity in “Merging of Opinions” and “Rational Learning”

D. Blackwell and L. Dubins (1962, Ann. Math. Statist.38, 882–886) showed that opinions merge when priors are absolutely continuous. E. Kalai and E. Lehrer (1993, Econometrica61, 1019–1045) use this result to show that players in a repeated game eventually play like a Nash equilibrium. We provide an alternative proof of merging of opinions that clarifies the role of absolute continuity while casting doubt on the relevance of the result. Persistent disagreement, the opposite of merging, allows the construction of a sequence of mutually favorable “bets.” By a law of large numbers, both agents are certain they will win these bets on average. This certain disagreement violates absolute continuity. Journal of Economic Literature Classification Numbers: C11, C69, C72, D83.     

Measures of inequality as an aggregation of individual preferences about income distribution: The arrowian case

An inequality preorder is a preorder on a simplex which satisfies symmetry and strict Schur-convexity (the mathematical equivalent of the principle of transfers of Pigou and Dalton). It is shown that we cannot aggregate individual inequality preorders to a collective one if we are interested in Arrow's aggregation rules. The proof uses an interesting result of Kalai, Muller and Satterthwaite (Public Choice 34 (1979), 87–97). Moreover, we prove further results for the aggregation of individual inequality indices when we allow cardinality and interpersonal comparibility of utility.     

Free access vs private ownership: A comparison

Weitzman (J. Econ. Theory8 (1974), 225–234) has established that under free access properties of average or better quality will be overutilised relative to the efficient private property equilibrium. This leaves open the question of what happens to the low quality properties. It is shown here that there are conflicting considerations and the outcome is ambigous. Necessary and sufficient conditions are obtained for less of a variable input to be attracted to a site when access is free than when a private owner makes a charge for access.