Knowledge that Transforms

This paper examines the nature of rational choice in strategic games.Although there are many reasons why an agent might select a Nash equilibrium strategy in a particular game, rationality alone does not require him to do so.A natural extension of widely accepted axioms for rational choice under uncertainty to strategic environments generates an alternative class of strategies, labelled "rationalizable."It is argued that no rationalizable strategy can be discarded on the basis of rationality alone, and that all rationally justifiable strategies are members of the rationalizable set.The properties of rationalizable strategies are studied, and refinements are considered.PROOF OF PROPOSITION 5.5: Since under the specified conditionsf(-) is a contraction mapping, Nash equilibrium is unique.We need only show P(G) = N*(G).Since P(G) is the intersection of an infinite sequence of compact, nested sets, it is compact.Consequently, we can define di = max d(s,, s,).s,,s, E-P,(G) Assume without loss of generality that d, > di Vi > 1.If point rationalizable strategies are not unique, then di > 0. Let s' and sj' be the strategies for which d(s'1, sj') = dl.There must exist t', t' e P(G)such that fl(t') = sj, and fl(t") = sj', with g,(t') = v1(t") (the first component doesn't effect fl( )).Now d(t', t") < ( d2 ) < d1(I-1)1/2. (i=2 J Further, d(f(t'), f(t")) > d(s', sj') = dl.So d(f(t), ft"))> d(t, t"I(I 1 ,/2

[A model of job-matching is considered, in which the set of employees hired by each firm, and the set of jobs accepted by each worker, are endogenously determined, as are the job descriptions settled on by each worker-firm pair. The set of outcomes that are in equilibrium, in the sense of being stable with respect to recontracting, is shown to be nonempty. It is shown that the interests of the firms and workers are polarized over the set of stable outcomes: There exists a firm-optimal stable outcome that is the best stable outcome for every firm and the worst for every worker, and a corresponding worker-optimal stable outcome that is best for every worker and worst for very firm. These results generalize and extend previous results for models of this type, and raise questions about the nature and underlying causes of such polarization of interests.]

[This article focuses on the desirability of quantity controls in an economy when the first best optimum is not attainable. Based on the analysis of constrained consumer demand, a formula for the desirability of small personalized compensated quotas is first established. Conclusions for the desirability of anonymous quotas: redistribution in kind, rationing, are derived. Actions on prices through taxes and quantity controls are compared. The analysis is also shown to have implications for the theory of optimum income taxation.]

Hours of work equations are derived from the constrained maximization of a utility function that is not separable over time and that varies with a household's demographic structure. These equations are fitted to observations on wage rates, nonlabor income, and other variables for husbands, wives, and unmarried women. The dependence of each household's current work and consumption behavior upon its work and consumption behavior in the past is examined closely and different interpretations of the relationship are confronted with the data.

Bibliography: p. 38-40.

This paper addresses the question of nonmyopic strategic behavior in an MDP planning procedure which is terminated when the rate of adjustment in the quantity of the public good is below some prespecified threshold. The problem is formulated as a dynamic game in which utility functions are additively separable. It is shown that the game possesses perfect Nash equilibria whose outcomes are Pareto optima. Moreover, any individually rational Pareto optimum can be attained through one of these Nash equilibria. Strategies in these equilibria involve a rate of revision in the quantity of the public good that is equal to the threshold level and insures monotonic convergence of the procedure in finite time.

This paper explores the extent to which standard, general equilibrium analysis of Pareto optima and of competitive equilibria can be applied to environments with moral hazard and adverse selection problems.Allowing for lotteries, contracts with random components, we first establish that an adverse-selection insurance economy, a moral-hazard insurance economy, a signaling economy, and a private-information labor market economy are all special cases of a simple, general structure.We then show that techniques for characterizing Pareto optimal contracts as solutions to concave programming problems are useful and nice and appear to be broadly applicable; allowing for lotteries, we show how to characterize the optimal allocations for the adverse-selection insurance and labor market economies.We then show that standard existence and optimality theorems for competitive equilibria apply in the linear space containing lotteries if agents with characteristics which are distinct and privately observed at the time of initial trading enter the economy-wide resource constraints in a homogeneous way (other kinds of diversity are not critical).For economies with moral hazard which satisfy the homogeneity condition, competitive contract markets single out a subset of the optima and thus can be consistent with apparent unemployment and with a random allocation of labor supplied though all households are averse to risk.The adverse-selection insurance and signaling economies, however, do not satisfy the homogeneity condition and are difficult to decentralize efficiently with a price system.