Knowledge that Transforms

[This paper develops a general, competitive model of commodity differentiation. The structure analyzed is sufficiently rich to admit the basic structures of many of the common models of commodity differentiation as special cases. Thus, the model provides a unifying framework within which alternative formulations of strategic product choice can be compared. It is shown that competitive equilibria exist under only mild restrictions on the underlying economic structure and vary continuously with endowments. Finally, some results relevant to all models of commodity differentiation featuring price taking consumers are presented. The results are shown to point to some potentially important methodological restrictions.]

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[The lecture investigates some consequences of a frequently observed phenomenon: There are once and for all costs of switching from one good to one of its substitutes. The decision to substitute then is an investment decision. Such substitution costs, in conjunction with problems of oppportunism, have frequently been seen as a reason for vertical integration. Reputation for a fair treatment of customers may enable suppliers to maintain market relations for goods involving substitution costs. A model looks at "competitive distance" between two goods with substitution costs. If future tastes are uncertain the model shows that with low rates of discount or high rates of market growth competitive distance declines as substitution costs rise. It is also shown that competitive distance rises with a rising rate of discount. Given the effectiveness of the reputation mechanism, numerical analysis shows that competitive distance is smaller in most cases with substitution costs than without substitution costs.]

When zero mean measurement error is added to the dependent variable for the nonlimit observations of the censored normal regression model, the conventional maximum likelihood estimator (Tobit) is inconsistent. Correct maximum likelihood estimation appears to be computationally difficult under various specifications for the distribution of the measurement error. Estimators based on either the expectation function or the conditional expectation function for uncensored observations remain consistent in the presence of measurement error. Eight such estimators are examined. The results of a numerical experiment suggest that several of these estimators are substantially more efficient than the conventional maximum likelihood estimator when measurement error exists and that they also will do reasonably well when it does not.

Lung-Fei Lee, Robert H. Porter, Switching Regression Models with Imperfect Sample Separation Information--With an Application on Cartel Stability, Econometrica, Vol. 52, No. 2 (Mar., 1984), pp. 391-418

[Introduction] To a large extent the cooperative theory of games has an altogether different appearance from the noncooperative theory. The noncooperative theory generally deals with games in either extensive form or normal form, while the cooperative theory is usually described in characteristic function form. One of the central concepts in the cooperative theory is that of the core, which is the set of utility allocations which no coalition can improve upon. This notion of the core and of the characteristic function form of a game depends heavily on the existence of a utility representation for players' preferences. Recently Gale and Mas-Colell [3] and Shafer and Sonnenschein [6] have proven theorems on the existence of a Nash equilibrium for noncooperative games in normal form in which the players' preferences over strategy vectors are not necessarily complete or transitive and so may fail to have a utility representation. Thus it might appear that the noncooperative theory is applicable in environments where the cooperative theory is not. In order to formulate theorems in the cooperative theory of games which can be applied to environments in which players may have nonordered preferences, the characteristic function must be reformulated in terms of physical outcomes as opposed to utility outcomes. The players' preferences can then be expressed in terms of the physical outcomes without the use of a utility function.

[The model considered is a two-equations model consisting of a binary choice equation and a regression equation. Tests for the bivariate normal distribution are derived for the truncated samples case and the censored samples case. The tests are Lagrangean multiplier tests for testing the bivariate normal distribution within the bivariate Edgeworth series of distributions. Simple intuitive interpretations for the statistics are provided.For the truncated case, the test compares with the estimated differences between some sample moments of order (r,s) for which r + s extgreater 2 and the corresponding hypothesized moments of the disturbances. For the censored case, the test is equivalent to the testing of some sample semi-invariants for which r + s extgreater 2 are zeros.]

[A generalization of the Nash bargaining solution is defined for two-person bargaining problems with incomplete information. These solutions form the smallest set satisfying three axioms: a probability-invariance axiom, an extension (or independence of irrelevant alternatives) axiom, and a random-dictatorship axiom. A bargaining solution can also be characterized as an incentive-compatible mechanism that is both equitable and efficient in terms of some virtual utility scales for the two players.]