On the impossibility of predicting the behavior of rational agents.

A foundational assumption in economics is that people are rational: they choose optimal plans of action given their predictions about future states of the world. In games of strategy this means that each player's strategy should be optimal given his or her prediction of the opponents' strategies. We demonstrate that there is an inherent tension between rationality and prediction when players are uncertain about their opponents' payoff functions. Specifically, there are games in which it is impossible for perfectly rational players to learn to predict the future behavior of their opponents (even approximately) no matter what learning rule they use. The reason is that in trying to predict the next-period behavior of an opponent, a rational player must take an action this period that the opponent can observe. This observation may cause the opponent to alter his next-period behavior, thus invalidating the first player's prediction. The resulting feedback loop has the property that, a positive fraction of the time, the predicted probability of some action next period differs substantially from the actual probability with which the action is going to occur. We conclude that there are strategic situations in which it is impossible in principle for perfectly rational agents to learn to predict the future behavior of other perfectly rational agents based solely on their observed actions.

Site of synthesis, tissue distribution, and lipophorin transport of hydrocarbons in Blattella germanica (L.) nymphs.

The site of hydrocarbon (HC) synthesis and the amount of HC in various tissues were investigated in relation to developmental stage in the last larval stadium of the German cockroach, Blattella germanica. Abdominal integument linearly incorporated [1-(14)C]propionate into HC for at least 6h in vitro, whereas other body parts synthesized little or no HC. The third through sixth abdominal sternites and tergites were the principal sites of synthesis. High rates of HC synthesis resulted in a fivefold increase in internal HC during the last stadium. We examined the distribution of HC in the hemolymph, fat body, and the developing imaginal cuticle. Hemolymph HC titer was relatively constant at approximately 8&mgr;g/&mgr;l. However, as hemolymph volume increased from 5 to 11&mgr;l in the first 4days of the last stadium, HC content increased and then remained stable the remainder of the stadium. Lipophorin, immunoprecipitated with adult lipophorin polyclonal antibodies, was the only HC carrier protein in nymphal hemolymph and its HC profile was identical to that of hemolymph and similar to that of the epicuticle. The concentration and total amount of hemolymph lipophorin increased until 3days before adult eclosion and declined immediately after ecdysis. The HC content of non-biosynthetic integument (legs, pronotum) doubled during formation of the imaginal cuticle, as did the HC content of sternites, which synthesize HC. HC content of fat body, however, increased threefold during the same period, suggesting that the fat body serves as a storage site for HC during cuticle formation. We conclude that in the last stadium HC is synthesized by abdominal oenocytes, loaded onto hemolymph lipophorin, and transported to fat body and both nymphal and imaginal cuticle. Hydrocarbons associate with the imaginal integument several days before eclosion.

Uptake of exogenous gangliosides by rat brain synaptosomes.

Synaptosomes incorporated mixed brain gangliosides at a rapid initial rate followed by a slower phase of net movement from the protein-associated fraction into the membrane core. The pattern of incorporated gangliosides reflected the pattern available for incorporation. Intact synaptosomes incorporated approximately 100 pmol GM1/mg protein. Synaptosomes preincubated with proteolytic enzymes (trypsin, chymotrypsin, and papain) at different pH values (6.2, 7.4, 7.8) incorporated more exogenous gangliosides than synaptosomes preincubated in buffer alone. This effect was maximal at pH 7.8, though analysis of variance revealed that the proteolytic treatment and pH effects were probably independent processes. Overall uptake of exogenous gangliosides correlated significantly with amount of membrane protein loss, indicating that initial access of exogenous gangliosides to synaptosomal membranes is retarded by cell-surface proteins. These results suggest synaptosomes as a useful alternative to cultured cells for investigating the interaction of gangliosides with other cell surface constituents.

Growth stimulation and chemotropic attraction of rat retinal ganglion cell axons in vitro by co-cultured optic nerves, astrocytes and astrocyte conditioned medium.

The effects of explants of optic nerves of different ontogenetic ages (P0 P14, adult), and of cultured astrocytes of various ages on the neurite regeneration of rat retinal ganglion cells (RGC) were assessed in vitro, using a three-dimensional culture system which allows the co-cultivation of various explants. Both co-cultured P0-P12 optic nerves and astrocyte cultures from P2 cerebral cortex stimulated the regeneration of neurites from the retinal explants after 3 days in culture. By contrast, P14 and older explants of the optic nerve, astrocytes from P17 optic nerve and astrocytes that had previously been grown in culture for more than 6 weeks had no effect on RGC neurite outgrowth. Moreover, both the P0-P12 optic nerve explants and the astrocytes from P2 cerebral cortex also seemed to have a chemotropic effect on the regenerating neurites, because the latter were longer on the side facing the co-explantat. The absence of a cellular bridge between retinal and optic nerve explants suggests that the effects are mediated by astroglia-derived diffusible neurite growth promoting factors. Accordingly, astrocyte-conditioned medium from P2 astrocytes also stimulated the outgrowth of neurites from the retinal explants. These findings show that immature astrocytes of a limited ontogenetic period release as yet unknown diffusible neurite growth-promoting factors which stimulate the regeneration of neurites from retinal explants.

The Webster method of apportionment.

Several results concerning the problem of U.S. Congressional apportionment are given which, together, indicate that a method first proposed by Daniel Webster (also known as the "Major Fractions" method) seems fairest when judged on the basis of criteria suggested by common sense and precedent.

A new method for congressional apportionment.

The problem of Congressional apportionment is explained together with a brief history of the methods used or considered for its solution. Reasons are given for rejecting the presently used method of equal proportions and for accepting a new method, the quota method, which is the unique method satisfying three essential axioms.