Dynamics of Individual Specialization and Global Diversification in Communities

We discuss a model of an economic community consisting of $N$ interacting agents. The state of each agent at any time is characterized, in general, by a mixed strategy profile drawn from a space of $s$ pure strategies. The community evolves as agents update their strategy profiles in response to payoffs received from other agents. The evolution equation is a generalization of the replicator equation. We argue that when $N$ is sufficiently large and the payoff matrix elements satisfy suitable inequalities, the community evolves to retain the full diversity of available strategies even as individual agents specialize to pure strategies.Comment: 13 pages, Late

Wavelength exponent for haze scattering in the tropics as determined by photoelectric photometers

Sun photometers using narrow-band interference filters, photoelectric sensors and solid-state operational amplifiers were constructed and intensive measurements of the haze extinction co-efficients at 0.40 and 0.60 μm wavelengths made at Poona (Lat. 18° N) over a one-year period. The most significant result obtained is that the wavelength exponent for the haze scattering as calculated from 520 pairs of simultaneous observations shows a median value of 0.5 and a mode of about 0.8. These are substantially lower than corresponding values found in the case of middle latitude stations. In general, the exponent is correlated positively with the turbidity itself in the case of wet haze, and under conditions of very clear and dry air it assumes near zero values. A marked diurnal variation in the value of the exponent occurs during the regimes of tropical continental air. The consequences of the prevailing lower values of α in relation to determination of the Ångström turbidity coefficient β in the tropics are briefly discussed

A new method for the determination of atmospheric turbidity

Atmospheric turbidity is usually measured using either a pyrheliometer fitted with a red RG630 filter or a Volz sun photometer, the turbidity coefficients so determined being designated as β and B, respectively. Both techniques are subject to error, the former in underestimating high turbidities and the latter in giving rise to errors at low turbidities. The present paper describes a new, simpler and less expensive method of evaluating β from measurements of direct and diffuse solar radiation, made as a routine at principal radiation stations. Using a theoretical model for determining the attenuation of solar radiation due to absorption and scattering by water vapour and other gases, dust and aerosols in the atmosphere, an expression for the ratio of diffuse to direct solar radiation D/IH is derived as a function of β. Then, from the hourly mean values of global and diffuse solar radiation routinely recorded at principal radiation stations, D/IH is calculated. β can now be readily evaluated using a special nomogram based on the formula relating β to D/IH. The values of β derived for Indian stations using the above technique show remarkable internal consistency and stability, proving its utility and reliabilit

Denumerable-Armed Bandits

This paper studies the class of denumerable-armed (i.e. finite- or countably infinitearmed) bandit problems with independent arms and geometric discounting over an infinite horizon, in which each arm generates rewards according to one of a finite number of distributions, or "types." The number of types in the support of an arm, as also the types themselves, are allowed to vary across the arms. We derive certain continuity and curvature properties of the dynamic allocation (or Gittins) index of Gittins and Jones (1974), and provide necessary and sufficient conditions under which the Gittins-Jones result identifying all optimal strategies for finite-armed bandits may be extended to infinite-armed bandits. We then establish our central result: at each point in time, the arm selected by an optimal strategy will, with strictly positive probability, remain an optimal selection forever. More specifically, for every such arm, there exists (at least) one type of that arm such that, when conditioned on that type being the arm's "true" type, the arm will survive forever and continuously with nonzero probability. When the reward distributions of an arm satisfy the monotone likelihood ratio property (MLRP), the survival prospects of an arm improve when conditioned on types generating higher expected rewards; however, we show how this need not be the case in the absence of MLRP. Implications of these results are derived for the theories of job search and matching, as well as other applications of the bandit paradigm

Switching Costs and the Gittins Index

The Theorem of Gittins and Jones (1974) is, perhaps, the single most powerful result in the literature on Bandit problems. This result establishes that in independent-armed Bandit problems with geometric discounting over an infinite horizon, all optimal strategies may be obtained by solving a family of simple optimal stopping problems that associate with each arm an index known as the dynamic allocation index or, more popularly, as the Gittins index. Importantly, the Gittins index of an arm depends solely on the characteristics of that arm and the rate of discounting, and is otherwise completely independent of the problem under consideration. These features simplify significantly the task of characterizing optimal strategies in this class of problems