This paper estimates depth of reasoning in an Iterative Best Response model using data from Weber (2003) ten-period repeated guessing game with no feedback. Different mixture models are estimated and the type (Level-0, Level-1, etc) of each player is determined in every round using the Expectation Maximization algorithm. The matrices showing the number of individuals transitioning among levels is computed in each case. It is found that most players either remain in the same level or advance to the next two levels they were in the previous period. The lowest levels (Level-0 and Level-1) have a higher probability of transitioning to a higher level than Level-2 or Level-3. Thus, we can conclude that subjects, through repetition of the task, quickly become more sophisticated strategic thinkers as defined by higher levels. However, in some specifications the highest levels have a relatively large probability of switching to a lower level in the next period. In general, depth of reasoning increases monotonically in small steps as individuals are subjected to the same task repeatedly.

This study investigates whether increases in elephant populations may influence the structure of African savannas, and consequently may affect other herbivores through changes in habitats. Two contrasting periods in terms of elephant population densities were compared in Hwange National Park, Zimbabwe: the early 1980s and the late 1990s. Elephant population density and other ungulate population densities were estimated for a c. 400-km2 area from road counts. Vegetation structure at the landscape scale was assessed using aerial photographs for the same area. All browsers and grazers declined between the early 1980s and the late 1990s, whereas elephants experienced a 16-fold increase. At the landscape scale, vegetation structure changed little with no evidence of an opening of the habitats. These results do not support any kind of medium-term facilitation between elephants and other herbivores. They rather suggest a negative effect of elephants on other herbivore species when elephants are present at high densities. This study rules out a scenario where the decrease of the different herbivore populations was caused by large changes in vegetation structure due to elephant activity.

In this paper we consider the operation of the move-to-front scheme where the requests form a Markov chain of N states with transition probability matrix P. It is shown that the configurations of items at successive requests form a Markov chain, and its transition probability matrix has eigenvalues that are the eigenvalues of all the principal submatrices of P except those of order N—1. We also show that the multiplicity of the eigenvalues of submatrices of order m is the number of derangements of N — m objects. The last result is shown to be true even if P is not a stochastic matrix.