Essays on robust mechanism design

Chapter 1: Under the average common value function, we select almost uniquely the mechanism that gives the seller the largest portion of the true value in the worst situation among all the direct mechanisms that are feasible, ex-post implementable and individually rational. Chapter 2: Strategy-proof, budget balanced, anonymous, envy-free linear mechanisms assign p identical objects to n agents. The efficiency loss is the largest ratio of surplus loss to efficient surplus, over all profiles of non-negative valuations. The smallest efficiency loss is uniquely achieved by the following simple allocation rule: assigns one object to each of the p−1 agents with the highest valuation, a large probability to the agent with the pth highest valuation, and the remaining probability to the agent with the (p+1)th highest valuation. When “envy freeness” is replaced by the weaker condition “voluntary participation”, the optimal mechanism differs only when p is much less than n. Chapter 3: One group is to be selected among a set of agents. Agents have preferences over the size of the group if they are selected; and preferences over size as well as the “stand-outside” option are single-peaked. We take a mechanism design approach and search for group selection mechanisms that are efficient, strategy-proof and individually rational. Two classes of such mechanisms are presented. The proposing mechanism allows agents to either maintain or shrink the group size following a fixed priority, and is characterized by group strategy-proofness. The voting mechanism enlarges the group size in each voting round, and achieves at least half of the maximum group size compatible with individual rationality.

Studies on the protective immune response to Plasmodium chabaudi in mice

Inbred strains of C5731 and NIH nice infected with the A/S strain of Plasmodium chaubaudi usually developed high parasitaemias but infections were rarely fatal in immunocompetent mice and in most mice the parasites could be eradicated within 53 days or less. The immune response of C57B1 and NTH mice to infection with the A/S strain of P. chabaudi was studied. The principle method used in this study for investigating the immune response of the mice was to examine the immunity conferred on syngeneic mice, either X-irradiated or non-irradiated, by transferring to them lymphoid cells or serum from immune or semi-immune donors. The lymphoid cell populations examined were unfractionated spleen cells, nylon wool column enriched subpopulations of thymus-derived lymphocytes (T cells) and the so-called bursa-derived lymphocytes (B cells), bone marrow cells and phagocytic cells. In the course of these experiments observations were made on the effect of X-irradiation on the subsequent growth and multiplication of the parasite. In addition, an in vitro assay for antibody-dependent cell mediated cytotoxicity was used to investigate the activity of splenic K cells during malaria infection. K cells are lymphoid cells which may include lymphocytes of an undefined category, but possess receptors for the Fc portion of antibody on their surface and have the ability to non-specifically lyse target cells coated in antibodies. a) The adoptive transfer of immunity to P.chabaudi with immune spleen cells. Spleen cells from mice which had previously been infected with P.chabaudi were able to confer some immunity on syngeneic mice which had been irradiated with 600 or 800 rads. The protection was detected as a shortened patent parasitaemia in immune cell recipients compared to controls. The early experiments indicated the value of using irradiated recipients rather than non-irradiated recipients. In irradiated mice, a) smaller numbers of immune cells were required to promote detectable immunity than in non-irradiated mice, b) there was an amplification of the difference in the duration of primary parasitaemias in recipients of immune cells and normal cells compared to non-irradiated mice and c) as the irradiated host is immunodepressed, the protective effect of donor cells can be examined with a reduced contribution by the hosts own immune system. An initial non-specific resistance to P.chabaudi infection was observed in irradiated mice, although the infection in most of these mice was subsequently more severe than in non-irradiated mice. The non-specific resistance could be reduced or abolished by injecting lymphoid cells into mice shortly after irradiation or by infecting irradiated mice more than 15 days after irradiation. Other workers suggest that following irradiation, the reticulo-endothelial system is stimulated at the time that the non-specific resistance to P.chabaudi was observed. b) the adoptive transfer of immunity in syngeneic mice with enriched subpopulations of splenic immune T cells, B. cells, bone marrow cells and phagocytes. Immunity to P.chabaudi could be adoptively transferred with enriched spleen subpopulations of immune T cells or immune B cells in mice which had been irradiated 600 or 300 rads. The protective effects of unfractionated immune cells was, however, usually better than that of either immune T or F cell subpopulations. In most experiments enriched immune T cell recipients were more likely to suffer relapsing patent parasitaemias than either enriched immune B cell recipients or unfractionated immune cell recipients. In one experiment a comparison was made of the course of P.chabaudi infection in mice which had been irradiated with either 600 rads or 300 rads and which received injections of different immune cells. A dose of 600 rads permits the immune system of mice to recover from the effects of irradiation, but a dose of 800 rads is lethal to mice unless lymphoid cells are injected after irradiation. It was found that in recipients of enriched immune T or B cells, which had been irradiated with 600 rads, the parasitaemia became subpatent before their equivalents irradiated with 800 rads, but that there was little difference in parasitaemias between recipients of unfractionated immune cells given 600 or 800 rads. Experiments in which enriched immune T cells and B cells were recombined and injected into syngeneic mice gave inconclusive results as to whether the immune subpopulations acted synergistically. Similar experiments in which immune subpopulations of lymphoid cells were recombined with normal subpopulations of lymphoid cells demonstrated that the latter cells did not enhance the protective effect of the former cells. Bone marrow cells from immune mice were able to confer some protection on syngeneic recipients, but were not as protective as enriched immune T cells or B cells. The results obtained in adoptive transfer experiments using phagocytic cells from the spleen of immune mice depended on the length of time spleen cells were incubated in petri-dishes at 37° C before harvesting the phagocytes. Using C57B1 mice, phagocytes harvested after 15 hours incubation were as protective as unfractionated immune cells in a cell transfer experiment, but phagocytes harvested after 16 hours incubation were not protective. Examination of NIH phagocytic cells after 2.5 hours incubation at 37°C, which were as protective as unfractionated immune spleen cells in a cell transfer experiment, demonstrated that the petri-dish adherent cells may have contained B lymphocytes. c) The passive transfer of immunity with serum from P.chabaudi infected mice. The passive transfer of serum from C57B1 mice which had been previously infected with P.chabaudi to normal or irradiated syngeneic mice demonstrated that the serum recipients were initially protected from infection. Irradiated mice, however, were delayed longer in the onset of parasitaemia compared to non-irradiated mice. Using NIH mice, sera were collected from unfractionated immune spleen cell recipients, enriched immune T cell recipients and normal spleen recipients on the 11th day of a P.chabaudi infection, just after peak parasitaemia, and also on the 14th day of infection. On day 14, all immune cells recipients and most of the enriched immune T cell recipients had become subpatent but all normal cell recipients still had patent infections. Sera collected from the different spleen cell recipients on the 11th day of infection and passively transferred to irradiated mice demonstrated little protection. Sera collected on the 14th day of infect ion, however, reflected the immune status of the donors in their protective properties in mice infected with P.chabaudi. The serum from unfractionated immune cell recipients was the most protective of the 3 sera when compared to normal NIH serum and the serum from enriched immune T cell recipients was slightly protective, but the serum from normal cell recipients produced an enhanced infection in mice infected with P.chabaudi. d) Antibody-dependent cell-mediated cytotoxicity of spleen cells in P.chabaudi infected mice. In a preliminary investigation of K cell activity in the spleens of P.chabaudi infected mice, it was found that there was an increased activity of K cells collected at around peak parasitaemia compared to the activity of K cells in non-infected mice, and that this increased activity could also be found in mice which had recently become subpatent. As the target cell for antibody-dependent cell-mediated cytotoxicity employed was the thick red blood cell, it is not known whether the K cell is involved in the killing of P.chabaudi parasites. These results suggest that both T cells and B cells and antibody may be important in the immune response to P.chabaudi in mice. Primed T cells may act as helper cells in the production of malarial antibodies, but, as enriched primed T cells could confer protection on immunodepressed mice, it is possible that a cell-mediated mechanism of immunity may also exist.