Secure implementation, network cost sharing and oligopolistic price discrimination

In chapter 1, we consider the possibility of Secure Implementation in Production Economies beyond the result provided in the Saijo et al. (2007) paper. We find a large class of SCFs to be securely implementable. The serial SCF and the widely studied Fixed Path SCFs which contains serial SCF as a special case are all special cases of our function.In chapter 2, which is a version of my work with Ruben Juarez, we consider the problem of sharing the cost of a network formed by choice of paths of agents to connect their demand nodes. Motivated by the inefficiency, instability and huge informational requirements of the widely used Shapley (Sh) cost sharing rules, we look for mechanisms in a setting of minimal informational requirement which overcome the said shortcoming. We characterize a class of such mechanisms under different notions of robust implementations. We also discover that voluntary participation is possible in this setup with no more inefficiency than that of Sh.In chapter 3, which is a version of my work with Levent Kutlu, we consider the aspect of price discrimination under oligopolistic setting. The environment has two stages of the game. In first stage the firms fight on the quantity they want to put in the market and then in the second stage they decide how to distribute that quantity among the buyers with different valuations. We characterize the unique NE of this game. The firms which ends up with higher quantity in the first stage sells to all the buyers whereas the smaller firm sells some of the high end buyers.