Strategic behaviour, equilibria and economic optimality in settings with competing interests

• Main Author: Polak, Ido David
• Other Authors: Nicolas Privault
• Format: Theses and Dissertations
• Language: English
• Published: 2017
• Subjects: DRNTU::Science::Mathematics::Applied mathematics::Game theory; DRNTU::Science::Mathematics::Applied mathematics::Optimization; DRNTU::Science::Mathematics::Probability theory
• Online Access: http://hdl.handle.net/10356/70664
• Institution: Nanyang Technological University

In settings with competing interests interacting agents need to take into consideration many details and parameters of the environment. Examples include strategies and payoffs, rules of the game or market and uncertainty. We present several contributions in this area. We examine firms in markets with stochastic, limited demand and their deterministic counterparts, both in sequential as well as simultaneous form. We characterise their equilibria and show that the stochastic setup can be seen as a smoothing of the deterministic version. In particular, in the simultaneous case, we exhibit the existence of an intermediate regime of the demand, in which there is a range of equilibria in the deterministic framework, but a single equilibrium in the stochastic setting. We illustrate our findings by plotting graphs numerically. Also, we present new results from exchange economies for the incentive ratio, a concept intended to measure the extent to which an equilibrium outcome can be manipulated. Unlike in Fisher markets, the benefits from manipulation in linear, Leontief and Cobb-Douglas exchange economies can be arbitrarily large. For Cobb–Douglas markets we show that we can break the upper bound from Fisher models even in markets with only three goods, but we also demonstrate that the incentive ratio is bounded by the number of commodities.