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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. ​Doctor of Philosophy (SPMS)

This paper introduces a class of games called the positive semidefinite games, for which we show the absence of mixed and nonstrict ESS's. As a result, a strategy is an ESS if and only if it is strict Nash. One famous example in this class of games is Rock{Paper{Scissors. For a smaller class of games called the positive definite games, we prove a similar result forThis paper introduces a class of games called the positive semidefinite games, for which we show the absence of mixed and nonstrict ESS's. As a result, a strategy is an ESS if and only if it is strict Nash. One famous example in this class of games is Rock{Paper{Scissors. For a smaller class of games called the positive definite games, we prove a similar result for NSS's. This result opens the door to a corollary: for doubly symmetric games, the existence of an ESS is assured. This is an interesting result because of the stronger dynamic stability properties of ESS's as compared to NSS's. The coordination games played on the identity matrix are an example of games in this latter class. NSS's. This result opens the door to a corollary: for doubly symmetricgames, the existence of an ESS is assured. This is an interesting result because of the stronger dynamic stability properties of ESS's as compared to NSS's. The coordination games played on the identity matrix are anexample of games in this latter class.