Cournot Competition as a Continuous State Space Markov Chain
| dc.contributor.advisor | Neeman, Joseph | |
| dc.creator | Halsey, Alexander | |
| dc.date.accessioned | 2021-05-19T15:17:47Z | |
| dc.date.available | 2021-05-19T15:17:47Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | The Cournot competition is a game in which two firms vie to produce the optimal quantity of a good. Perfectly rational and fully informed firms would produce the quantities given by the Nash equilibrium, the point at which neither firm could improve their payoff by changing their action. Although the Nash equilibrium for the Cournot competition is well understood, there are several proposed models describing how firms that are not fully informed or perfectly rational might still learn the Nash equilibrium. Two commonly used models are fictitious play and the successive best response strategy. I build on these by using a Markov chain, a model for the evolution of random systems, to capture the probabilistic behavior of imperfect firms. Most of the theory and applications of Markov chains deals with finite or countable state spaces. In order to make sense in the context of game theory, the theory of Markov chains on arbitrary state spaces must first be presented. I will provide the relevant results for general state space theory, then describe its novel applications for learning Nash equilibria in the Cournot model. | en_US |
| dc.description.department | Mathematics | en_US |
| dc.identifier.uri | https://hdl.handle.net/2152/85750 | |
| dc.identifier.uri | http://dx.doi.org/10.26153/tsw/12701 | |
| dc.language.iso | eng | en_US |
| dc.relation.ispartof | Honors Theses | en_US |
| dc.rights.restriction | Open | en_US |
| dc.subject | Markov chain | en_US |
| dc.subject | general state space | en_US |
| dc.subject | Nash equilibrium | en_US |
| dc.subject | Cournot competition | en_US |
| dc.title | Cournot Competition as a Continuous State Space Markov Chain | en_US |
| dc.type | Thesis | en_US |