Abstract
This thesis is to address three questions on price competition and one question in statistical application in physics that has a possible application in economics. The aim of the first paper is to investigate the equilibrium in a dynamic Bertrand duopoly where firms do not know the cost of other firms and firms face an avoidable sunk cost when they decide to enter the market. In this model, firms are allowed to monitor rival's entry decision before making their pricing decision. Firms are also allowed to communicate with each other via announcements before they make the entry decision. I show that there exists two classes of PureStrategy BayesianNash equilibria in this game. In one class of equilibrium only the low cost firms enter, and in the other class of equilibrium only one firm enters while the other stays out irrespective of their types. This is a new existence result and the paper provides full characterization of the Perfect Bayesian Equilibria (PBE). Communication among firms is just `cheap talk' and has no effect on the set of equilibria in this game. Oneshot price competition among identical firms facing avoidable fixed cost generally leads to a permanent inefficiency when costs are unknown. This stems from the fact that the market is not served with positive probabilities. However, in reality, firms interact repeatedly. My second paper shows that market inefficiency in the oneshot game can be restored with infinitely repeated interaction among competing rms. I demonstrate that with infinite interaction of firms in a Bertrand setting, competing firms can selfimpose collusive conduct via communication. I provide a characterization of the Perfect Public Equilibrium (PPE) where firms collude and as a part of this equilibrium firms employ asymmetric penal codes. In this game, preplay communication has a positive value which is absent in the oneshot game. The results indicate that the presence of an avoidable fixed cost in this setting makes it easier for firms to collude.
In the third paper, I consider a Bertrand duopoly where one firm's cost is publicly
known and the other firm's cost is private information. In this paper, we provide a full characterization of the [?] of this game under equal market sharing rule. We point out that onesided cost uncertainty and bounded known cost type is sufficient to guarantee the existence of the PSBNE.
Finally, in the fourth paper we use basic techniques from econometrics and statistics, in particular Ordinary Least Square regression and Pearson's rank correlation method, to study second order fluctuations along the fluid side of the melting line of the Lennard Jones (LJ). We use Molecular Dynamic computer simulation to generate data on the cross correlation between the configurational part of the pressure and potential energy the repulsive and attractive parts of the potential energy. By using the statistical techniques we notice a qualitative change along the melting line.
In the third paper, I consider a Bertrand duopoly where one firm's cost is publicly
known and the other firm's cost is private information. In this paper, we provide a full characterization of the [?] of this game under equal market sharing rule. We point out that onesided cost uncertainty and bounded known cost type is sufficient to guarantee the existence of the PSBNE.
Finally, in the fourth paper we use basic techniques from econometrics and statistics, in particular Ordinary Least Square regression and Pearson's rank correlation method, to study second order fluctuations along the fluid side of the melting line of the Lennard Jones (LJ). We use Molecular Dynamic computer simulation to generate data on the cross correlation between the configurational part of the pressure and potential energy the repulsive and attractive parts of the potential energy. By using the statistical techniques we notice a qualitative change along the melting line.
Original language  English 

Qualification  Ph.D. 
Awarding Institution 

Supervisors/Advisors 

Award date  13 Apr 2016 
Publication status  Unpublished  2016 