In this paper, we fully characterize the Nash Equilibrium in the winner-take-all Bertrand Game, showing that a mixed strategy profile is a Nash Equilibrium, if and only if it is a zero operating profit one, and there exist at least two players whose bids are all unprofitable. Compared with...

The development of internet technology has reshaped the market structure for many products. We study the price competition problem between online stores and offline stores, by allowing consumers' preferences to be more favorable towards online shopping. We consider 3 scenarios: (1) market with...