In this paper, we give a ‘direct’ construction of the endomorphism ring of supersingular elliptic curves over a prime field Fp from ‘ideal classes’ of Q( √−p). We use the result to prove that the result of Kaneko on ‘minimal’ CM liftings of such supersingular elliptic curves is a best possible result. We also prove that the result of Elkies on ‘minimal’ CM liftings of all supersingular elliptic...

We show that bounded monopoly profits are essential for the uniqueness of the Bertrand paradox (zero profit) outcome. Otherwise, a folk theorem obtains for one-shot homogeneous product Bertrand games: any positive (but finite) payoff vector can be achieved in a symmetric mixed-strategy Nash equilibrium. JEL Numbers: D43, C72

in this note we review a simple criterion, due to ekedahl, for superspecial curves defined over finite fields.using this we generalize and give some simple proofs for some well-known superspecial curves.

The author describes a series of matrix choice games illustrating monopoly, shared monopoly, Cournot, Bertrand, and Stackelberg behavior given either perfect complements or perfect substitutes. The games are created by using a spreadsheet to fill out a profit table given the choices of two players. One player selects the column, the other the row, and the table gives the profit of the row choos...

We study continuous time Bertrand oligopolies in which a small number of firms producing similar goods compete with one another by setting prices. We first analyze a static version of this game in order to better understand the strategies played in the dynamic setting. Within the static game, we characterize the Nash equilibrium when there are N players with heterogeneous costs. In the dynamic ...

In this paper, taking the factor of product service provided by manufacturers into consideration, a static Bertrand duopoly game with is studied first, in which these two oligarchs produce differentiated products. A dynamic bounded rationality established using gradient mechanism. Keeping adjustment speeds relatively small range may help long-term stable operation market. It found that there an...

In this paper we propose a theory of Bertrand competition where firms form beliefs by considering only a subset of the available variables. This theory of coarse updating leads to equilibria where firms set prices according to constant mark-up strategies, which is consistent with the empirical evidence found in survey data. Moreover it leads to higher prices than the standard theory, which is i...