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

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...

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...

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Consider a Bertrand model in which each rm may be inactive with a known probability, so the number of active rms is uncertain. This simple model has a mixed-strategy equilibrium in which industry pro ts are positive and decline with the number of rms, the same features which make the Cournot model attractive. Unlike in a Cournot model with similar incomplete information, Bertrand pro ts always ...

This work extends some classical results of Bertrand curves to timelike ruled and developable surfaces using the E. Study map. provides support define two which are offset in sense Bertrand. It is proved that every surface has a if only an equation should be satisfied among their dual invariants. In addition, new theorems concerning developability offsets gained.

The title of this book refers to Bertrand Russell's The Principles of Mathematics, but it does not deal with Russell's ideas. Jaakko Hintikka sees his book in a similar role to that enjoyed by Russell's, almost a century ago. It is 'crisis science', aimed at establishing a new paradigm in the foundations of mathematics. Hintikka presents a new formalism and a new logic, together with a new sema...