Bertand Competition and the Existence of Pure Strategy Nash Equilibrium in Markets with Adverse Selection

Anastasios Dosis 1, 2
1 ESSEC
ESSEC Business School, Economics Department
Abstract : I analyse a market with adverse selection in which companies competè a la Bertrand by offering menus of contracts. Contrary to Rothschild and Stiglitz (1976), I allow for any finite number of types and states and more general utility functions. I define the generalised Rothschild-Stiglitz Profile of Actions (RSPA), and I show that, in every possible market, if the RSPA is efficient, it is also a pure strategy Nash equilibrium profile of actions. On the contrary, I show that in markets in which the RSPA is not efficient, preferences admit an expected utility representation with strictly increasing and strictly concave VNM utilities and a weak sorting condition holds, no pure strategy Nash equilibrium exists.
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Anastasios Dosis. Bertand Competition and the Existence of Pure Strategy Nash Equilibrium in Markets with Adverse Selection. 2016. ⟨hal-01285185⟩

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