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Riley (1979)'s reactive equilibrium concept addresses problems of equilibrium existence in competitive markets with adverse selection. The game-theoretic interpretation of the reactive equilibrium concept in Engers and Fernandez (1987) yields the Rothschild-Stiglitz (1976)/Riley (1979) allocation as an equilibrium allocation, however multiplicity of equilibrium emerges. In this note we imbed the reactive equilibrium's logic in a dynamic market context with active consumers. We show that the Riley/Rothschild-Stiglitz contracts constitute the unique equilibrium allocation in any pure strategy subgame perfect Nash equilibrium.
We analyse a 2-period competitive insurance market which is characterized by the simultaneous presence of standard moral hazard and adverse selection with regard to consumer time preferences. It is shown that there exists an equilibrium in which patient consumers use high effort and buy a profit-making insurance contract with high coverage, whereas impatient consumers use low effort and buy a contract with low coverage or even remain uninsured. This finding may help to explain why positive profits and the opposite of adverse selection with regard to risk types can sometimes be observed empirically. JEL Classification: D82, G22