Title: Ambiguity aversion as a route to randomness in a duopoly game

Abstract: The global dynamics is investigated for a duopoly game as in Singh & Vives (1984) where the perfect-foresight hypothesis is relaxed and firms are worst-case maximizers (maxmin preferences as in Gilboa & Schmeidler (1989)). Ignoring that products are perfect substitute and ignoring the sensitivity of price to quantity, the unique and globally stable Cournot-Nash equilibrium of the complete-information duopoly game losses stability when firms are not aware if they are playing a duopoly game, as it is, or an oligopoly game with more than two competitors. This finding resembles Theocharis’s condition for the stability of the Cournot-Nash equilibrium in oligopolies without uncertainty, see Theocharis (1960). Differently from complete-information oligopoly games, coexisting attractors, disconnected basins of attractions and chaotic dynamics emerge when the Cournot-Nash equilibrium losses stability. This difference in the global dynamics is due to the nonlinearities introduced by the worst-case approach to uncertainty, which mirror in bimodal best-reply functions. The investigation reveals that chaotic dynamics are caused, and at the same time source, of uncertainty.