Modeling innovation and regulation thanks to game theory: Bertrand competition

Abstract

One uses the model which has been already presented in articles by the author: competition through prices (Bertrand competition), the demands being deduced from the consumers ‘utilities. One can highlight three phenomena: “Monopolistic competition”: The products sold are enough differentiated, each firm having its “garden”, its customers it keeps provided its price is not higher than the others’ prices. The criterium “buy and close down” profitable: when to buy and close down is profitable, the incentive to merge is stronger. It is a sign of saturated market. The “non-differentiating innovation”: One can model it. Each utility (u1, u2, u3) becomes (u1 + K, u2 + K, u3 + K), K > 0. One demonstrates, thanks to tractable examples, that non-differentiating innovation can trigger the criterium “buy and close down profitable”. The products are less differentiated than at the start (“monopolistic competition” the “buy and close down” being not profitable). It incites firms to choose disruption.