The dynamics of economic games based on product differentiation

The time evolution of dynamic triopoly games is modeled by a discrete dynamical system obtained by the iteration of a three-dimensional map. We present in this paper four games: a rational Cournot triopoly, a rational Bertrand triopoly, a Puu triopoly with quantity competition, and a cooperative Cournot triopoly game. For each game, the Nash equilibrium of the game is computed and complete analytical and numerical studies of the stability conditions for the fixed points, which are the Nash equilibria, are given. The analysis of bifurcations which cause qualitative changes in the behavior of games and cause loss of stability of Nash equilibrium is investigated through numerical explorations.