Identifying reaction functions in differential oligopoly games

Lambertini, Luca ; Mantovani, Andrea (2004) Identifying reaction functions in differential oligopoly games. p. 29. DOI 10.6092/unibo/amsacta/1556.

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Abstract

We investigate the issue of strategic substitutability/complementarity in differential games. We prove that instantaneous best replies exist if Hamiltonian functions are multiplicative in the control variables. Otherwise, if the Hamiltonians are addively separable w.r.t. controls, a dominant strategy emerges for each player. In this case, however, imposing stationarity on the differential equations of states, one can still identify best replies at the steady state, which is ruled out by definition in static games.

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