TY  - GEN
AB  - This paper presents a numerical method for the characterization of Markov-perfect
equilibria of symmetric differential games exhibiting coexisting stable steady states.
The method relying on the calculation of ’local value functions’ through collocation
in overlapping parts of the state space, is applicable for games with multiple state
variables. It is applied to analyze a piecewise deterministic game capturing the dynamic
competition between two oligopolistic firms, which are active in an established
market and invest in R&D. Both R&D investment and an evolving public knowledge
stock positively influence a breakthrough probability, where the breakthrough generates
the option to introduce an innovative product on the market. Additionally, firms
engage in activities influencing the appeal of the established and new product to consumers.
Markov-perfect equilibrium profiles are numerically determined for different
parameter settings and it is shown that for certain constellations the new product
is introduced with probability one if the initial strength of the established market is
below a threshold, which depends on the initial level of public knowledge. In case the
initial strength of the established market is above this threshold, the R&D effort of
both firms quickly goes to zero and with a high probability the new product is never
introduced. Furthermore, it is shown that after the introduction of the new product
the innovator engages in activities weakening the established market, although it is
still producing positive quantities of that product.
DA  - 2016
DO  - 10.4119/unibi/2915594
KW  - Markov-Perfect Equilibrium
KW  - Skiba Curve
KW  - Collocation
KW  - R&D Competition
KW  - Product Innovation
LA  - eng
PY  - 2016
SN  - 2196-2723
SP  - 21-
TI  - Numerical Analysis of Markov-Perfect Equilibria with Multiple Stable Steady States: A Duopoly Application with Innovative Firms
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29155943
Y2  - 2024-11-22T01:34:11
ER  -