A COMPETITION GAME WITH KNOWLEDGE ACCUMULATION AND SPILLOVERS

Gian Italo Bischi and Fabio Lamantia ()
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Fabio Lamantia: Dipartimento O.A.A.P., Facoltà di Economia, Università della Calabria, Via Pietro Bucci 3B-3C, I 87036, Arcavacata di Rende (CS), Italy

International Game Theory Review (IGTR), 2004, vol. 06, issue 03, 323-341

Abstract: In this paper a repeated game is proposed to model competition among firms, with profit maximizing resource allocation. The proposed model differs from the usual competition models because efforts that players exert are not seen as sunk costs, but they accumulate to form a stock of knowledge that has a cost-reducing effect. In modelling knowledge accumulation, we also consider the (knowledge) spillovers, that is, involuntary leakage of useful technological information. The game withnboundedly rational agents is modelled by a2n-dimensional discrete dynamical system, whose state variables are theR&Defforts and the stock of accumulated knowledge of each firm involved in the competition. The model is characterized by some counteracting forces: Efforts are costly but can increase future profits; immediate expenditures of each firm can have cost-reducing effects in the long run, since accumulated knowledge can decrease both own costs and competitors' ones, because of spillover effects. In the case of two homogeneous firms we prove the existence of a unique equilibrium and its stability. Starting from these analytic results, numerical simulations are performed in order to study the effects induced by heterogeneities between the players on stability and transient dynamics, as well as the influence of the main parameters on the basins of attraction.

Keywords: Competition games; R&D; spillovers; dynamical systems; stability; oscillations; Subject Classification: 91A; Subject Classification: 91B; Subject Classification: 70K; Subject Classification: 70K20 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0219198904000241

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