A Competition Game With Knowledge Accumulation and Spillovers

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 with n boundedly rational agents is modelled by a 2n-dimensional discrete dynamical system, whose state variables are the R&D efforts 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.

Complexity and Geographical Economics

“…Following Bischi and Lamantia (2004), a first step in this direction can be found in Bischi and Lamantia (2010), where an R&D network game with knowledge accumulation is analyzed. However, both the cost reduction effect and the capacity to exploit spillovers (i.e.…”

“…Nelson 1982;Levinthal 1989, 1990;Confessore and Mancuso 2002), but it usually can be only partially "capitalized" because knowledge tends to depreciate itself as time goes on, according to the obsolescence rate of information and technology. In Bischi and Lamantia (2010), a general framework is proposed to describe an industry, evolving in discrete time, where firms invest in R&D efforts in order to increase their overall knowledge level, otherwise subject to obsolescence (see Bischi and Lamantia 2004;Petit and Tolwinski 1999;Petit et al 2000). More precisely, time t investments in R&D by firm i , denoted by E i .t/ increases the time t total (or accumulated) knowledge of firm i , which is given by…”

“…A similar formulation of knowledge accumulation was also employed in Bischi and Lamantia (2004), where an increment of total knowledge has a cost-reducing effect, as a firm i has a marginal cost function at time t of the form…”

Measurement on the Complexity Entropy of Dynamic Game Models for Innovative Enterprises under Two Kinds of Government Subsidies

“…Firstly, two firms determine their prices by maximizing their profits in the second stage. Then, in the first stage we assume that both players are bounded rational [23], when the enterprises are making decisions at period t, because of the limitation of obtaining information, neither party of the competitors can learn about the exact innovation output decisions that its rival makes, so the decisions they make are based on the incomplete information, and the decisions are not made by maximizing the profits but by maximizing the marginal profit effect instead.…”

Best response dynamics with level-n expectations in two-stage games

“…Best response dynamics under non-rational expectations has been hardly analyzed in the context of R&D choice in oligopolies. A rare exception is Bischi and Lamantia (2004) where a dynamic model of R&D choices is studied under the assumption of naive expectations. However, in their setting competition on the market is represented in reduced form, such that the game repeatedly played by the firms has one-stage structure.…”