We present a continuous-time generalization of the seminal research and development model of d’Aspremont and Jacquemin (Am Econ Rev 78(5):1133–1137, 1988) to examine the trade-off between the benefits of allowing firms to cooperate in research and the corresponding increased potential for product market collusion. We show the existence of a solution to the optimal investment problem using a combination of results from viscosity theory and the theory of planar dynamical systems. In particular, we show that there is a critical level of marginal cost at which firms are indifferent between doing nothing and starting to develop the technology. We find that colluding firms develop further a wider range of initial technologies, pursue innovations more quickly, and are less likely to abandon a technology. Product market collusion could thus yield higher total surplus.
2017 / Grabisch, M., A. Mandel, A. Rusinowska and E. Tanimura
Strategic influence in social networks
Mathematics of Operations Research, Vol. 43, 29-50
We consider a model of influence with a set of nonstrategic agents and two strategic agents. The nonstrategic agents have initial opinions and are linked through a simply connected network. They update their opinions as in the DeGroot model. The two strategic agents have fixed and opposed opinions. They each form a link with a nonstrategic agent in order to influence the average opinion that emerges due to interactions in the network. This procedure defines a zero-sum game whose players are the two strategic agents and whose strategy set is the set of nonstrategic agents. We focus on the existence and the characterization of pure strategy equilibria in this setting. Simple examples show that the existence of a pure strategy equilibrium does depend on the structure of the network. We characterize equilibrium with two notions: the influenceability of target agents, and their centrality, which in our context we call “intermediacy.” We also show that when the two strategic agents have the same impact, symmetric equilibria emerge as natural solutions. In the case where the impacts are uneven, the game has only equilibria in mixed strategies, the high impact agent focuses on his own centrality/intermediacy and the influenceability of his opponent’s target while the low influence agent focuses on the influenceability of his own target.
2016 / Colombo L. and H. Dawid
Complementary Assets, Start-Ups and Incentives to Innovate
International Journal of Industrial Organization, Vol. 44, 177-190
We examine to what extent market conditions facilitating start-up formation affect firms' R&D investment and profits. We consider a model in which R&D efforts of an incumbent firm generate partly tacit technological know-how embodied in a key R&D employee, who might use it to form a start-up. The availability of complementary assets influences whether new firms are created and determine expected profits for start-up's founders. A large availability of complementary assets has the direct effect that the generation of start-ups is fostered. However, as a strategic effect, the incentives of incumbents to invest in R&D may be reduced because of the increased danger of knowledge loss occurring through start-up formation. We characterize the effects of an increase in the availability of complementary assets, showing that counter-intuitively there are cases in which it induces an increase in incumbents' R&D investment.
Two agents endowed with different categorisations engage in bargaining to reach an understanding and agree on a common categorisation. We model the process as a simple non-cooperative game and demonstrate three results. When the initial disagreement is focused, the bargaining process has a zero-sum structure. When the disagreement is widespread, the zero-sum structure disappears and the unique equilibrium requires a retraction of consensus: two agents who individually associate a region with the same category end up rebranding it under a different category. Finally, we show that this last equilibrium outcome is Pareto dominated by a cooperative solution that avoids retraction; that is, the unique equilibrium agreement may be inefficient.
2014 / Colombo, L., G. Femminis and A. Pavan
Information Acquisition and Welfare
The Review of Economic Studies, Vol. 81, 1438–1483
We study information acquisition in a flexible framework with strategic complementarity or substitutability in actions and a rich set of externalities that are responsible for possible wedges between the equilibrium and the efficient acquisition of information. First, we relate the (in)efficiency in the acquisition of information to the (in)efficiency in the use of information and explain why efficiency in the use does not guarantee efficiency in the acquisition. Next, we show how the acquisition of private information affects the social value of public information (i.e., the comparative statics of equilibrium welfare with respect to the quality of public information). Finally, we illustrate the implications of our results in a few applications that include beauty contests, monetary economies with price-setting complementarities, and economies with negative production externalities
2014 / Colombo, L. and H. Dawid
Strategic Location Choice under Dynamic Oligopolistic Competition and Spillovers
Journal of Economic Dynamics and Control, Vol. 48, 288-307
This paper investigates firms׳ optimal location choices explicitly accounting for the role of inwards and outwards knowledge spillovers in a dynamic Cournot oligopoly with firms that are heterogeneous in their ability to carry out cost-reducing R&D. Firms can either locate in an industrial cluster or in isolation. Technological spillovers are exchanged between the firms located in the cluster. It is shown that a technological leader has an incentive to locate in isolation only if her advantage exceeds a certain threshold, which is increasing in firms׳ discount rate, in industry dispersion, and in the intensity of knowledge spillovers. Scenarios are identified where although it is optimal for the technological leader to locate in isolation, from a welfare perspective it would be desirable that she locates in the cluster.
2013 / Quax R., A. Apolloni and P.M.A. Sloot
The diminishing role of hubs in dynamical processes on complex networks
Journal of the Royal Society Interface,, Vol. 10(88)
It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here, we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics when compared with intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein–protein interaction network and a neural network, suggesting that it might indeed be a widespread property in nature.
2013 / Quax, R., D. Kandhai and P. M. Sloot
Information dissipation as an early-warning signal for the Lehman Brothers collapse in financial time series
In financial markets, participants locally optimize their profit which can result in a globally unstable state leading to a catastrophic change. The largest crash in the past decades is the bankruptcy of Lehman Brothers which was followed by a trust-based crisis between banks due to high-risk trading in complex products. We introduce information dissipation length (IDL) as a leading indicator of global instability of dynamical systems based on the transmission of Shannon information and apply it to the time series of USD and EUR interest rate swaps (IRS). We find in both markets that the IDL steadily increases toward the bankruptcy, then peaks at the time of bankruptcy and decreases afterwards. Previously introduced indicators such as ‘critical slowing down’ do not provide a clear leading indicator. Our results suggest that the IDL may be used as an early-warning signal for critical transitions even in the absence of a predictive model.
2008 / Mancusi M.L.
International Spillovers and Absorptive Capacity: A Cross-Country Cross-Sector Analysis Based on Patents and Citations
This paper brings together the issues of knowledge spillovers and absorptive capacity, by assessing the role of prior R&D experience in enhancing a country's ability to understand and improve upon external knowledge. International spillovers are found effective in increasing innovative productivity in laggard countries, while technological leaders are a source rather than a destination of knowledge flows. Quantitative estimates of the effect of absorptive capacity on innovative performance, through knowledge spillovers, show that absorptive capacity increases the elasticity of a laggard country's innovation to international spillovers, while its marginal effect is negligible for countries at the technological frontier.
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