Global Innovation Contests
2. The Model
2.2. The Knowledge-Creation Process
2.3. Production Technology
2.5. Innovation Contests
2.6. National Labor Markets
3. The Growth Effects of Globalization
3.1. Trade Openness
3.2. Multinational Firms
4. Concluding Remarks
Data Availability Statement
Conflicts of Interest
Derivation of Equation (23)
Patterns of Production in the Integrated-World Equilibrium
The term Schumpeterian growth refers to a particular type of R&D-based (exogenous or endogenous) long-run growth generated through the introduction of new products or processes according to Schumpeter’s  description of the process of creative destruction.
For example, in their survey of more that 30 such studies, Lewer and Van den Berg  report that about 9 percent of cross-sectional and more than 15 percent of time-series growth regressions find a negative or non-significant correlation between trade and growth. In his more recent survey of studies of trade reforms in the late 1980s and early 1990s, Irwin  affirms the heterogeneity of the effects of these reforms on economic growth across developing countries. However, he also concludes that this effect is positive.
Amiti et al.  and Fajgelbaum et al.  describe the evolution of the 2018-19 trade war and analyze its economic effects. Marioti  offers an overview of the global economic consequences of the Russian-Ukrainian war. See also Stiglitz  and Bhagwati  who provide influential overviews of, as well as valuable reflections on, the pros and cons of globalization. Morgan et al.  discuss, among other things, geopolitical types of stress on globalization through policymakers’ widespread reliance on economic sanctions as tools of foreign policy.
A famous case of contested innovation (in which incumbent firms managed to suppress the introduction of a higher-quality product) is Tucker 48. This was an automobile invented by Preston Tucker in 1948 that had better safety and speed features than existing models. In 1949, after producing 50 cars, the company was forced to declare bankruptcy due to negative publicity initiated by the news media, a Securities and Exchange Commission investigation, and a heavily publicized stock fraud trial with unproven allegations. Tucker claimed that the Big Three automakers and Michigan Senator Homer S. Ferguson played instrumental roles in the Tucker Corporation’s bankruptcy.
In contrast, Dinopoulos and Syropoulos  assume that the production of RPAs uses only high-skilled labor, whereas the production of R&D services and manufacturing of final products uses only low-skilled labor.
Salient contributions to the general literature on contests include: Skaperdas  who axiomatized contest success functions; Clark and Riis  who examined rent-seeking contests with multiple winners and showed that rent is fully dissipated as the number of players grows large; Gradstein and Konrad  who focused on contests with multiple rounds when random factors are important; and, Baye and Hoppe  who analyzed the conditions under which rent-seeking contests are strategically equivalent to innovation tournaments. Influential works on elimination contests include: Rosen  who demonstrated that an elimination contest requires an extra prize for the overall winner to maintain performance incentives throughout the game; Brown and Minor  who argued that elimination tournaments often are designed to identify high-ability candidates in environments where innate talent cannot be readily observed; Stracke et al.  who investigated the incentives provided by single prizes versus multiple prizes; Cohen et al.  who examined the incentives provided by head starts awarded to the winners of early rounds; and Fu and Wu  who explored the optimal disclosure scheme in elimination contests to show that transparency yields a higher expected winner’s total effort while opacity leads to greater total effort.
The dynamic structure of our model also differentiates it significantly from the contributions of Dinopoulos and Syropoulos  who model the international diffusion of expertise as an outcome of appropriative imitation and costly self protection, and from Camacho et al.  who investigate how insecurity in the outlays of knowledge conditions the incentives of technology leaders to share their knowhow and of laggards to accept it.
This insight is rooted in the celebrated Stopler-Samuelson  theorem which provides a formal link between commodity prices as real rewards (wages) to factor owners (workers).
The integrated equilibrium is defined as the steady-state equilibrium that would emerge if, in addition to free trade in goods, all factors of production were perfectly mobile internationally. In other words, the integrated-world equilibrium treats the global economy as a closed economy in which, as standardly assumed, all goods and resources are intersectorally mobile.
The FPE set is defined as the set of possible allocations of factor endowments between the two countries that ensure factor prices (wages) do not differ internationally, goods are produced under the skill intensities that emerge in the integrated-world equilibrium, and every factor of production is fully employed in each country.
Importantly, using the terminology of Parente and Prescott , one could think of rent-protection activities as a barrier to innovation and growth that serves the purpose of removing the scale-effects property while preserving the endogenous nature of long-run Schumpeterian growth.
In general, parameter may differ across countries and may depend on the resources devoted to enforcing the protection of intellectual property. Ginarte and Park  provide more information and evidence on cross-country differences in the strength of patent protection for a sample of 110 countries. However, to keep the analysis simple and direct, in this paper we assume that this parameter is identical across countries.
See Varian  for more details on the properties of unit-cost functions.
A proper modeling of skill formation requires an endogenous division of population between high-skilled and low-skilled labor that results in a higher wage rate for high-skilled workers as compared to the wage rate for low-skilled workers, as shown in Dinopoulos and Segerstrom . To maintain our focus on the interaction between skill abundance and skill intensities, we abstract from issues associated with endogenous skill formation.
We assume that, if two products command the same quality-adjusted price, consumers buy the higher quality product, although they are formally indifferent between the two products.
The Economist (10-22-2005) reported that IBM, a top patent holder, pledged 500 out of its 3,248 software patents at the time to the open-source community and placed them in a patent “commons”. In addition, Friedman  documents the fascinating case of “Apache”, a web server that was developed by an open-source self-organized scientific community in the absence of any patent protection.
For example, constant per-capita consumption expenditure () implies that , as indicated by (11). Moreover, the per-capita levels of RPAs , of R&D services , and of manufacturing output are also constant over time and identical across industries. Equation (15) implies that the long-run price of final consumption good p is also time invariant. Equation (3) implies that the per-capita level of RPAs satisfies , which is also constant over time and equal across industries. As a result, Equation (15) implies that per-capita value of innovation is also time invariant and thus the long-run value of grows at the constant rate of population growth ; that is, .
See Grossman and Helpman () for further details.
For instance, in quality-ladders growth models where innovation either improves the quality of intermediate inputs or results in total factor productivity improvements, captures the level of final per-capita output. See Grossman and Helpman  for additional details.
Inequality can be expressed in terms of skill intensities for . The definition of implies and yields . Thus,
O’Rourke and Williamson  document the factor-price reversal in Great Britain, which occurred in period 1840-1936. During that period the country went from a relatively closed-economy status to an open-economy status following the liberalization of the grain trade and the acceleration of technological progress stemming from the industrial revolution. Globalization and technological progress were equally important in generating this long-run change in factor prices.
Because there is a continuum of structurally identical industries of measure one, the output of each activity aggregated over all industries equals its indusry-level output. For example, the aggregate per-capita output of RPAs is equal to
One can easily check how the results of the analysis would change if one modified the ranking of skill intensities displayed in Assumption 1.
This assumption is supported by the empirical studies of Katz and Murphy , Huang and Whalley , Ciccone and Peri , and Autor et al. , which conclude that the value of the elasticity of substitution between low-skilled and high-skilled labor is significantly higher than unity (about 1.50).
If the skill intensity of RPAs is lower than that of R&D, then a sufficient condition for a downward-sloping relative demand for high-skilled labor is that the elasticity of factor substitution in manufacturing of final goods must be sufficiently greater than one and that the elasticities of factor substitution in the other two activities must be equal or greater than unity.
Ventura  has used the concept of an integrated-world equilibrium to analyze the effects of trade on growth in the context of the Ramsey (as opposed to an R&D-based) growth model. While feasibility and complexity considerations confine our analysis to a comparison of steady-steady equilibria, Ventura also analyzes the transitional dynamics associated with a move from autarky to free trade.
The distribution of per-capita factor endowments between Home and Foreign in the integrated-world equilibrium is illustrated by point in Figure A1 of Appendix B.
However, if the skill intensity of R&D exceeds the skill intensity of PRAs, then globalization causes Home’s long-run growth to fall and Foreign’s long-run growth to rise. Of course, one could readily introduce factor intensity reversals and obtain the same changes in the growth rate of both countries as they move from autarky to the integrated-world equilibrium.
For instance, Lewer and Van den Berg , who have surveyed an extensive set of empirical studies that include more than 190 cross-section and more than 400 time series regressions, report that about 9 percent of the cross sectional regressions and 18 percent of the time series regressions find a non-positive correlation between trade and GNP growth. In addition, Warciarg and Welch (Appendix 4) list 13 countries that have experienced negative or zero post-liberalization growth changes. Ben-David  documents the effect of economic integration on per-capita income for the original European Union (EU) members during the formation of the EU. Finally, Irwin  argues that the extensive trade reforms of the late 1980s and early 1990s increased average economic growth by about 1.0–1.5 percentage points but the growth effect was heterogeneous across developing countries.
The reasons for this property can be attributed to the assumptions that (i) all industries are symmetric, and (ii) the various activities within each industry are connected to each other dynamically. One could add another degree of freedom by assuming the existence of an outside-good produced under perfect competition, as in Dinopoulos et al.  and Grossman and Helpman , or by introducing differences in skill intensities in the production of final goods. This extension of the model is straightforward.
Furthermore, if the skill intensity of R&D is higher than the corresponding intensity of RPAs the model generates outsourcing of RPAs (as opposed to R&D services) for endowment-distribution points located in the interior of triangle OAB.
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Dinopoulos, E.; Syropoulos, C.; Tsoulouhas, T. Global Innovation Contests. Games 2023, 14, 18. https://doi.org/10.3390/g14010018
Dinopoulos E, Syropoulos C, Tsoulouhas T. Global Innovation Contests. Games. 2023; 14(1):18. https://doi.org/10.3390/g14010018Chicago/Turabian Style
Dinopoulos, Elias, Constantinos Syropoulos, and Theofanis Tsoulouhas. 2023. "Global Innovation Contests" Games 14, no. 1: 18. https://doi.org/10.3390/g14010018