Abstract
This study examines a three-stage game involving three firms that make sequential decisions regarding their locations, participate in quality-enhancing research and development (R&D) with spillover effects, and establish pricing strategies. In contrast to the potential for maximal differentiation observed in duopolies, adding a third firm consistently results in only moderate locational differentiation because of a diminished need to circumvent competition. Interestingly, the firm positioned in the middle incurs the highest R&D costs despite potential free-riding by competitors, driven by the strategic need to offset its competitive disadvantage. The presence of R&D spillover encourages firms to choose closer proximity, enhancing consumer surplus and social welfare by reducing prices and transportation costs, even as R&D investment and product quality may decline. The dynamics and implications of expanding the model to include a fourth firm are also explored, further enriching the understanding of competitive strategies in multi-firm markets.
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