Learning in games with strategic complementarities revisited

Fictitious play is a classical learning process for games, and games with strategic complementarities are an important class including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond games with a unique equilibrium, global convergence has only been claimed for games with diminishing returns [V. Krishna, Learning in games with strategic complementarities, HBS Working Paper 92-073, Harvard University, 1992]. This result remained unpublished, and it relies on a specific tie-breaking rule. Here we prove an extension of it by showing that the ordinal version of strategic complementarities suffices. The proof does not rely on tie-breaking rules and provides some intuition for the result

The convergence of fictitious play in games with strategic complementarities: A Comment

In a recent article, Hahn [Hahn, S. (2008). The convergence of fictitious play in games with strategic complementarities. Economics Letters 99, 2, 304-306] claims to prove convergence of fictitious play in games with strategic complementarities. I show here that the proof is flawed and convergence remains an open question.Fictitious play; Strategic complementarities; Supermodular games

Spillovers Reconsidered: Analysing Economic Welfare under complementarities in R&D

We analyse economic welfare in R&D intensive industries under varying assumptions on the spillover process. The focus lies on spillover processes with complementary R&D investments such as those modelling absorptive capacity. There spillovers give rise to both negative and positive externalities. We show that the rationale for public policy intervention is strengthened where spillovers also have positive effects. This conclusion is based on the supermodularity of the spillover process and the investment game. We characterise a large class of spillover processes with similar implications for public policy. We show that results of much empirical work on absorptive capacity extend to this class of models

Spillovers Reconsidered: Analysing Economic Welfare under Complementarities in R&D

We analyse economic welfare in R&D intensive industries under varying assumptions on the spillover process. The focus lies on spillover processes with complementary R&D investments such as those modelling absorptive capacity. There spillovers give rise to both negative and positive externalities. We show that the rationale for public policy intervention is strengthened where spillovers also have positive effects. This conclusion is based on the supermodularity of the spillover process and the investment game. We characterise a large class of spillover processes with similar implications for public policy. We show that results of much empirical work on absorptive capacity extend to this class of models.spillovers, complementarity, absorptive capacity, supermodularity, oligopolistic R&D

Spillovers Reconsidered: Analysing Economic Welfare under complementarities in R&D

We analyse economic welfare in R&D intensive industries under varying assumptions on the spillover process. The focus lies on spillover processes with complementary R&D investments such as those modelling absorptive capacity. There spillovers give rise to both negative and positive externalities. We show that the rationale for public policy intervention is strengthened where spillovers also have positive effects. This conclusion is based on the supermodularity of the spillover process and the investment game. We characterise a large class of spillover processes with similar implications for public policy. We show that results of much empirical work on absorptive capacity extend to this class of models.spillovers; complementarity; absorptive capacity; supermodularity; oligopolistic R&D

Merger failures

This paper proposes an explanation as to why some mergers fail, based on the interaction between the pre- and post-merger processes. We argue that failure may stem from informational asymmetries arising from the pre-merger period, and problems of cooperation and coordination within recently merged firms. We show that a partner may optimally agree to merge and abstain from putting forth any post-merger effort, counting on the other partner to make the necessary efforts. If both follow the same course of action, the merger goes ahead but fails. Our unique equilibrium allows us to make predictions on which mergers are more likely to fail.Mergers, Synergies, Asymmetric Information, Complementarities

Social Networks

We survey the literature on social networks by putting together the economics, sociological and physics/applied mathematics approaches, showing their similarities and differences. We expose, in particular, the two main ways of modeling network formation. While the physics/applied mathematics approach is capable of reproducing most observed networks, it does not explain why they emerge. On the contrary, the economics approach is very precise in explaining why networks emerge but does a poor job in matching real-world networks. We also analyze behaviors on networks, which take networks as given and focus on the impact of their structure on individuals’ outcomes. Using a game-theoretical framework, we then compare the results with those obtained in sociology.random graph, game theory, centrality measures, network formation, weak and strong ties

Social Networks

We survey the literature on social networks by putting together the economics, sociological and physics/applied mathematics approaches, showing their similarities and differences. We expose, in particular, the two main ways of modeling network formation. While the physics/applied mathematics approach is capable of reproducing most observed networks, it does not explain why they emerge. On the contrary, the economics approach is very precise in explaining why networks emerge but does a poor job in matching real-world networks. We also analyze behaviors on networks, which take networks as given and focus on the impact of their structure on individuals’ outcomes. Using a game-theoretical framework, we then compare the results with those obtained in sociology.Random Graph; Game Theory; Centrality Measures; Network Formation; Weak

Heterogeneity and Uniqueness in Interaction Games

Incomplete information games, local interaction games and random matching games are all special cases of a general class of interaction games (Morris (1997)). In this paper, we use this equivalence to present a unified treatment of arguments generating uniqueness in games with strategic complementarities by introducing heterogeneity in these different settings. We also report on the relation between local and global heterogeneity, on the role of strategic multipliers and on purification in the three types of interaction game.Heterogeneity, Uniqueness, Global games

Asymmetric Vertical Integration

We examine vertical backward integration in a reducedform model of successive oligopolies. Our key findings are: (i) There may be asymmetric equilibria where some firms integrate and others remain separated, even if firms are symmetric initially; (ii) Efficient firms are more likely to integrate vertically. As a result, integrated firms also tend to have a large market share. The driving force behind these findings are demand/mark-up complementarities in the product market. We also identify countervailing forces resulting from strong vertical foreclosure, upstream sales and endogenous acquisition costs.successive oligopolies, vertical integration, effciency, foreclosure