Rabah Amir

University of Iowa, Iowa City, Iowa, United States

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Publications (91)38.94 Total impact

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    ABSTRACT: This paper investigates the choice of a licensing mechanism by the holder of a patent whose validity is uncertain. Focusing first on weak patents, i.e. patents that have a high probability of being invalidated by a court if challenged, we show that the patent holder finds it optimal to use a per-unit royalty contract if the strategic effect of an increase in a potential licensee's unit cost on the equilibrium industry profit is positive. The latter condition ensures the superiority of the per-unit royalty mechanism independently of whether the patent holder is an industry insider or outsider, and is shown to hold in a Cournot (resp. Bertrand) oligopoly with homogeneous (resp. di¤erentiated) products under general assumptions on the demands faced by …rms. We then examine the optimal licensing of patents that are uncertain but not necessarily weak. As a byproduct of our analysis, we contribute to the oligopoly literature by o¤ering some new insights of independent interest regarding the effects of cost variations on Cournot and Bertrand equilibria..
  • Michael Troege, Rabah Amir, Jim Y. Jin
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    ABSTRACT: The paper demonstrates that in a simple asymmetric n-country world with Cournot competition, constant returns and linear demand, free trade with integrated markets can reduce world welfare as well as total output and consumer surplus, without excluding countries or driving firms out of the market. We derive precise conditions for how trade affects these parameters and demonstrate that the effects of trade are linked. In particular we show that if free trade hurts a country’s consumers it will always benefit its firms, which implies that the country is exporting, which implies an increase in the country’s output, which implies that the country’s welfare increases. Finally we re-establish the optimality of trade under either symmetric costs or under free entry and exits.
    SSRN Electronic Journal 01/2013;
  • Rabah Amir, Jim Y. Jin, Michael Troege
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    ABSTRACT: This note corrects some oversights in Dong and Yuan (2010). We show, in particular, that their condition for intra-industry trade to reduce global welfare can never be satisfied. Using a new example, we demonstrate that, nevertheless, their fundamental insight remains correct: Under Cournot competition, trade can reduce global welfare when firms and countries are asymmetric.
    10/2012;
  • Rabah Amir, Isabel Grilo, Jim Jin
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    ABSTRACT: This paper provides general conditions on the direct demand functions in a Bertrand duopoly with differentiated substitute products and constant marginal costs, that allow an unambiguous ranking of firms' equilibrium payoffs between sequential play (with both order of moves) on the one hand, and simultaneous play on the other. The main results are that (i) when prices are strategic complements, both firms prefer sequential moves (with either order) to simultaneous moves, (ii) when prices are strategic substitutes, both firms prefer simultaneous moves to moving second in sequential play, and (iii) in the mixed strategic substitute/complement case, one firm is as in (i) and the other as in (ii). Thus, sequential moves would plausibly endogenously emerge in cases (i) and (iii), with one specified leader in the latter case. The analysis relies crucially on the theory of supermodular games, and is conducted at a high level of generality, dispensing with concavity-type assumptions, and taking into account both the issues of existence and possible non-uniqueness of the different equilibria involved.
    International Game Theory Review 11/2011; 01(03n04).
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    ABSTRACT: This paper investigates sequential manufacturer–retailer price determination and channel performance under possible misrepresentation by one member of its privately known cost. To the standard double marginalization game, we add a preliminary stage where the manufacturer (alternately the retailer) announces its privately known constant marginal cost. We prove that the manufacturer has no incentive to misrepresent its cost, and we give respective sufficient conditions on the demand function for the retailer to overreport and to underreport costs. Depending on the shape of the demand function, opportunistic behavior by the retailer may lower or raise the manufacturer’s profit and channel performance.
    International Journal of Economic Theory 05/2011; 7(2):157 - 178. · 0.38 Impact Factor
  • Rabah Amir
    Manchester School 01/2011; 79(1):1-5. · 0.26 Impact Factor
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    Rabah Amir, Michael Troege
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    ABSTRACT: Recent deregulation of the banking sector in the US and in Europe allows commercial banks to hold equity in non-financial firms. We develop a model to investigate the effects of bank equity stakes in firms on credit market competition. The main result is that an equity stake confers a competitive advantage to the holding bank, which in equilibrium results in decreased competition in credit markets and higher interest rates being charged to firms. However, regulatory limits on the size of a bank’s stake may, under certain conditions, be counterproductive: they could actually strengthen the equity-owning bank’s competitive advantage. Our findings shed new light on the role of equity in lending relationships, and highlight that, in addition to the well-known prudential aspects, there is an antitrust dimension in the separation of banking and commerce. KeywordsBanking and commerce–Regulation and antitrust–Glass–Steagall act–Gramm–Leach–Bliley act–Auctions
    Annals of Finance 01/2011; 7(1):31-52.
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    ABSTRACT: We consider the standard two-stage game of R&D and Cournot competition with ex ante identical firms but depart from the literature in assuming that R&D is characterized by mildly, instead of strongly, decreasing returns to scale. We establish that only extreme R&D levels are possible at equilibrium, and that for a broad range of parameters, equilibria are asymmetric in R&D levels, possibly leading one firm to endogenously exit. This provides a simple link between returns to scale in R&D and industry polarization, including shake-outs. A novelty is that exit may be triggered by positive opportunities in a strategic setting. Given the original nature of our R&D equilibrium, a complete welfare analysis is conducted, including a possible role for R&D subsidies.
    International Journal of Industrial Organization 01/2011; 29(4):386-398. · 0.84 Impact Factor
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    ABSTRACT: Duopoly firms engaged in a standard two-stage game of R&D and Cournot competition are caught in a prisoner's dilemma for their R&D decisions whenever spillover effects are low. This effect works to the advantage of consumers and society. This result provides an interesting perspective on the well-known wedge between private and social incentives for R&D. The prisoner's dilemma is the key effect behind this wedge under low spillovers. The latter take over when sufficiently high, as is widely recognized. This mutually exclusive nature of the prisoner's dilemma and significant spillovers also serves to explain the incentives to form R&D cartels.
    Manchester School 12/2010; 79(1):81 - 99. · 0.26 Impact Factor
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    Rabah Amir
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    ABSTRACT: This paper considers a general class of discounted Markov stochastic games characterized by multidimensional state and action spaces with an order structure, and one-period rewards and state transitions satisfying some complementarity and monotonicity conditions. Existence of pure-strategy Markov (Markov-stationary) equilibria for the …nite (in…nite) horizon game, with nondecreasing –and possibly discontinuous –strategies and value functions, is proved. The analysis is based on lattice programming, and not on concavity assumptions. Selected economic applications that …t the underlying framework are described: dynamic search with learning, long-run competition with learning-by-doing, and resource extraction.
    10/2010;
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    ABSTRACT: The paper examines a game-theoretic model of a financial market in which asset prices are determined endogenously in terms of a short-run equilibrium. Investors use general, adaptive strategies (portfolio rules) depending on the exogenous states of the world and the observed history of the game. The main goal is to identify portfolio rules, allowing an investor to "survive," i.e. to possess a positive, bounded away from zero, share of market wealth over an infinite time horizon. The model under consideration combines a strategic framework characteristic for stochastic dynamic games with an evolutionary solution concept (survival strategies), thereby linking two fundamental paradigms of game theory.
    Annals of Finance 08/2010;
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    ABSTRACT: The paper examines a game-theoretic evolutionary model of an asset market with endogenous equilibrium asset prices. Assets pay dividends that are partially consumed and partially reinvested. The investors use general, adaptive strategies (portfolio rules), distributing their wealth between assets, depending on the exogenous states of the world and the observed history of the game. The main goal is to identify strategies, allowing an investor to "survive," i.e. to possess a positive, bounded away from zero, share of market wealth over the whole infinite time horizon. This work brings together recent studies on evolutionary finance with the classical topic of non-cooperative market games.
    Mathematics and Financial Economics 01/2010;
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    ABSTRACT: This paper is an attempt to develop a unified approach to symmetry-breaking in strategic models arising in industrial organization by constructing two general classes of two-player symmetric games that always possess only asymmetric pure-strategy Nash equilibria. These classes of games are characterized in some abstract sense by two general properties: payoff nonconcavities and some form of strategic substitutability. Our framework relies on easily verified assumptions on the primitives of the game, and relies on the theory of supermodular games. The underlying natural assumptions are satisfied in a number of two-stage models with an investment decision preceding product market competition. To illustrate the generality and wide scope for application of our approach, we present some existing models dealing with R&D, capacity expansion and information provision, which motivated this study.
    Journal of Economic Theory 01/2010; · 1.24 Impact Factor
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    ABSTRACT: The paper investigates prices and the deadweight loss in multi-product monopoly (MPM) with linear demand and constant marginal costs. We examine MPM with three commonly used demand structures: standard heterogeneous products, vertically (quality) and horizontally (spatially) differentiated products. Contrary to existing results we find that in all three cases a product's price depends only on specific characteristics of that product, independent of product interactions, the characteristics of other goods and even the number of other goods. We also show that in all three models the deadweight loss due to monopoly pricing is equal to half the total monopoly profit.
    06/2009;
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    ABSTRACT: The paper examines a game-theoretic model of a financial market in which asset prices are determined endogenously in terms of short-run equilibrium. Investors use general, adaptive strategies depending on the exogenous states of the world and the observed history of the game. The main goal is to identify strategies, allowing an investor to "survive," i.e. to possess a positive, bounded away from zero, share of market wealth over the in?nite time horizon. This work links recent studies on evolutionary ?nance to the classical topic of games of survival pioneered by Milnor and Shapley in the 1950s.
    Swiss Finance Institute, Swiss Finance Institute Research Paper Series. 02/2009;
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    ABSTRACT: L'int�r�t de l'approche par les jeux globaux ("global games'') est pr�cis�ment d'ancrer les anticipations sur des variables exog�nes r�elles. On peut ainsi garder l'aspect auto-r�alisateur des anticipations mais en restaurant l'unicit� de l'�quilibre et donc un meilleur pouvoir pr�dictif du mod�le. Nous illustrons ces m�canismes sur deux exemples. Le premier a trait au choix r�sidentiel d'agents qui ont une pr�f�rence "identitaire''. Le second a trait � la contagion de paniques bancaires d'un pays � un autre. De mani�re plus g�n�rale, tous les jeux qui pr�sentent des compl�mentarit�s strat�giques sont susceptibles d'�tre analys�s au moyen des techniques des "global games''. Il convient toutefois de rappeler que les techniques utilis�es demeurent assez sp�cifiques: l'incertitude strat�gique porte essentiellement sur les croyances de premier degr� des autres acteurs. Or, si de mani�re plus g�n�rale on suppose que cette incertitude peut porter sur des ordres plus �lev�s, les conclusions des mod�les peuvent changer. Ainsi, Weinstein et Yildiz (2004) montrent que dans un oligopole de Cournot, il y a une tr�s grande multiplicit� d'�quilibres si on suppose que l'incertitude porte sur les croyances de niveaux suffisamment �lev�s.
    Games and Economic Behavior 01/2009; 65(1):1-6. · 0.83 Impact Factor
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    Rabah Amir, Francis Bloch
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    ABSTRACT: This paper investigates the effects of entry in two-sided markets where buyers and sellers act strategically. Applying new tools from supermodular optimization/games, sufficient conditions for different comparative statics results are obtained. While normality of one good is sufficient for the equilibrium price to be increasing in the number of buyers, normality of both goods is required for equilibrium bids and sellers' equilibrium utilities to be increasing in the number of buyers. When the economy is replicated, normality of both goods and gross substitutes guarantee that the equilibrium of the strategic market game converges monotonically (in quantities) to the competitive equilibrium. Simple counter-examples are provided to settle other potential conjectures of interest.
    Games and Economic Behavior 01/2009; · 0.83 Impact Factor
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    Rabah Amir, Natalia Lazzati
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    ABSTRACT: This paper provides a thorough analysis of oligopolistic markets with positive demand-side network externalities and perfect compatibility. The minimal structure imposed on the model primitives is such that industry output increases in a firm's rivals' total output as well as in the expected network size. This leads to a generalized equilibrium existence treatment that includes guarantees for a nontrivial equilibrium, and some insight into possible multiplicity of equilibria. We formalize the concept of industry viability and show that it is always enhanced by having more firms in the market. We also characterize the effects of market structure on industry performance, with an emphasis on departures from standard markets. As per-firm profits need not be monotonic in the number of competitors, we revisit the concept of free entry equilibrium for network industries. The approach relies on lattice-theoretic methods, which allow for a unified treatment of various general results in the literature on network goods. Several illustrative examples with closed-form solutions are also provided.
    Journal of Economic Theory 01/2009; · 1.24 Impact Factor
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    Rabah Amir, Igor V. Evstigneev, Le XU
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    ABSTRACT: The paper examines a game-theoretic evolutionary model of a financial market with endogenous equilibrium asset prices. Assets pay dividends that are partially consumed and partially reinvested. The traders use general, adaptive strategies (portfolio rules), distributing their wealth between assets, depending on the exogenous states of the world and the observed history of the game. The main goal is to identify strategies, allowing an investor to "survive," i.e. to possess a positive, bounded away from zero, share of market over the whole infinite time horizon. This work brings together recent studies on evolutionary finance with the classical topic of non-cooperative market games.
    Swiss Finance Institute, Swiss Finance Institute Research Paper Series. 12/2008;
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    ABSTRACT: We consider the standard two-stage game of R&D and Cournot competition with ex ante identical …rms but depart from the literature in assuming that R&D is characterized by mildly, instead of strongly, decreasing returns to scale. We establish that only extreme R&D levels are possible at equilibrium, and that for a broad range of parameters, equilibria are asymmetric in R&D levels, possibly leading one …rm to endogenously exit. This provides a simple link between returns to scale in R&D and industry polarization, including shake-outs. A novelty is that exit may be triggered by positive opportunities in a strategic setting. Given the original nature of our R&D equilibrium, a complete welfare analysis is conducted, including a possible role for R&D subsidies. JEL codes: D43, L10, C72. Key words : R&D and industry dynamics, returns to scale in R&D, endoge-nous heterogeneity, exit. We are grateful to Nikolaos Georgantzis, Jim Jin, Stanley Reynolds and Michael Troege for helpful conversations on the topic of this paper.
    07/2008;

Publication Stats

1k Citations
38.94 Total Impact Points

Institutions

  • 2007–2013
    • University of Iowa
      • Department of Economics
      Iowa City, Iowa, United States
  • 1998–2013
    • The University of Arizona
      • Department of Economics
      Tucson, Arizona, United States
  • 2010
    • Warsaw School of Economics
      Warszawa, Masovian Voivodeship, Poland
  • 2009
    • ESCP Europe
      Londinium, England, United Kingdom
  • 2004
    • McGill University
      • Department of Economics
      Montréal, Quebec, Canada
    • University of Zurich
      • Department of Banking and Finance - IBF
      Zürich, ZH, Switzerland
  • 2003
    • Catholic University of Louvain
      Walloon Region, Belgium
  • 2001–2003
    • The University of Manchester
      Manchester, England, United Kingdom
  • 1999–2003
    • University of Southern Denmark
      Odense, South Denmark, Denmark
  • 2000
    • IT University of Copenhagen
      København, Capital Region, Denmark
  • 1998–2000
    • Odense University Hospital
      Odense, South Denmark, Denmark
  • 1996
    • Universität Mannheim
      • Department of Economics
      Mannheim, Baden-Wuerttemberg, Germany