Stability and trembles in extensive-form games

A leading solution concept in the evolutionary study of extensive-form games is Selten (1983) notion of limit ESS. This note demonstrates that a limit ESS does not imply neutral stability, and that it may be dynamically unstable (almost any small perturbation takes the population away). These problems arise due to an implicit assumption that “mutants” are arbitrarily rare relative to “trembling” incumbents. Finally, I present a novel definition that solves this issue and has appealing properties.     

WHOLESALE PRICES AND COURNOT‐BERTRAND COMPETITION

This note considers the competing vertical structures framework with Cournot‐Bertrand competition downstream. It shows that the equilibrium wholesale price paid by a Cournot (Bertrand)‐type retailer is above (below) marginal costs of a corresponding manufacturer. This result contrasts with the one under pure competition downstream (i.e., Cournot or Bertrand), where the wholesale price is set below (above) marginal costs in case of a Cournot (Bertrand) game at the retail level.     

On the Dynamic Foundation of Evolutionary Stability in Continuous Models

We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept, evolutionary robustness, which is stronger than the previous concepts. Evolutionary robustness ensures dynamic stability for replicator dynamics in doubly symmetric games. Journal of Economic Literature Classification Numbers: C70, 72.     

Evolutionarily stable conjectures and other regarding preferences in duopoly games

We study the evolutionary selection of conjectures in duopoly games when players have other regarding preferences, i.e. preferences over payoff distributions. In both the Cournot and Bertrand duopoly games, the consistent conjectures are independent of other regarding preferences. Both duopoly games have evolutionarily stable conjectures that depend on other regarding preferences but that do not coincide with the consistent conjectures. For increasingly spiteful preferences, the evolutionarily stable conjectures implicate low quantities in the Cournot game and high prices in the Bertrand game, whereas the inverse relationships hold for the consistent conjectures. We discuss our findings in the context of ultimate and proximate causation.     

VERs and Price Undertakings under the WTO*

Under the rules of the WTO, governments are prohibited from negotiating voluntary export restraints (VERs) but may negotiate price undertakings (i.e. import price minima). While these two policies can have identical effects in models of perfect competition, they can have very different economic consequences with imperfect competition. The model presented here shows that in a model of international Bertrand duopoly, a VER can result in lower domestic prices and profits than a price minimum regime. This suggests that price undertakings should also be prohibited under the WTO.     

The value of information in oligopoly with demand uncertainty

This paper discusses the value of information in supermodular and submodular games, using a simple duopoly model where the level of demand is uncertain. It is shown that the value of information issuperadditive (resp.,subadditive) between players if the game issupermodular (resp.,submodular). For example, in a Bertrand (resp., Cournot) market with (possibly imperfect) substitute products, one firm's information acquisition increases (resp., decreases) the other firm's incentive to acquire the same information. Furthermore, when the game is either supermodular or submodular, the value of information is higher when the player isexpected to be informed according to the opponent's belief than when the player is expected to be uninformed; this result is reversed when the game has asymmetric modularity (i.e., one player's action is substitutional to the other's, and the latter's action is complemental to the former's). These qualitative observations have a potential to be applied to a larger class of games with uncertainty where payoffs are smooth (e.g., twice continuously differentiable) in actions and states.     

Quality Uncertainty as Resolution of the Bertrand Paradox

It is well‐known that product differentiation eliminates the Bertrand paradox (i.e. marginal cost pricing under duopoly). While differentiation is often justified with reference to the consumer's ‘preference for variety’, the conditions under which such a preference is likely to arise are rarely considered. We investigate this question in a setting in which uncertainty about product quality can endogenously generate either convex or non‐convex preferences. We show that even when two goods are ex ante homogeneous, quality uncertainty can eliminate the Bertrand paradox.     

Biased managers with network externalities

In network industry under Cournot and Bertrand competition, we examine a model when owners of firms hire biased managers who have incorrect market demand. Contrast to previous studies, we show that (i) regardless of the strength of network externalities when consumers form the responsive and passive expectations, owners realize strategic advantage by hiring biased managers to be more aggressive under Cournot and Bertrand competition, (ii) firms prefer facing passive expectations for the weak network externalities and vice versa for the strong network exteranlities under Bertrand and Cournot competition, (iii) if the network size is sufficiently large, then the prisoner's dilemma that firms hire aggressive managers no longer exists under both competition modes. As with no delegation case, we obtain the different rankings of firms' profit depending on both network externalities and forming of expectations under Cournot and Bertrand competition.     

The power of ESS: An experimental study

Abstract. Our experimental design mimics a traditional evolutionary game framework where players are matched pairwise to play a symmetric 33 bimatrix game that has two Nash equilibria. One equilibrium is an evolutionary stable state, or ESS; the other is an equilibrium in dominated strategies. Our primary experimental result is the observation that the ESS becomes extremely attractive when subjects have minimal information about the payoff functions, although the dominated equilibrium assures the highest equilibrium payoff. The attractiveness of the ESS is only moderate when players are completely informed about the 33 payoff matrix. Correspondence to: S.K. Berninghaus     

Using co-evolutionary programming to simulate strategic behaviour in markets

This paper describes the use of a genetic algorithm (GA) to model several standard industrial organisation games: Bertrand and Cournot competition, a vertical chain of monopolies, and a simple model of an electricity pool. The intention is to demonstrate that the GA performs well as a modelling tool in these standard settings, and that evolutionary programming therefore has a potential role in applied work requiring detailed market simulation. The advantages of using a GA over scenario analysis for applied market simulation are outlined. Also explored are the way in which the equilibria discovered by the GA can be interpreted, and what the market analogue for the GA process might be.     

Reciprocal Dumping with Product Differentiation*

This paper examines if international trade can reduce total welfare in an international oligopoly with differentiated goods. We show that intra‐industry trade, i.e. “reciprocal dumping,” can result in lower total surplus than autarky in a Cournot model for any degree of product differentiation. Moreover, trade can reduce welfare compared to autarky in a Bertrand model when the local markets are sufficiently competitive and products are sufficiently close substitutes. Otherwise it unambiguously increases welfare.     

Long run equilibria in an asymmetric oligopoly

Summary. Consider an oligopolistic industry composed of two groups (or populations) of firms, the low cost firms and the high cost firms. The firms produce a homogeneous good. I study the finite population evolutionarily stable strategy defined by Schaffer (1988), and the long run equilibrium in the stochastic evolutionary dynamics based on imitation and experimentation of strategies by firms in each group. I will show the following results. 1) The finite population evolutionarily stable strategy (ESS) output is equal to the competitive (or Walrasian) output in each group of the firms. 2) Under the assumption that the marginal cost is increasing, the ESS state is the long run equilibrium in the stochastic evolutionary dynamics in the limit as the output grid step, which will be defined in the paper, approaches to zero. Received: September 19, 1997; revised: June 18, 1998     

Profits and competition under alternative technologies in a unionized duopoly with product differentiation

This paper aims at investigating if the conventional wisdom (i.e. an increase of competition linked to a decrease in the degree of product differentiation always reduces firms׳ profits) can be reversed in a unionized duopoly model. We show that a decrease in the degree of product differentiation may affect wages, hence profits, differently, depending on both the firms׳ production technology and the mode of competition in the product market. Specifically, under constant returns to labour, the “reversal result” can apply under both Cournot and Bertrand competition, but it is more likely when firms compete in quantities. By contrast, under decreasing returns, profits can increase with competition but only if firms compete in prices.     

Divisionalisation and Cournot Competition Yield Bertrand Outcomes

Bertrand and Cournot model are the main frameworks in the analysis of oligopolistic competition. The outcomes from them are however different. Using a simultaneous-move two-stage game, this article shows that, in a homogeneous product market with fairly general demand, the Bertrand outcomes can be achieved by a combination of divisionalisation and ensuing Cournot competition. This finding can be viewed as an extension to or complements of Kreps and Scheinkman (1983), who show that Cournot outcomes can be achieved by quantity precommitment and Bertrand competition.     

国际资本流动、经济扭曲与宏观稳定--当前经济增长态势分析

本文针对当前中国所面临的资本流动新格局(即大量非FDI流入) ,分析了国际资本流动引起宏观不稳定的机制,以及通过对冲与资本管制方式应对资本流动冲击的局限。论文的核心是引入经济扭曲概念,建立了带扭曲因素的资本流动与宏观稳定模型,强调扭曲的存在会使波动加剧。因此,为应对资本流动新格局,政策当局需要尽快完善非FDI监控体系、矫正各种经济扭曲,并促使宏观调控模式由数量型向价格型转变     

内生时机选择下国有和外资银行的利率竞争

结合中国银行业的背景,本文建立了国有和外资银行以利率为决策变量的 Bertrand 和 Stackelberg 混合寡占模型,并以内生时机选择为思路,前瞻性地探讨了国有和外资银行的竞争格局和时机选择问题.研究发现:(1)在一定参数范围内,国有银行较外资银行有更低的存款利率.在国有化程度较小时,Bertrand下的国有银行利润大于其作为领导者的利润;(2)在国有银行做领导者的利率竞争中,国有和外资银行存款利率会随着国有化程度及二者存款收益的增加而上升;(3)在私有化程度很高且二者存款收益相等时,利率竞争扩展博弈的SPNE是国有银行领先,外资银行跟随.     

Comparing Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D

We compare the Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D competition. If a firm’s marginal cost is lower than that of its rival, then this firm (its rival) is referred to as the more (less) efficient firm. Under each mode of competition, there are three types of equilibria: blockaded-entry, deterred-entry, and accommodated-entry. Moreover, the presence of R&D investment makes it harder for the less efficient firm to survive. Cournot competition entails a unique equilibrium, whereas Bertrand competition may yield two equilibria. It is harder for the less efficient firm to survive under Bertrand competition than under Cournot competition. Versus Cournot competition, Bertrand competition yields higher industry output, and it shifts production from the less efficient firm to the more efficient firm. This result, together with the known size effect, explains the following three findings. First, the more efficient firm has a normal output ranking, whereas the less efficient firm may demonstrate an output reversal. Second, the more efficient firm may demonstrate a R&D reversal, whereas the less efficient firm has a normal R&D ranking (its Cournot R&D effort exceeds its Bertrand R&D effort). Third, Bertrand competition is more welfare-efficient than Cournot competition.     

Destruction and settlement norms as determinants of conflict: An evolutionary perspective

This paper studies conflict in a simple bargaining framework using an evolutionary game-theoretic approach. Our findings suggest that a player does not always regard the winning probability as an acceptable settlement rule. He accepts a division according to winning probability when the destruction caused to him in conflict is more than a threshold, which in turn depends on cost of conflict to the opponent and the size of the population. Further, our analysis shows that the norms with positive weight to disagreement payoff are effective against conflict, and incentivize peace. Contrary to the findings of extant studies carried out in finite population evolutionary game setting, the settlement possibility set is identical under both ESS and Nash equilibrium in our model with settlement norms.     

Mixed Competition and Patent Licensing

This paper studies the patent licensing decision of an insider patentee when two firms engage in a mixed (Cournot–Bertrand or Bertrand–Cournot) competition where one firm adopts the quantity strategy while the other uses the price strategy and vice versa. If either the fixed fee or royalty is applied, then the licensor prefers the fixed fee when the licensor takes the quantity strategy, while the licensee uses the price strategy (Cournot–Bertrand). If the two‐part tariff is applied, then the two‐part tariff is more likely to be adopted by the licensor under Cournot–Bertrand than under Bertrand–Cournot competition.