Repeated price competition between individuals and between teams

We conducted an experimental study of price competition in a duopolistic market. The market was operationalized as a repeated game between two “teams” with one, two, or three players in each team. We found that asking (and winning) prices were significantly higher in competition between individuals than in competition between two- or three-person teams. There were no general effects of team size, but prices increased with time when each team member was paid his or her own asking price and decreased when the team's profits were divided equally. This result is consistent with a simple model of individual learning.     

The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labor union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function.     

Tax Competition in Vertically Differentiated Markets with Environmentally Conscious Consumers

This paper analyses the effects of tax competition on environmental product quality, pollution and welfare in a two-country, vertically differentiated, international duopoly, in which consumers are environmentally conscious. The firm in each country chooses first the environmental quality of its product (which reflects the emissions generated in the production process) and then the price. In equilibrium one country will be more polluted than the other because firms choose different levels of environmental quality of their products. We find that a country’s optimal commodity tax is higher if the domestic firm is the more polluting supplier. Furthermore, non-cooperative commodity tax rates are inefficiently high in equilibrium. This is because, in this framework with environmentally aware consumers, commodity taxes affect the choice of firms regarding their emissions. Therefore, a domestic tax reduction not only raises the profits of the foreign firm but also lowers its emission levels, resulting in higher welfare for the other country. We also analyse the optimal cooperative and non-cooperative commodity and emission taxes with border tax adjustments. With these two policy instruments available, commodity taxes are higher.     

A generalized framework for endogenous timing in duopoly games and an application to price-quantity competition

This paper extends the analysis of duopoly market by distinguishing two types of competition: (i) the basic form of competition where each firm is unrestricted in its choice of price and quantity and (ii) the non-basic form of competition where firms’ strategic choices over price and quantity are limited a priori. Our analysis focuses on the former rather than the latter. Under a very general setting of concave industrial revenue and asymmetric convex costs, we show that each firm typically makes more profit in the subgame perfect Nash equilibrium (SPNE) of the leader-follower price-quantity competition, one of the basic competition forms, than in the SPNE of the leader-follower price competition and that each firm always makes more profit under simultaneous move price-quantity competition than under simultaneous move price competition. We establish a generalized framework for endogenous timing in duopoly games which is capable of embodying and overcoming the inconsistency across the existing three frameworks in the field. We highlight the advantages of a 3-period general framework.     

ENDOGENOUS TIMING AND STRATEGIC CHOICE: THE COURNOT‐BERTRAND MODEL

Cournot establishes a Nash equilibrium to a duopoly game under output competition; Bertrand finds a different Nash equilibrium under price competition. Both treat the strategic choice variable (output versus price) and the timing of play as exogenous. We investigate Cournot‐Bertrand models where one firm competes in output and the other competes in price in both static and dynamic settings. We also develop a general model where both the timing of play and the strategic choice variables are endogenous. Consistent with the conduct of Honda and Scion, we show that Cournot‐Bertrand behaviour can be a Nash equilibrium outcome.     

Price Stability in Open Economies

This paper studies the theoretical conditions under which price stability is the optimal policy in a two-country open-economy model with imperfect competition and price stickiness. Special conditions on the levels of country-specific distortionary taxation and the intratemporal and intertemporal elasticities of substitution need to be satisfied. These restrictions apply to both cooperative and non-cooperative settings. Importantly, we show that cooperative and non-cooperative solutions do not coincide despite market completeness and producer currency pricing. We study the conditions under which quadratic approximations of single countries' welfare can be correctly evaluated by relying only on log-linear approximations of the equilibrium conditions.     

Codetermination,Price Competition and the Network Industry

This research develops a tractable two‐stage non‐cooperative game with complete information describing the behaviour of price‐setting firms that must choose to be profit maximisers or bargainers under codetermination in a network industry with horizontal product differentiation. The existing theoretical literature has already shown that codetermination might arise as the endogenous market outcome in a strategic competitive quantity‐setting duopoly. In sharp contrast with this result, the present article shows that codetermination does never emerge as a Nash equilibrium in a price‐setting non‐network duopoly. Then, it aims at highlighting the role of network externalities in determining changes of paradigm of the game and letting codetermination become a sub‐game perfect Nash equilibrium when prices are strategic substitutes or strategic complements. This equilibrium may be Pareto efficient. Results allow distinguishing between mandatory codetermination and voluntary codetermination. The article also proposes a model of endogenous codetermination according to which every firm may choose to bargain with its own corresponding union bargaining unit only whether the firm's bargaining strength is exactly the profit‐maximising one. The equilibrium outcomes emerging in this case range from a uniform Nash equilibrium, in which both firms are codetermined, to mixed Nash equilibria, in which only one of them chooses to be codetermined. These results are ‘network depending’ and do not hold in a non‐network duopoly.     

Domestic environmental policy and international cooperation for global commons

The paper analyzes the strategic behavior of several countries engaged in capital accumulation, pollution mitigation, and environmental adaptation in the context of an environmental common good. Both cooperative and non-cooperative strategies are discussed. The non-cooperative strategy is a dynamic game in which each country makes its own environmental decision following the open-loop Nash equilibrium. The cooperative social planner problem assumes an international environmental agreement in force. The non-cooperative and cooperative solutions are compared in the symmetric case of two countries and extended to several identical countries. It is shown that the non-cooperative strategy in multi-country world leads to over-production, over-consumption, over-pollution, and over-adaptation.     

QUANTITY PRECOMMITMENT AND BERTRAND COMPETITION YIELD COURNOT OUTCOMES: A CASE WITH PRODUCT DIFFERENTIATION*

Using a simple model of two-stage duopoly game, this paper shows that Bertrand-like price competition on a differentiated goods market, following a simultaneous endogenous choice of production capacity, yields the Cournot-like outcomes.     

Strategic Pricing when Electricity is Storable

In this paper, we develop a simplified oligopoly model where hydro generators engage in dynamic Bertrand competition. Each player uses a Markov strategy based on the state of water reservoirs at the beginning of each period. The replenishing of water reservoirs, which affects generators' productive capacity, is governed by a stochastic process. Also, a price cap, i.e. a maximum bid allowed, is imposed on the market. We develop valuable insights for regulatory policy in predominantly hydro based electricity markets, including the effects of price caps, the efficiency of dispatch under strategic behavior and the likelihood of collusion.     

不完全合作、非合作博弈的逻辑:企业与行业协会价格串谋行为分析

串谋企业涉及的利益主体主要是企业、行业协会与监管者,频频发生的行业协会参与企业价格串谋实际上是不同利益主体之间博弈的结果.他们之间的博弈是不完全合作、非合作博弈.笔者建立了串谋企业及其行业协会、监管者之间的博弈分析模型,认为影响企业及其行业协会价格串谋概率高低的主要因素是制度安排、串谋成本与监管力度等.     

Informational properties of the Nash solutions of two stochastic nonzero-sum games

Within the framework of stochastic two-person nonzero-sum games, we deal with two commonly used models in engineering and economics—namely, the LQG (Linear-Quadratic-Gaussian) and the duopoly problems. We investigate how variations in information available to either player affect the equilibrium Nash strategies for these two models, whose existence and uniqueness have been proven in the paper. We show that for the LQG model better information for either player results in lower average Nash costs for both players; whereas for the duopoly model better information for one player helps him alone to achieve a higher average Nash profit, and it hurts the other player in the sense that his average Nash profit decreases. We further relate these properties of the Nash solutions for these two games to some of the distinct features of zero-sum games and team problems.     

Strategic competition and optimal parallel import policy

Abstract In a two‐country Hotelling type duopoly model of price competition, we show that parallel import (PI) policy can act as an instrument of strategic trade policy. The home firm’s profit is higher when it cannot price discriminate internationally if and only if the foreign market is sufficiently bigger than the domestic one. The key mechanism in the model is that the home firm’s incentive to keep its domestic price close to the optimal monopoly price affects its behavior during price competition abroad. We also analyze the welfare implications of PI policies and show that our key insights extend to quantity competition.     

Strategic Product R&D Investment Policy under International Rivalry in the Presence of Demand Spillover Effects

Abstract

We develop a model of product (i.e., quality-improving) research and development (R&D) investment competition in a horizontally differentiated duopoly. In particular, based on a third-country market model, we consider the optimal product R&D investment policy under international rivalry in the presence of demand spillover effects associated with improving the quality level of a product. We show how the optimality of a non-cooperative and a cooperative R&D investment policy depends on the strength of demand spillover effects. Furthermore, we consider the same issues in the case of heterogeneous consumers and alternative utility functions.     

Endogenous timing in private and mixed duopolies with emission taxes

This paper examines an endogenous timing game in product differentiated duopolies under price competition when emission tax is imposed on environmental externality. We show that a simultaneous-move (sequential-move) outcome can be an equilibrium outcome in a private duopoly under significant (insignificant) environmental externality, but this result can be reversed in a mixed duopoly. We also show that when environmental externalities are significant, public leadership yields greater welfare than private leadership, and that public leadership is more robust than private leadership as an equilibrium outcome. Finally, we find that privatization can result in a public leader becoming a private leader, but this worsens welfare.     

Auctions as coordination devices

This paper develops an economic argument relating auctions to high market prices. At the core of the argument is the claim that market competition and bidding in an auction should be analyzed as part of one game, where the pricing strategies in the market subgame depend on the bidding strategies during the auction. I show that when there are two licenses for sale the only equilibrium in the overall game that is consistent with the logic of forward induction is the one where firms bid an amount (almost) equal to the profits of the cooperative market outcome and follow a cooperative pricing strategy in the market game resulting in high prices. With three or more licenses the auction format co-determines whether or not the forward induction argument works.     

Evolutionary stability in repeated extensive games played by finite automata

We discuss the emergence of cooperation in repeated Trust Mini-Games played by finite automata. Contrary to a previous result obtained by Piccione and Rubinstein (1993), we first prove that this repeated game admits two Nash equilibria, a cooperative and a non-cooperative one. Second, we show that the cooperative equilibrium is the only (cyclically) stable set under the so-called best response dynamics.     

Global dynamics in repeated games with additively separable payoffs

This paper studies the global dynamics of a class of infinitely repeated two-player games in which the action space of each player is an interval, and the one-shot payoff of each player is additively separable in actions. We define an immediately reactive equilibrium (IRE) as a pure-strategy subgame perfect equilibrium such that each player's action is a stationary function of the opponent's last action. We completely characterize IREs and their dynamics in terms of certain indifference curves. Our results are used to show that in a prisoners' dilemma game with mixed strategies, gradual cooperation occurs when the players are sufficiently patient, and that in a certain duopoly game, kinked demand curves emerge naturally.     

Voluntary provision of a pure public good as the game of ‘chicken’

The voluntary exchange model, where the amount of a public good and contributions to its cost are simultaneously determined, is treated as a (2×2) non-cooperative non-constant-sum game. Three conceptually different types of games emerge. One of them is ‘Chicken’; each player can gain by pre-emptively threatening to pay nothing—unless the other player acts likewise. ‘Zero public goods’ is thus a possible outcome of voluntary exchange, even though it is Pareto inferior.     

Endogenous Timing in a Mixed Duopoly: Price Competition

The endogenous order of moves is analyzed in a mixed duopoly for differentiated goods, where firms choose whether to set prices sequentially or simultaneously. It is shown that, in contrast to the private duopoly where firms set prices sequentially, in the mixed duopoly firms choose prices simultaneously. Moreover, the result obtained in the mixed duopoly under price competition differs from the one under quantity competition, since in the latter case decisions are taken sequentially.