Optimal punishments in linear duopoly supergames with product differentiation

We analyze optimal penal codes in both Bertrand and Cournot supergames with product differentiation. We prove that the relationship between optimal punishments and the security level (individually rational discounted profit stream) depends critically on the degree of supermodularity in the stage game, using a linear duopoly supergame with product differentiation. The security level in the punishment phase is reached only under extreme supermodularity, i.e., when products are perfect substitutes and firms are price setters. Finally, we show that Abreu's rule cannot be implemented under Cournot behavior and strong demand complementarity between products.     

Competition Policy as Strategic Trade with Differentiated Products

The paper analyzes how countries use competition policy as a tool for strategic trade. In the model, two countries export to a third country. Each exporting country is endowed with a set of differentiated products. Each government chooses the number of exporters for its country and the products that each exporter sells in the first period, and a tax policy in the second period. Firms choose prices or quantities independently in the third period. In the unique subgame‐perfect equilibrium, both countries group all their products within a single firm—the “national champion policy.” We study the implication of different assumptions about the timing of the game.     

Entry and Vertical Differentiation

This paper analyzes the entry of new products into vertically differentiated markets where an entrant and an incumbent compete in quantities. The value of the new product is initially uncertain and new information is generated through purchases in the market. We derive the (unique) Markov perfect equilibrium of the infinite horizon game under the strong long run average payoff criterion. The qualitative features of the optimal entry strategy are shown to depend exclusively on the relative ranking of established and new products based on current beliefs. Superior products are launched relatively slowly and at high initial prices whereas substitutes for existing products are launched aggressively at low initial prices. The robustness of these results with respect to different model specifications is discussed. Journal of Economic Literature Classification Numbers: C72, C73, D43, D83.     

On the Irrelevance of Risk Attitudes in Repeated Two-Outcome Games

We study equilibrium and maximin play in supergames consisting of the sequential play of a finite collection of stage games, where each stage game has two outcomes for each player. We show that for two-player supergames in which each stage game is strictly competitive, in any Nash equilibrium of the supergame, play at each stage is a Nash equilibrium of the stage game provided preferences over certain supergame outcomes satisfy a natural monotonicity condition. In particular, equilibrium play does not depend on risk attitudes. We establish an invariance result for games with more than two players when the solution concept is subgame perfection. Journal of Economic Literature Classification Numbers: C72, C9.     

QUANTITY VERSUS PRICE IN A HOMOGENEOUS PRODUCT DUOPOLY*

In a simple homogeneous product setting, the paper looks at the debate on whether firms should choose quantity or price as their strategic variable. It examines a two-stage game between firms with symmetric costs in which the firms choose the strategic mode of operation in the first period and then, in the second period, price or output are chosen simultaneously according to the mode chosen in the first stage. In this game it is possible to have two Nash equilibria where either both play in quantities or both play in prices. One firm choosing price and the other quantity can never be a Nash equilibrium in the two-stage game. Both choosing quantity is always a Nash equilibrium. Both choosing prices may be a Nash equilibrium only in some situations: the structure of the cost functions decides this issue.     

Product Downsizing and Hidden Price Increases: Evidence from Japan's Deflationary Period

In this paper, we empirically examine the extent to which product downsizing occurred during the deflationary period in Japan, as well as the effects of product downsizing on prices and quantities sold. Using scanner data on prices and quantities for all products sold at about 200 supermarkets over the last 10 years, we find that about one third of product replacements were accompanied by a size/weight reduction. We also find that a 1‐percentage point larger size/weight reduction is associated with a 0.45‐percentage point larger price decline, resulting in an effective price increase. Finally, we show that the quantities sold decline with product downsizing, and that the responsiveness of the quantity sold to size/weight changes is almost the same as the price elasticity, indicating that consumers are as sensitive to size/weight changes as they are to price changes. Our results suggest that the Japanese consumer price index may be downwardly biased rather than upwardly biased.     

A DYNAMIC ENTRY AND PRICE GAME WITH CAPACITY INDIVISIBILITY

Strategic market interaction is here modelled as a two‐stage game in which potential entrants choose capacities and next active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are economies of scale. In the simplest version of the model with a single production technique, the equilibrium turns out to depend on the ratio between the level of total output at the long‐run competitive equilibrium and the firm's minimum efficient scale: if that ratio is sufficiently large (the market is sufficiently ‘large’), then the competitive price emerges at a subgame‐perfect equilibrium of the capacity and price game; if not, then the firms randomize in prices on the equilibrium path. The role of the market size for the competitive outcome is shown to be even more important if there are several available production techniques.     

The Strategic Effects of Batch Processing

We study a duopoly game in which firms commit to a batch technology before competing in sales quantities. Adopting a batch technology requires the quantity produced to equal an integer number of batches and allows sales to be less than production. When larger batch sizes lower unit production costs (as in the U.S. airline industry with its economies of density), subgame perfect equilibrium sales quantities are unique and more competitive than the Cournot equilibrium quantities of a one‐shot game with continuous total cost functions. When larger batch sizes yield higher unit costs, equilibrium production can exceed equilibrium sales.     

Coordinated Punishment and the Evolution of Cooperation

In this paper, we analyze a team trust game with coordinated punishment of the allocator by investors and where there is also a final stage of peer punishment. We study the effect of punishment on the reward and the investment decisions, when the effectiveness and cost of coordinated punishment depend on the number of investors adhering to this activity. The interaction takes place in an overlapping‐generations model with heterogeneous preferences and incomplete information. The only long‐run outcomes of the dynamics are either a fully cooperative culture (FCC) with high levels of trust and cooperation and fair returns or a non‐cooperative culture with no cooperation at all. The basin of attraction of the FCC is larger; the higher the institutional capacity of coordinated punishment, the higher the level of peer pressure and the smaller the individual cost of coordinated punishment.     

Would Excess Capacity in Public Firms Be Socially Optimal?

We analyse oligopolistic interactions between a welfare-maximizing public firm and a profit-maximizing private firm in a repeated game. We find that the public firm can hold excess capacity as a strategic punishment device to sustain a subgame perfect equilibrium which is welfare-superior to the static Nash equilibrium. Basically, potential punishment from the public firm in the dynamic game can make the self-interested private firm behave in the public interest. Furthermore, if capacity is endogenous, public excess capacity can occur in a welfare efficient equilibrium when the cost of public capacity investment is higher than that of private investment.     

Conflict technology in cooperation: The group size paradox revisited

This paper studies the implications of punishment‐induced conflict in a public goods game. It shows, under plausible assumptions, how larger group size sometimes enhances punishing behavior in social dilemmas and hence supports higher levels of cooperation. Unlike existing approaches that focus on uncoordinated punishment, I consider punishment as a coordinated activity that may be resisted by those being punished and study the implications of punishment‐induced conflict situations. Developing a conflict model of punishment and combining it with a standard public good game, I show that coordinated punishment can yield the concentration effect of punishment, leading to a larger group advantage; that is, the larger the group, the easier it becomes to organize cooperation. The key idea is that when punishers coordinate their punishment, punishers as a coalition successfully divide defectors and punish each defector one by one. Surprisingly, even when coordination among punishers decays as group size increases, as long as the rate of decaying remains relatively slow the larger group advantage still obtains.     

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.     

Repeated Protection for Sale

This paper addresses whether the efficient equilibria characterized by Grossman and Helpman's one‐shot protection‐for‐sale game are renegotiation‐proof in an infinitely repeated setting. We propose a simple strategy profile that can support the efficient, truthful equilibrium in each period as a strongly renegotiation‐proof subgame perfect equilibrium. This result provides another plausible reason to explain why the truthful equilibrium may be focal in the game of protection‐for‐sale. In addition, when the timing of the contributions is specified explicitly, the special interest groups should minimize the upfront payment to the government before policy implementation to reduce the possibility of the collapse of such relational contracts.     

Debt as a collusive device in an oligopoly supergame

This paper explores the impact of debt holdings on the output decisions of firms in an oligopoly supergame with stochastic demand fluctuations. It is demonstrated that when perfect collusion is not feasible then there exist circumstances in which increased debt holdings may facilitate tacit collusion. This occurs because higher debt levels act as a credible commitment device which lowers the payoffs accruing to a firm when it defects from the tacitly collusive equilibrium. It is further shown that in these circumstances firms may have an incentive to hold debt for strategic purposes which promote collusion.     

Strategic Buyers and Privately Observed Prices

A model of finitely repeated price competition between two sellers with differentiated goods and a large buyer is analyzed. The set of pure strategy sequential equilibria is investigated under public and private monitoring. With private monitoring, i.e., when prices are not observable to the competing sellers, all sales are made by the better seller and the set of repeated game equilibrium payoffs coincides with the stage game subgame perfect equilibrium payoffs. This is in sharp contrast to the game with perfect monitoring where the folk theorem obtains. Journal of Economic Literature Classification Numbers: C72, D43.     

TIME TO MARKET AND IMPATIENT CUSTOMERS

We analyse the decision of firms about when to launch their products on the market when they produce differentiated goods and compete on prices. We find two subgame perfect equilibria: one in which the high‐quality firm holds its leadership in quality, and another in which the low‐quality firm leapfrogs its rival. When the initial level of differentiation is high enough, the low‐quality firm always launches first. Finally, we extend this model to analyse commercial piracy. We obtain that pirates are highly unlikely to launch the illegal copy first because they would bear a higher penalty and a higher risk of being detected.     

Trade Liberalization and Cartel Stability

Can reduced trade barriers promote a collusive understanding about not exporting into each others domestic markets? Reduced trade costs increase the short‐run gains from starting exporting, but can also make the long‐run punishment of such a strategy harsher. If collusion on prices is supported by a trigger strategy, a reduction in trade costs weakens competition in the sense that collusion is easier to sustain. In a corresponding model with collusion on quantities, this conclusion is reversed. The authors also discuss how results change if grim trigger strategies are replaced by stick‐and‐carrot punishments.     

Price leadership and firm size asymmetry: an experimental analysis

We use laboratory experiments to examine the effect of firm size asymmetry on the emergence of price leadership in a price-setting duopoly with capacity constraints. Independent of the level of size asymmetry, the unique subgame perfect equilibrium of our timing game predicts that the large firm is the price leader. Experimental data show that price leadership by the large firm is frequent, but simultaneous moves are also often observed. Profit outcomes in the previous period affect the subjects’ decisions to announce or wait in a way that hampers convergence to the equilibrium. Furthermore, while both small and large firms display a strong tendency to wait to announce their price when firm size asymmetry is low, they often set prices early when size asymmetry is high. Prices are higher when price setting is sequential rather than simultaneous and when firm size asymmetry is high. Hence, price leadership by either type of firm has an anti-competitive effect that is more pronounced when the size difference between firms is large.     

Cooperation Norms in Multiple‐Stage Punishment

We analyze the interplay between cooperation norms and people’s punishment behavior in a social‐dilemma game with multiple punishment stages. By combining multiple punishment stages with self‐contained episodes of interaction, we are able to disentangle the effects of retaliation and norm‐related punishment. An additional treatment provides information on the norms bystanders use in judging punishment actions. Partly confirming previous findings, punishment behavior and bystanders’ opinions are guided by an absolute norm. This norm is consistent over decisions and punishment stages and requires full contributions. In the first punishment stage, our results suggest a higher personal involvement of punishers, leading to a nonlinearity defined by the punishers’ contribution. In later punishment stages, the personal‐involvement effect vanishes and retaliation kicks in. Bystanders generally apply the same criteria as punishers in all stages.     

Punishment paths and cartel size

Using a ‘Dominant-group-fringe’ model, we show that the choice of a subgame perfect Nash equilibrium (SPNE) punishment path in the event that unilateral defection occurs depends upon the common discount parameter, and that when the discount parameter is given the punishment path may depend upon the size of the dominant group. The choice of punishment path is thus endogenous. A striking result is that only for sufficiently small dominant groups in sufficiently small industries are there cases where costs affect these choices. Consequently, costs are irrelevant to the choice of punishment in industries with a large number of firms.