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Introduction to the Non-Cooperative Approach to Coalition Formation: The Case of the Blu-Ray/HD-DVD Standards' War

2010; Routledge; Volume: 23; Issue: 4 Linguagem: Inglês

10.1080/08997764.2010.527206

1532-7736

Nabyla Daidj, Cristina Grazia, Abdelhakim Hammoudi,

Game Theory and Applications

Abstract The concepts of the theory of endogenous coalition formation have not been utilized much to analyze issues in the field of applied economics. In this paper, we show how these concepts make a relevant and innovative contribution to these issues. We first illustrate the fundamentals of this theory and we present the concept of internal and external cartel stability. We provide an illustration of this concept through a basic example of an oligopoly in a cartelization situation. Then, we show the relevance of these concepts by analyzing the battle between the high-definition DVD-player standards: Sony's Blu-Ray and NEC/Toshiba's HD-DVD. Notes 1There are now well-known game typologies that represent different levels and natures of conflicts: the prisoner's dilemma, battle of sexes, and chicken game. These classical two-player game typologies have been extensively used in a wide range of fields (economics, politics, sociology, management, etc.) and illustrate, in both a simple and rigorous manner, to what extent the rivalry among players affects incentives to coordination and the related problems (e.g., see CitationGibbons, 1992). 2See Nash (1950). 3A solution whereby a “cooperative” situation is implemented (i.e., a situation that improves each player's outcome with respect to the non-cooperative situation) may be to modify the game by introducing a third party that punishes deviations or to consider an infinitely repeated game that might enable players to “self-punish” deviations that are observed at a given stage of a game (e.g., see CitationAbreu, 1988; CitationFriedman, 1971; CitationFudenberg & Maskin, 1986; CitationLambertini, Podder, & Sasaki, 1998). 4This concept (Nash, 1951) has opened up the possibility of applying Game Theory and a very high number of games, which involve an arbitrary but finite number of players and strategies. The situation in which each player chooses the best strategy available to him, given the strategies chosen by the others, is referred to as the Nash equilibrium. For more details on the historical background of the works of John Nash and their repercussions on Game Theory, refer to CitationMyerson (1999). The Nash equilibrium has been commented on by numerous authors, among them CitationKreps (1990). 5This type of game is quite complex, and we do not tackle it in this work (see CitationBloch, 1995, Citation1996). 6D'Aspremont, Jacquemin, Gabszewicz, and Weymark (1983) considered the situation of the CitationMarkham (1951) price leadership model where a cartel that does not include all the firms on the market fixes the market price as a leader. This is done by anticipating the quantities chosen (at this price) by all firms that do not adhere to the cartel (these firms being de facto price takers). 7The concept of stability, according to this definition, implies that players have a two-option space of strategies (subscribe or not). This binary subscription decision results from the fact that only one cooperative project is offered to the players. Thus, the expected structure is de facto a single-coalition structure, the players outside the coalition having chosen to play independently. They then form what we call the “fringe,” which consists of players having chosen not to cooperate. However, the previously defined concept of stability can be extended to a context where there are several cooperative projects that players can freely choose. Players no longer decide whether to subscribe to a project or not, but announce which project they want to participate in, keeping in mind that they can also choose to stay on the fringe (e.g., see CitationYi & Shin, 2000). We do not deal with this framework here, whose technical complexity is not compatible with the aim of this article. 8Some analysts consider that the DVD Forum selected Toshiba's format as the successor to DVD because the company promised it would be completed sooner than Sony's Blu-Ray. 9As Kretschmer and Muehlfeld (2006, p. 32) explained, the battle between Sony and Toshiba “apart from generating incompatibility losses, creates scope for third parties outside the two alliance blocks, such as Samsung, to step into the standardization gap by offering hardware compatible with both networks (Smith, 2005).''” 10There have been many “announcement effects” about the next DVD standard, and the strategic stakes for both Sony and Toshiba are very high. Communication on their Web sites is moreover revealing of their commitment. For more details, see Sony and Toshiba's Websites at http://www.blu-raydisc.com/Index.html and http://www.hddvdprg.com/eng/about/charter.html, respectively. 11Component manufacturers must also be added to have a complete list of the parties. 12This chronology of the game can be debated. We could have assumed that manufacturers move at the first stage of the game and studios at the second stage. In general, the sequence to choose depends on the context and notably on which stage (upstream or downstream) “leads” the game. Here, we assume that the studios' moves imply (as a reaction) moves by the manufacturers. To determine the leader stage, it is necessary to develop a detailed microeconomic analysis, which goes beyond the scope of this article. Although it may be questionable, we have chosen the aforementioned sequence on the basis of the battle's outcome. The latter was strongly influenced by the studios' decisions (notably, Warner Brothers') that influenced the manufacturers' decisions. Therefore, the studios are likely to be the “leaders” of this game. 13A non-symmetrical framework may arise, for example, when a studio or manufacturer induces a different marginal benefit (or loss) to the coalition that he joins or leaves. This means that studios or manufacturers are heterogeneous in terms of their characteristics (size, costs, technology, knowledge, etc.) and that it is probably more realistic than the symmetric assumption. However, the model of endogenous coalition formation with asymmetric context is technically very complex (see CitationGiraud-Héraud & Hammoudi, 1999) and, thus, inappropriate given the aim of this article. 14The objective here is to propose a strategic approach rather than a microeconomic analysis of the HD-DVD/Blu-Ray battle. Notably, the aim is to illustrate through the concepts of endogenous coalition formation how certain types of interdependences affect the structure's evolution toward the final outcome. 15This assumption enables us to simplify the following reasoning: To find the (integer) size, which ensures the stability, it is sufficient to consider the integer part of the (real) solution m of the equation (Δ B(n, m) = 0). 16The internal stability of the coalition S 1 D is Δ B(n, m) = B 1(n, m) – B 2(N – n, M – m + 1) > 0, and it is equivalent to . The external stability of the coalition S 1 D is Δ B(n, m) = B 2(N – n, M – m) – B 1(n, m + 1) > 0, and it is equivalent to . 17Needless to say, the result depends on the payoff functions chosen in the example. 18We can cite, among others, the prisoner's dilemma, the battle of sexes, and the chicken game (CitationDaidj & Hammoudi, 2007; CitationGibbons, 1992). 19For example, Paramount and Warner Bros. in 2005, then Warner Bros. in 2008, and Paramount and DreamWorks in 2007. 20The aim is to illustrate in the simplest way both the upstream and downstream interdependence and a field of application of coalition stability concepts. 21As, for example, the Warner Brothers' turnaround that benefited the Blu-Ray format.