Sequential formation of coalitions through bilateral agreements

• Autores: Inés Macho Stadler, Nicolás Porteiro, David Pérez Castrillo
• Localización: Abstracts of the Fifth Spanish Meeting on Game Theory and Applications / coord. por Jesús Mario Bilbao Arrese , Francisco Ramón Fernández García , 2002, ISBN 84-472-0733-1, pág. 18
• Idioma: inglés
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• Resumen

  • In many cases, it is very difficult for big coalitions to form and the players only have the possibility of forming small coalitions. However, this does not mean that once some coalitions are formed, they cannot decide to continue with the process of forming bigger entities. The banking sector provides several examples of such a sequential process of mergers. In Spain, the now called SCH is the outcome of the merger of the Banco de Santander with the Banco Central Hispano, which in turn was issued of the merger of banks Central and Hispano.

    Similarly, banks Bilbao and Vizcaya first merged to form the BBV and then this new entity merged with the Banco Argentaria to form the BBVA.

    We model the formation of coalitions as a sequential process in which, at each moment in time, only two existing coalitions can decide to merge. We study the subgame perfect equilibria of such a game. In particular, we consider a market where identical firms facing linear demand compete a la Cournot. At each period, firms take decisions on quantity. To concentrate our analysis on the incentives to form coalitions, we assume that production is a short-term decision. Also, at each period, two randomly chosen coalitions in the existing partition can merge. A merger means forming a cartel where the decision on the total level of production by the partners is made jointly. The decision on the merger is made taking into account the long-term profits.

    As Salant, Switzer, and Reynolds (1983) pointed out, two firms (or coalitions) will not be interested in merging if they only consider the present period profits and there are at least three firms (coalitions) in the industry. Their result extends easily to our model: If the firms� discount rate is low enough, they will not merge at any period in the unique Markov perfect equilibrium of the game. Hence, all firms will stay as singlentons.

    The situation when firms are forward looking is more interesting. In this case, firms may want to merge even if they lose profits in the short run. We prove that, when the firms� discount factor is high enough, that is, when firms are patient enough, and there are enough firms in the industry, then the final outcome of any subgame perfect equilibria is the grand coalition. The firms will form coalitions sequentially so that they end up all together. Moreover, in the process of forming coalitions, the firms will accept some of the mergers and will reject others. We will characterize the paths (the coalition structures) that the firms will follow in order to surely arrive to the grand coalition The fact that the grand coalition can result as the equilibrium of a game of coalition formation in a linear Cournot model is in contrast with other results in the literature of coalition formation. Interestingly, it is the fact that only a pair of coalitions can merge at each period (so bigger coalitions cannot form) which allows reaching the grand coalition. Even if this restriction to bilateral agreements is ex-ante bad for the formation of coalitions, since it reduces the choice set of the firms, it ex-post results in an impulse to the process of merging.

    The reason is that the bilateral nature of the negotiation induces the coalitions to be formed gradually, in such a way that the incentives of all the players can be made simultaneously compatible.