Box 1.1. Game theory and strategic management (adapted from [DAI 10])
Games can be non-cooperative or cooperative. In non-cooperative games, players move according to an individualistic behavior, without taking into account the general interest, i.e. they exclusively pursue their own interests.
Cooperative games describe specific situations in which players jointly seek a collectively satisfying solution. In this framework, communication among players is possible. In this field, games are often based on the âcake-sharingâ problem, i.e. the allocation of the aggregated outcome that results from a common cooperative action: âcoreâ notion, Nash bargaining solution [NAS 50]. It is about determining an allocation that gives each player (or initial coalition of players) at least the payoff that he might individually obtain through an independent action. Nevertheless, as shown by the classical prisonerâs dilemma, playersâ individualistic strategies make it difficult to implement the cooperative solution. The gameâs outcome does not always represent the collectively optimal (Pareto optimal) solution. Hence, when that the agreement is closed and each player is sure that the others respect it, he may attempt to unilaterally deviate. This deviation (or treason) strategy enables him to obtain a better payoff than that of cooperation. This phenomenon has been treated with scepticism by game theorists, who wonder whether it is possible to stabilize an agreement when players are free to act.
The solution to implementing the âcooperativeâ situation, i.e. the situation that improves each playerâs outcome with respect to the non-cooperative situation, can 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 âself-punishâ deviations that are observed at a given gameâs stage (see, for example, [FRI 71, LAM 98, ABR 88, FUD 86]).
In this vein, the theory of endogenous coalition formation [HAR 83, BAL 00, BLO 95, BLO 96, RAY 97, RAY 99] argues that a stable cooperation/coordination is that to which players spontaneously adhere without constraints or irreversible commitments. Hence, only self-enforcing cooperation/coordination is stable, i.e. it is not threatened by playersâ unilateral deviations, because it results from playersâ voluntary adhesions.
The non-cooperative approach to coalition formation thus puts forward the idea that coalitions result from playersâ decisions rather than from the negotiation of contractual agreements. Hence, each player decides whether to adhere to a cooperative (or to a coordinated project), or in more difficult cases, he chooses the coalition to be part of, without being required to respect any agreement. The decision to âsubscribeâ, or âcooperateâ, thus represents a strategic variable like any other chosen within the framework of a specific non-cooperative game, the related strategic space being taken into account. Coalitions thus emerge as the outcome of a non-cooperative game through voluntary playersâ adhesions. A coordination that pertains to the adhesion variable does not imply playersâ commitment, which is rather related to the cooperative approach to coalition formation. More generally, we can state that coalition formation is endogenous.
Grant [GRA 91] considers that game theory has several valuable contributions to make to strategic management: