The role of commitment in repeated games

Abstract

We model the role of commitment in noncooperative games by means of what we call unilateral commitments. We study their impact within the framework of repeated games with complete information. To do so, we revisit the main folk theorems for repeated games with complete information and check up to what extent the assumptions needed in the classic models can be relaxed in the model with unilateral commitments.

Strategic absentmindedness in finitely repeated games

“…Let us now introduce the concept of unilateral commitment, which has been used, for example, in García-Jurado et al (2000) and García-Jurado and González-Díaz (2006). In those papers folk theorems for finitely repeated games with unilateral commitments are obtained.…”

“…We also show that these absentmindedness compromises can be seen as a special case of unilateral commitments regarding the deletion of strategies, as the ones considered, for instance, in García-Jurado and González-Díaz (2006).…”

“…They prove that every outcome which is strictly preferred to the minimax outcome by all players can be supported by a Nash equilibrium when the basic game is sufficiently repeated. Other papers like García-Jurado and González-Díaz (2006) and Renou (2008) explore how the players' ability of making unilateral commitments to some of their strategies affect equilibrium payoffs.…”

Transfers, contracts and strategic games

“…Selten (1965)) of the contract game is empty because of the nonexistence of equilibria in seemingly irrelevant subgames, we focus attention on the notion of virtual subgame perfect equilibrium (cf. García-Jurado and Gonzalez-Díaz (2006)). This notion seems especially relevant and suitable in our framework.…”

Essential collections for equilibrium concepts

“…In García-Jurado and González-Díaz (2006), the authors use the virtual version of subgame perfect equilibrium to get a folk theorem for a class of repeated games in which the existence of subgame perfect equilibria is not guaranteed. Also, the equilibrium notion used in Osborne (1993) is very close to the virtual version of subgame perfect equilibrium.…”