The Role of Commitments in Repeated Games

1. The Role of Commitments in Repeated Games Ignacio García-Jurado Julio González-Díaz Universidad de Santiago de Compostela

2. Some preliminary comments This lecture is connected with the paper: I. García-Jurado, L. Méndez-Naya and F. Patrone. “Unilateral commitments in finitely repeated games”. International Game Theory Review 2, 129-139. 2000. In that paper we considered the following problem: under what conditions can constructive results (payoff vectors greater than minimax) be supported by a Nash equilibrium in finitely repeated games with unilateral commitments? Here we consider the next problem: under what conditions can constructive resultsbe supported by a subgame perfect equilibrium in finitely repeated games with unilateral commitments?

3. Some preliminary comments A finitely repeated game with unilateral commitments is a finitely repeated game with a previous stage in which players can announce that they will not use some of their strategies in the repeated game. It is not uncommon that in real-life conflicts some players announce that they will not use some of their strategies before the interaction starts. • A department that makes the commitment of not hiring its own graduate students. • A firm announcing a limited edition of a certain product. • A party announcing during the election campaign that they are not going to make certain alliances. • …

4. Some preliminary comments Delegation is a mechanism for unilateral commitment. We approach the problem making use of non-cooperative game theory. In non-cooperative game theory it is assumed that all the possibilities of the players have been included as formal moves in the game, in contrast to cooperative game theory which assumes that players can make binding agreements outside of the detailed rules that have been specified. For simplicity, in this presentation we concentrate on finite games. However, our results can be easily extended to broader classes of games.

5. A finitely repeated game

6. A finitely repeated game with unilateral commitments

7. An Example

9. Our objective Subgame Perfect Equilibrium Nash Equilibrium

10. Our results Virtually Subgame Perfect Equilibrium Nash Equilibrium

11. Our results Virtually Subgame Perfect Equilibrium Nash Equilibrium

15. Our results Virtually Subgame Perfect Equilibrium Nash Equilibrium

16. A Final Example

17. The Role of Commitments in Repeated Games Ignacio García-Jurado Julio González-Díaz Universidad de Santiago de Compostela