Groupe d’études et de recherche en analyse des décisions

Selection of cooperative equilibria in differential games via bargaining solutions

Simon Hoof Université Paderborn, Danemark

We study an equilibrium selection device for cooperative trigger equilibria in n-person noncooperative differential games based on classic bargaining solutions. Payoffs are nontransferable and discounting is potentially asymmetric. Before the game starts the agents bargain over a n-tuple of stationary Markovian strategies. The agents can agree on any individual rational strategy profile. Grim trigger strategies support the agreement as an equilibrium. We study properties of the Nash, Kalai-Smorodinsky and Egalitarian bargaining solution. For the symmetric game they yield the same and efficient solution. We further investigate an advertising differential game with asymmetric discounting numerically. It turns out that the patient agent favors the Nash, over the Kalai-Smorodinsky, over the Egalitarian solution and vice versa for the impatient one.

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