Hello, I am trying to compute a Stackelberg-Nash equilibrium of a game, where the leader gives signals to the followers whom tries to find a NE in a non cooperative game. We may assume that the costs are linear and that the followers plays an aggregate game. Thank you for your answers.
I'd suggest two methods: (1) Run an agent simulation and characterize the long term distributions of aggregate best replies, and (2) Use reinforcement learning to fashion an aggregate strategy for followers.
Hi Dr Moffit, thank you for your reply.
But i m still wondering for the first method, how can we proove that it Will converge To the stackeleberg nash equilibrium ? If i understood your suggestion we might fall in a bash equilibrium between agents and the aggregate and this is not what we are looking for.
Best regards
For an ordinary Stackelberg game with one leader and one follower, you first maximize for the follower treating the leader's move as a fixed constant. This gives the best response for the follower, and allows finding expressions for both players' payoffs in terms of the leader's move. With this expression you then maximize for the leader.
For the situation with N followers, first find the equilibrium for the subgame in terms of the leader's signal (treating the signal as an unknown constant). This gives the followers' best response and allows writing the leader's payoff as a function of the signal. Next maximize the leader's payoff with respect to the signal, which gives the equilibrium solution.
Hi Fabio,
But this suggest that we can have an expression for the follower's best response. However, for complex payoff functions it's nearly impossible to get that.
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