Computing Stackelberg Equilibrium with Memory in Sequential Games

by   Aditya Aradhye, et al.

Stackelberg equilibrium is a solution concept that describes optimal strategies to commit: Player 1 (the leader) first commits to a strategy that is publicly announced, then Player 2 (the follower) plays a best response to the leader's commitment. We study the problem of computing Stackelberg equilibria in sequential games with finite and indefinite horizons, when players can play history-dependent strategies. Using the alternate formulation called strategies with memory, we establish that strategy profiles with polynomial memory size can be described efficiently. We prove that there exist a polynomial time algorithm which computes the Strong Stackelberg Equilibrium in sequential games defined on directed acyclic graphs, where the strategies depend only on the memory states from a set which is linear in the size of the graph. We extend this result to games on general directed graphs which may contain cycles. We also analyze the setting for approximate version of Strong Stackelberg Equilibrium in the games with chance nodes.


page 1

page 2

page 3

page 4


Computation of Stackelberg Equilibria of Finite Sequential Games

The Stackelberg equilibrium solution concept describes optimal strategie...

Double-oracle sampling method for Stackelberg Equilibrium approximation in general-sum extensive-form games

The paper presents a new method for approximating Strong Stackelberg Equ...

Efficient Stackelberg Strategies for Finitely Repeated Games

We study the problem of efficiently computing optimal strategies in asym...

Safe Search for Stackelberg Equilibria in Extensive-Form Games

Stackelberg equilibrium is a solution concept in two-player games where ...

Robust Commitments and Partial Reputation

Agents rarely act in isolation -- their behavioral history, in particula...

On the Inducibility of Stackelberg Equilibrium for Security Games

Strong Stackelberg equilibrium (SSE) is the standard solution concept of...

Be a Leader or Become a Follower: The Strategy to Commit to with Multiple Leaders (Extended Version)

We study the problem of computing correlated strategies to commit to in ...