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Pessimistic Leader-Follower Equilibria with Multiple Followers

Stefano Coniglio, Nicola Gatti, Alberto Marchesi
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
We focus on the pessimistic case where, among many equilibria, one minimizing the leader's utility is chosen (the opposite case is computationally trivial).  ...  We show that the problem is NP-hard even with only two followers, and propose an exact exponential-time algorithm which, for any number of followers, either finds an equilibrium when the game admits a  ...  Conclusions In this paper, we have shown that the problem of computing a pessimistic leader-follower equilibrium with multiple followers playing pure strategies simultaneously and noncooperatively is NP-hard  ... 
doi:10.24963/ijcai.2017/25 dblp:conf/ijcai/Coniglio0M17 fatcat:bvpx7cl4lrcfhmh2atxskj6zw4

Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games

Kai Wang, Lily Xu, Andrew Perrault, Michael K. Reiter, Milind Tambe
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
A growing body of work in game theory extends the traditional Stackelberg game to settings with one leader and multiple followers who play a Nash equilibrium.  ...  Using the unbiased gradient estimate, we implement the gradient-based approach to solve three Stackelberg problems with multiple followers.  ...  Stackelberg Games With a Single Leader and Multiple Followers In this paper, we consider a Stackelberg game composed of one leader and n followers.  ... 
doi:10.1609/aaai.v36i5.20457 fatcat:gb5p3flggbajbcjdbhwqwkhsmm

Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games [article]

Kai Wang, Lily Xu, Andrew Perrault, Michael K. Reiter, Milind Tambe
2021 arXiv   pre-print
A growing body of work in game theory extends the traditional Stackelberg game to settings with one leader and multiple followers who play a Nash equilibrium.  ...  This approach also addresses cases with multiple equilibria and arbitrary equilibrium selection procedures by back-propagating through a sampled Nash equilibrium.  ...  Methods for rithms to find Nash equilibria with economic applications. finding leaderfollower equilibria with multiple followers.  ... 
arXiv:2106.03278v2 fatcat:bngkws7q7zcfvfdcyurtredxba

An Existence Result for Hierarchical Stackelberg v/s Stackelberg Games

Ankur A. Kulkarni, Uday V. Shanbhag
2015 IEEE Transactions on Automatic Control  
The resulting equilibrium problems are plagued by the nonuniqueness of follower equilibria and nonconvexity of leader problems whereby the problem of providing sufficient conditions for existence of global  ...  In Stackelberg v/s Stackelberg games a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers.  ...  We know of no existence results for equilibria of the pessimistic formulation.  ... 
doi:10.1109/tac.2015.2423891 fatcat:k2p76tb2jvbqfnxmzm4y3ukrha

Bilevel programming methods for computing single-leader-multi-follower equilibria in normal-form and polymatrix games

Nicola Basilico, Stefano Coniglio, Nicola Gatti, Alberto Marchesi
2019 EURO Journal on Computational Optimization  
While the single-follower case has been investigated since the inception of bilevel programming with the seminal work of von Stackelberg, results for the case with multiple followers are only sporadic  ...  In this work, we consider Stackelberg games with two or more followers who play a (pure or mixed) Nash equilibrium once the leader has committed to a (pure or mixed) strategy, focusing on normal-form and  ...  Therefore, the set of followers' equilibria in the leader-follower game is the same as that of the original two-player game.  ... 
doi:10.1007/s13675-019-00114-8 fatcat:5p6al3qvkngihcsqdplcu22yye

Beliefs correspondences and equilibria in ambiguous games

Giuseppe De Marco, Maria Romaniello
2011 International Journal of Intelligent Systems  
Hence we consider a multiple prior approach and subjective beliefs correspondences which represent an exogenous ability of each player to put restrictions on beliefs over outcomes consistently with the  ...  Finally we analyze particular beliefs correspondences: beliefs given by correlated equilibria and by ambiguity levels on events.  ...  The second example is devoted to the equilibrium analysis in the noisy leader game (Bagwell (1982) ) and, in this case, ambiguity depends only on the incomplete information problem in presence of multiple  ... 
doi:10.1002/int.21515 fatcat:2oxlbmyj5reyxegmsu5t2jy5iq

Methods for finding leader--follower equilibria with multiple followers [article]

Nicola Basilico, Stefano Coniglio, Nicola Gatti
2017 arXiv   pre-print
While the case with a single follower has been thoroughly investigated, results with multiple followers are only sporadic and the problem of designing and evaluating computationally tractable equilibrium-finding  ...  In this work, we focus on the fundamental case where multiple followers play a Nash equilibrium once the leader has committed to a strategy---as we illustrate, the corresponding equilibrium finding problem  ...  In this paper, we focus on the fundamental case of leader-follower games with multiple followers where the latter play simultaneously in a noncooperative way, thus playing an NE for any commitment of the  ... 
arXiv:1707.02174v1 fatcat:rp2pqa67czcn5hkem7gamou2re

Computing the Strategy to Commit to in Polymatrix Games

Giuseppe De Nittis, Alberto Marchesi, Nicola Gatti
2018 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
In this paper, we look for efficiently solvable games with multiple followers who play either optimistically or pessimistically, i.e., breaking ties in favour or against the leader.  ...  Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world applications, this is unlikely.  ...  In this paper, we provide new results on the computation of leader-follower equilibria with multiple followers.  ... 
doi:10.1609/aaai.v32i1.11456 fatcat:iprwvr3ysfgp3ocr6tusgen6l4

Ambiguity, social opinion and the use of common property resources

Dimitrios Diamantaras, Robert P. Gilles
2011 Journal of Economic Behavior and Organization  
In this paper we argue that ambiguity, combined with social opinion formation can be represented as part of a game-theoretic equilibrium concept that transcends the standard Nash equilibrium concept, applied  ...  We conclude that social opinion formation in most cases has a significant impact on equilibrium common property resource usage. * We thank Cees Withagen for an enlightening discussion with one of the authors  ...  Symmetric ambiguity Following the formal definitions in the previous section, the symmetric ambiguity equilibria can now be formulated as the Nash equilibria for the modified commons game Γ s (λ, γ) with  ... 
doi:10.1016/j.jebo.2011.03.008 fatcat:mydoge2odvb55iy7wdenr2ooh4

MULTI-LEADER-FOLLOWER GAMES: MODELS, METHODS AND APPLICATIONS

Ming Hu, Masao Fukushima
2015 Journal of the Operations Research Society of Japan  
The multi-leader-follower game serves as an important model in game theory with many applications in economics, operations research and other fields.  ...  We then give some applications as well as solution methods of multi-leader-follower games.  ...  He also gave a counterexample to show that, when all leaders with identical cost functions make different decisions, the game could reach multiple equilibria.  ... 
doi:10.15807/jorsj.58.1 fatcat:5a5oqt4hwrbj7b26h6rochde5y

Computing the Strategy to Commit to in Polymatrix Games (Extended Version) [article]

Giuseppe De Nittis, Alberto Marchesi, Nicola Gatti
2018 arXiv   pre-print
In this paper, we look for efficiently solvable games with multiple followers who play either optimistically or pessimistically, i.e., breaking ties in favour or against the leader.  ...  Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world applications, this is unlikely.  ...  In this paper, we provide new results on the computation of leader-follower equilibria with multiple followers.  ... 
arXiv:1807.11914v1 fatcat:evp4juntbrb55a6scye7ijg6ue

Computing a Pessimistic Stackelberg Equilibrium with Multiple Followers: The Mixed-Pure Case

Stefano Coniglio, Nicola Gatti, Alberto Marchesi
2019 Algorithmica  
Although the optimistic and pessimistic versions of the problem, i.e., those where the single follower breaks any ties among multiple equilibria either in favour or against the leader, are solved with  ...  In this paper, we investigate the setting of a normal-form game with a single leader and multiple followers who, after observing the leader's commitment, play a Nash equilibrium.  ...  First, we formulate the problem as a pessimistic bilevel programming problem with multiple followers.  ... 
doi:10.1007/s00453-019-00648-8 fatcat:n2euamp3rfelfkbn76wptq7w7m

On the consistency of leaders' conjectures in hierarchical games

Ankur A. Kulkarni, Uday V. Shanbhag
2013 52nd IEEE Conference on Decision and Control  
First, since follower equilibria need not be unique, conjectures made by leaders regarding follower equilibria may not be consistent at equilibrium.  ...  In this model each leader makes conjectures while also requiring that his conjectures are consistent with those made by other leaders.  ...  Existence of equilibria To the best of our knowledge there are no general existence results for hierarchical games with two levels of hierarchy, let alone multiple levels.  ... 
doi:10.1109/cdc.2013.6760042 dblp:conf/cdc/KulkarniS13 fatcat:im7tc5rez5esrhwjely3h4avly

Aggregate Demand Management with Multiple Equilibria

Huberto M. Ennis, Todd Keister
2003 Social Science Research Network  
We study optimal government policy in an economy where (i) search frictions create a coordination problem and generate multiple Pareto-ranked equilibria and (ii) the government finances the provision of  ...  multiple equilibria.  ...  However, as is common in models with trading frictions, our model has multiple equilibria for a broad range of parameter values.  ... 
doi:10.2139/ssrn.2184540 fatcat:oexvy3cwbvcazmqybmls62cj5u

Endogenous Stackelberg Leadership

Eric van Damme, Sjaak Hurkens
1999 Games and Economic Behavior  
Hence, the low cost firm will emerge as the endogenous Stackelberg leader. Journal of Economic Literature Classification Numbers: C72, D43.  ...  the second and sixth inequalities follow from the best response properties, and the fifth inequality follows since player 2 is more pessimistic when the prior ism.)  ...  Related papers either put firms in asymmetric positions to start with, or add exogenous uncertainty (about production costs or market demand), or admit multiple equilibrium outcomes.  ... 
doi:10.1006/game.1998.0687 fatcat:dzudoagxgbdozk4hns4as27tjy
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