Computing Stackelberg strategies in stochastic games

Significant recent progress has been made in both the computation of optimal strategies to commit to (Stackelberg strategies), and the computation of correlated equilibria of stochastic games. In this letter we discuss some recent results in the intersection of these two areas. We investigate how valuable commitment can be in stochastic games and give a brief summary of complexity results about computing Stackelberg strategies in stochastic games.

[1]  A. Gibbard Manipulation of Voting Schemes: A General Result , 1973 .

[2]  M. Satterthwaite Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[3]  M. Trick,et al.  The computational difficulty of manipulating an election , 1989 .

[4]  A. Rubinstein,et al.  Bargaining and Markets , 1991 .

[5]  S. Bikhchandani Auctions of Heterogeneous Objects , 1999 .

[6]  Daniel Lehmann,et al.  Combinatorial auctions with decreasing marginal utilities , 2001, EC '01.

[7]  Uriel Feige,et al.  On maximizing welfare when utility functions are subadditive , 2006, STOC '06.

[8]  Vincent Conitzer,et al.  Computing the optimal strategy to commit to , 2006, EC '06.

[9]  J. Flandrin,et al.  Arranging the Meal: A History of Table Service in France , 2007 .

[10]  Hans Peters,et al.  Anonymous voting and minimal manipulability , 2007, J. Econ. Theory.

[11]  Noam Nisan,et al.  Elections Can be Manipulated Often , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[12]  Ariel D. Procaccia,et al.  Frequent Manipulability of Elections: The Case of Two Voters , 2008, WINE.

[13]  Vincent Conitzer,et al.  A sufficient condition for voting rules to be frequently manipulable , 2008, EC '08.

[14]  Sarit Kraus,et al.  Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games , 2008, AAMAS.

[15]  Manish Jain,et al.  Computing optimal randomized resource allocations for massive security games , 2009, AAMAS.

[16]  Sarit Kraus,et al.  Using Game Theory for Los Angeles Airport Security , 2009, AI Mag..

[17]  Vincent Conitzer,et al.  Learning and Approximating the Optimal Strategy to Commit To , 2009, SAGT.

[18]  Bernhard von Stengel,et al.  Leadership games with convex strategy sets , 2010, Games Econ. Behav..

[19]  Sarit Kraus,et al.  Robust solutions to Stackelberg games: Addressing bounded rationality and limited observations in human cognition , 2010, Artif. Intell..

[20]  Guy Kindler,et al.  The Geometry of Manipulation: A Quantitative Proof of the Gibbard-Satterthwaite Theorem , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[21]  Vincent Conitzer,et al.  Computing optimal strategies to commit to in extensive-form games , 2010, EC '10.

[22]  Manish Jain,et al.  Security Games with Arbitrary Schedules: A Branch and Price Approach , 2010, AAAI.

[23]  Piotr Faliszewski,et al.  AI's War on Manipulation: Are We Winning? , 2010, AI Mag..

[24]  Vincent Conitzer,et al.  Complexity of Computing Optimal Stackelberg Strategies in Security Resource Allocation Games , 2010, AAAI.

[25]  Milind Tambe,et al.  Security and Game Theory: IRIS – A Tool for Strategic Security Allocation in Transportation Networks , 2011, AAMAS 2011.

[26]  Manish Jain,et al.  Quality-bounded solutions for finite Bayesian Stackelberg games: scaling up , 2011, AAMAS.

[27]  Tim Roughgarden,et al.  Welfare guarantees for combinatorial auctions with item bidding , 2011, SODA '11.

[28]  Haim Kaplan,et al.  Non-price equilibria in markets of discrete goods , 2011, EC '11.

[29]  Vincent Conitzer,et al.  Commitment to Correlated Strategies , 2011, AAAI.

[30]  Gabriel D. Carroll A Quantitative Approach to Incentives: Application to Voting Rules (Job Market Paper) , 2011 .

[31]  Charles Lee Isbell,et al.  Quick Polytope Approximation of All Correlated Equilibria in Stochastic Games , 2011, AAAI.

[32]  Noam Nisan,et al.  A Quantitative Version of the Gibbard-Satterthwaite Theorem for Three Alternatives , 2011, SIAM J. Comput..

[33]  Vincent Conitzer,et al.  Computing Optimal Strategies to Commit to in Stochastic Games , 2012, AAAI.

[34]  Thanh Nguyen,et al.  Coalitional bargaining in networks , 2012, EC '12.

[35]  Éva Tardos,et al.  Bayesian sequential auctions , 2012, EC '12.

[36]  Elchanan Mossel,et al.  A quantitative Gibbard-Satterthwaite theorem without neutrality , 2011, STOC '12.

[37]  Vasilis Syrgkanis,et al.  Bayesian Games and the Smoothness Framework , 2012, ArXiv.

[38]  Thanh Nguyen,et al.  Local bargaining and endogenous fluctuations , 2012, EC '12.

[39]  Renato Paes Leme,et al.  Sequential auctions and externalities , 2011, SODA.

[40]  Bo An,et al.  PROTECT: a deployed game theoretic system to protect the ports of the United States , 2012, AAMAS.

[41]  Yevgeniy Vorobeychik,et al.  Computing Stackelberg Equilibria in Discounted Stochastic Games , 2012, AAAI.

[42]  R. Berry,et al.  The Role of Search Friction in Networked Markets ’ Stationarity , 2012 .

[43]  Michal Feldman,et al.  Simultaneous auctions are (almost) efficient , 2012, STOC '13.