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Program equilibria and discounted computation time

Lance Fortnow
2009 Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge - TARK '09  
We develop a new model of program equilibrium using general computational models and discounting the payoffs based on the computation time used.  ...  Tennenholtz's model allowed each player to produce a "loop-free" computer program that had access to the code for both players.  ...  I presented the ideas on discounted time in complexity in Section 6.2 at a rump session at the 2008 Conference on Computational Complexity and in my weblog [Fortnow 08] and thank those who game me comments  ... 
doi:10.1145/1562814.1562833 dblp:conf/tark/Fortnow09 fatcat:7wfarot2bjbbtdrtzub4r77yz4

Bounding Rationality by Discounting Time [article]

Lance Fortnow, Rahul Santhanam
2009 arXiv   pre-print
We define a new notion of bounded rationality, where the payoffs of players are discounted by the computation time they take to produce their actions.  ...  We also give general results for discounted games over countable action spaces, including showing that any game with bounded and computable payoffs has an equilibrium in our model, even if each player  ...  Acknowledgements We thank Ehud Kalai for suggesting the factoring game to us and to Ehud and Amin Saberi for useful discussions. We also thank the anonymous reviewers for many useful suggestions.  ... 
arXiv:0911.3162v1 fatcat:2kywohnrpre4fkq3o5yn7ew5fq

Page 9427 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
Summary: “Markov decision processes (MDPs) with discounted cost are equivalent to processes with a finite-random duration, and, hence, the discount factor models a (random) time horizon for the life of  ...  Along with the characterization of vertices and rays of ¥, a computationally verifiable necessary condition for the vertices is given.  ... 

Page 2936 of Mathematical Reviews Vol. , Issue 91E [page]

1991 Mathematical Reviews  
The computer was programmed to stop the bargaining after 20 periods. Only 7 (out of 324) games were so terminated.  ...  The results are applied to Prisoner’s dilemma, Cournot- and Bertrand duopoly, respectively, and to advertising games. Except in the Bertrand case for large discount factors WRP equilibria do exist.  ... 

Page 823 of Mathematical Reviews Vol. , Issue 85b [page]

1985 Mathematical Reviews  
Special attention is paid to the computation of the optimal control parameters.” White, D. J. 85b:90087 Multi-objective infinite-horizon discounted Markov decision processes. J. Math. Anal.  ...  and average per unit time reward cases.” 85b:90093 Rockafellar, R.  ... 

Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example

Lilia Maliar, Serguei Maliar
2015 Dynamic Games and Applications  
The literature that conducts numerical analysis of equilibrium in models with hyperbolic (quasi-geometric) discounting reports difficulties in achieving convergence.  ...  We propose two types of restrictions that can rule out the multiplicity: boundary conditions and shape restrictions on equilibrium policy functions.  ...  We thank the editors Edward Prescott and Kevin Reffett for many useful comments and suggestions.  ... 
doi:10.1007/s13235-015-0177-8 fatcat:afy2bxsmw5bsvosx72yyxuwxii

Page 5279 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
In addition, we show that three mathematical programs are linear- time solvable.” 97h:90091 90D05 90A14 Ding, Xie Ping (PRC-SCHN; Chengdu) Coincidence theorems and equilibria of generalized games.  ...  (FIN-HUT-SA; Espoo) Distributed computation of Pareto solutions in n-player games. (English summary) Math. Programming 74 (1996), no. 1, Ser. A, 29-45.  ... 

Power napping with loud neighbors

Bruce DeBruhl, Christian Kroer, Anupam Datta, Tuomas Sandholm, Patrick Tague
2014 Proceedings of the 2014 ACM conference on Security and privacy in wireless & mobile networks - WiSec '14  
We leverage the zero-sum and finite-horizon properties of our model to design a simple polynomial-time algorithm to compute optimal randomized strategies for both players.  ...  By computing Nash equilibria for our game models, we explore what kind of performance guarantees can be achieved both for the sender and jammer, when playing against an optimal opponent.  ...  Sandholm and Kroer are supported by the NSF under grants IIS-1320620, CCF-1101668 and IIS-0964579, as well as the CMU Center for Computational Thinking funded by Microsoft Research.  ... 
doi:10.1145/2627393.2627406 dblp:conf/wisec/DeBruhlKDST14 fatcat:wqenwixxyfcgfgidhe6btlpiwu

Page 5362 of Mathematical Reviews Vol. , Issue 86k [page]

1986 Mathematical Reviews  
Comput. 17 (1985), no. 1, 1-35.  ...  When the optimal program is monotonic, capital is shown to increase with an increase in the discount factor. A counterexample in the case of oscillating programs is discussed.  ... 

Page 4890 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
Jn(6, x)/n be the average expected cost per unit time, let Jg(d, x) be the expected total discounted cost for a discount fac- tor B € (0,1), and let vg(x) = infsc, Jg(d,x), mg = infyes Ug(x).  ...  (NL-TILB-EN; Tilburg) Pareto equilibria for bimatrix games. (English summary) Comput. Math. Appl. 25 (1993), no. 10-11, 19-25.  ... 

Computing equilibria in discounted dynamic games

Andriy Burkov, Brahim Chaib-draa
2015 Applied Mathematics and Computation  
Game theory (GT) is an essential formal tool for interacting entities; however computing equilibria in GT is a hard problem.  ...  The existence of multiple game states makes the problem of computing equilibria in such games extremely difficult.  ...  discounted average payoffs, including pure and mixed action equilibria, stationary and non-stationary equilibria.  ... 
doi:10.1016/j.amc.2015.07.068 fatcat:hh5y33vmsbefvltg3zqh7troji

Infinitely repeated games with public monitoring and monetary transfers

Susanne Goldlücke, Sebastian Kranz
2012 Journal of Economic Theory  
We develop an efficient algorithm to compute the set of pure strategy public perfect equilibrium payoffs for each discount factor.  ...  We also show how all equilibrium payoffs can be implemented with a simple class of stationary equilibria that use stick-and-carrot punishments. Emails: sohlendo@uni-bonn, skranz@uni-bonn.de.  ...  /kranz/software.htm For a description of the software and several examples, see Kranz (2010) . approximations for the equilibrium payoff sets for several discount factors remains computationally expensive  ... 
doi:10.1016/j.jet.2012.01.008 fatcat:wql5ek3mvra4dkxjsq5krfzbdm

CIM Systems: An Introduction to Computer-Integrated Manufacturing

Linda C. Hendry
1994 Journal of the Operational Research Society  
Mitcuett, Jr: CIM Systems: An Introduction to Computer-Integrated Manufacturing F. THUUSMAN: Optimality and Equilibria in Stochastic Games J. A. GANLEY and J. S.  ...  This long time gap serves to emphasize not only that average cost problems are much harder than discounted ones but also that the theory for games is considerably more complex than for the corresponding  ... 
doi:10.1057/jors.1994.12 fatcat:ior5szpcunecbi4njjyldofati

Page 2225 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
In the simple case of 2 players “alternative play” Pareto optimal results are obtained asymptotically for perfect equilibria of discounted coordination games.  ...  Bourdache-Siguerdidjane and M. Fliess, Automatica J. IFAC 23 (1987), no. 3, 365-372; MR 88e:93054], the authors present a method for computing Nash equilibria in feedback strategies.  ... 

Page 3455 of Mathematical Reviews Vol. , Issue 93f [page]

1993 Mathematical Reviews  
The author also considers the mo- ment problem for discrete-time quasi-discounted models, in which the discounted factors are varying with time. These models are of more practical interest.  ...  Gerhard Hiibner (Hamburg) 93f:90181 90C40 Lin, Yuan Lie (PRC-TSI-AM) A continuous-time discounted optimal Markov-decision model and its relation with discrete-time quasidiscounted optimal models—the case  ... 
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