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Program equilibria and discounted computation time

2009
*
Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge - TARK '09
*

We develop a new model of

doi:10.1145/1562814.1562833
dblp:conf/tark/Fortnow09
fatcat:7wfarot2bjbbtdrtzub4r77yz4
*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 ...##
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Bounding Rationality by Discounting Time
[article]

2009
*
arXiv
*
pre-print

We define a new notion of bounded rationality, where the payoffs of players are

arXiv:0911.3162v1
fatcat:2kywohnrpre4fkq3o5yn7ew5fq
*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. ...##
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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. ...##
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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. ...##
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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. ...##
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Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example

2015
*
Dynamic Games and Applications
*

The literature that conducts numerical analysis of equilibrium in models with hyperbolic (quasi-geometric)

doi:10.1007/s13235-015-0177-8
fatcat:afy2bxsmw5bsvosx72yyxuwxii
*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. ...##
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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. ...##
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Power napping with loud neighbors

2014
*
Proceedings of the 2014 ACM conference on Security and privacy in wireless & mobile networks - WiSec '14
*

We leverage the zero-sum

doi:10.1145/2627393.2627406
dblp:conf/wisec/DeBruhlKDST14
fatcat:wqenwixxyfcgfgidhe6btlpiwu
*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. ...##
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Page 5362 of Mathematical Reviews Vol. , Issue 86k
[page]

1986
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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. ...

##
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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. ...##
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Computing equilibria in discounted dynamic games

2015
*
Applied Mathematics and Computation
*

Game theory (GT) is an essential formal tool for interacting entities; however

doi:10.1016/j.amc.2015.07.068
fatcat:hh5y33vmsbefvltg3zqh7troji
*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*. ...##
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Infinitely repeated games with public monitoring and monetary transfers

2012
*
Journal of Economic Theory
*

We develop an efficient algorithm to

doi:10.1016/j.jet.2012.01.008
fatcat:wql5ek3mvra4dkxjsq5krfzbdm
*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 ...##
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CIM Systems: An Introduction to Computer-Integrated Manufacturing

1994
*
Journal of the Operational Research Society
*

Mitcuett, Jr: CIM Systems: An Introduction to

doi:10.1057/jors.1994.12
fatcat:ior5szpcunecbi4njjyldofati
*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 ...##
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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. ...##
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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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