Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
110 tokens/sec
GPT-4o
56 tokens/sec
Gemini 2.5 Pro Pro
44 tokens/sec
o3 Pro
6 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Game Theory with Simulation of Other Players (2305.11261v2)

Published 18 May 2023 in cs.GT

Abstract: Game-theoretic interactions with AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to simulate an AI agent (for example because its source code is known), which allows others to accurately predict the agent's actions. This could lower the bar for trust and cooperation. In this paper, we formalize games in which one player can simulate another at a cost. We first derive some basic properties of such games and then prove a number of results for them, including: (1) introducing simulation into generic-payoff normal-form games makes them easier to solve; (2) if the only obstacle to cooperation is a lack of trust in the possibly-simulated agent, simulation enables equilibria that improve the outcome for both agents; and however (3) there are settings where introducing simulation results in strictly worse outcomes for both players.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (30)
  1. A geometric view of parametric linear programming. Algorithmica, 8(1):161–176, 1992.
  2. Robust cooperation in the prisoner’s dilemma: Program equilibrium via provability logic. arXiv preprint arXiv:1401.5577, 2014.
  3. R. Eric Barnes. Rationality, dispositions, and the newcomb paradox. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 88(1):1–28, 10 1997.
  4. Trust, reciprocity, and social history. Games and economic behavior, 10(1):122–142, 1995.
  5. Jesse Clifton. Cooperation, conflict, and transformative artificial intelligence: A research agenda. Effective Altruism Foundation, March, 4, 2020.
  6. Computing the optimal strategy to commit to. In Proceedings of the 7th ACM conference on Electronic commerce, pages 82–90, 2006.
  7. New complexity results about nash equilibria. Games and Economic Behavior, 63(2):621–641, 2008.
  8. Cooperative and uncooperative institution designs: Surprises and problems in open-source game theory. arXiv preprint arXiv:2208.07006, 2022.
  9. Andrew Critch. A parametric, resource-bounded generalization of Löb’s theorem, and a robust cooperation criterion for open-source game theory. Journal of Symbolic Logic, 84(4):1368–1381, 12 2019.
  10. Lance Fortnow. Program equilibria and discounted computation time. In Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge, pages 128–133, 2009.
  11. Counterfactuals and two kinds of expected utility. In William L. Harper, Robert Stalnaker, and Glenn Pearce, editors, Ifs. Conditionals, Belief, Decision, Chance and Time, volume 15 of The University of Western Ontario Series in Philosophy of Science. A Series of Books in Philosophy of Science, Methodology, Epistemology, Logic, History of Science, and Related Fields, pages 153–190. Springer, 1981.
  12. Game theory with translucent players. International Journal of Game Theory, 47(3):949–976, 2018.
  13. Sequential equilibrium in games of imperfect recall. ACM Transactions on Economics and Computation, 9(4):1–26, 2021.
  14. J. V. Howard. Cooperation in the prisoner’s dilemma. Theory and Decision, 24:203–213, 5 1988.
  15. Solving stackelberg games with uncertain observability. In AAMAS, pages 1013–1020, 2011.
  16. On the value of commitment. Autonomous Agents and Multi-Agent Systems, 28(6):986–1016, 2014.
  17. R. Preston McAfee. Effective computability in economic decisions. https://vita.mc4f.ee/PDF/EffectiveComputability.pdf, 1984. Accessed: 2022-12-14.
  18. Robert Nozick. Newcomb’s problem and two principles of choice. In Nicholas Rescher et al., editor, Essays in Honor of Carl G. Hempel, pages 114–146. Springer, 1969.
  19. Extracting money from causal decision theorists. The Philosophical Quarterly, 2021.
  20. Caspar Oesterheld. Robust program equilibrium. Theory and Decision, 86(1):143–159, 2 2019.
  21. Caspar Oesterheld. A note on the compatibility of different robust program equilibria of the prisoner’s dilemma. arXiv preprint arXiv:2211.05057, 2022.
  22. Derek Parfit. Reasons and Persons. Oxford University Press, 1984.
  23. Ariel Rubinstein. Modeling Bounded Rationality. Zeuthen Lecture Book Series. The MIT Press, 1998.
  24. Walter Rudin. Real and Complex Analysis. Mathematics. McGraw.. HiII, 1987.
  25. Multiagent systems: Algorithmic, game-theoretic, and logical foundations. Cambridge University Press, 2008.
  26. Exploring the when and why of Schadenfreude. Social and Personality Psychology Compass, 3(4):530–546, 2009.
  27. Why take both boxes? Philosophy and Phenomenological Research, 99(1):27–48, 7 2017.
  28. Moshe Tennenholtz. Program equilibrium. Games and Economic Behavior, 49(2):363–373, 11 2004.
  29. Heinrich von Stackelberg. Marktform und Gleichgewicht. Springer, 1934.
  30. Bernhard von Stengel and Shmuel Zamir. Leadership games with convex strategy sets. Games and Economic Behavior, 69(2):446–457, 2010.
User Edit Pencil Streamline Icon: https://streamlinehq.com
Authors (3)
  1. Vojtech Kovarik (15 papers)
  2. Caspar Oesterheld (19 papers)
  3. Vincent Conitzer (75 papers)
Citations (13)

Summary

We haven't generated a summary for this paper yet.

X Twitter Logo Streamline Icon: https://streamlinehq.com