{"type":"ScholarlyArticle","title":"Game Theory with Simulation of Other Players","authors":[{"name":"Vojtěch Kovařík","slug":"vojtech-kovarik","given":"Vojtěch","family":"Kovařík","affiliation":"Foundations of Cooperative AI Lab (FOCAL) , Carnegie Mellon University"},{"name":"Caspar Oesterheld","slug":"caspar-oesterheld","given":"Caspar","family":"Oesterheld","affiliation":"Foundations of Cooperative AI Lab (FOCAL) , Carnegie Mellon University"},{"name":"Vincent Conitzer","slug":"vincent-conitzer","given":"Vincent","family":"Conitzer","affiliation":"Foundations of Cooperative AI Lab (FOCAL) , Carnegie Mellon University"}],"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 first formally define games in which one player can simulate another at a cost, and derive some basic properties of such games. Then, we prove a number of results for such games, 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 (3) however, there are settings where introducing simulation results in strictly worse outcomes for both players.","doi":"10.24963/ijcai.2023/312","url":"https://ijcai.org/proceedings/2023/312","pdf":"https://ijcai.org/proceedings/2023/0312.pdf","markdown":"https://ijcai.org/proceedings/2023/312.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/312","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":312,"pages":{"first":2800,"last":2807},"keywords":["Game Theory and Economic Paradigms: GTEP: Noncooperative games"],"videos":[],"references":[{"position":1,"raw":"[Adler and Monteiro, 1992] Ilan Adler and Renato DC Mon- teiro. A geometric view of parametric linear programming. Algorithmica, 8(1):161-176, 1992.","title":"Ilan Adler and Renato DC Monteiro. A geometric view of parametric linear programming","authors":"Monteiro Adler","year":"1992","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Barasz et al., 2014] Mihaly Barasz, Paul Christiano, Benja Fallenstein, Marcello Herreshoff, Patrick LaVictoire, and Eliezer Yudkowsky. Robust cooperation in the prisoner's dilemma: Program equilibrium via provability logic. arXiv preprint arXiv:1401.5577, 2014.","title":"Robust cooperation in the prisoner's dilemma: Program equilibrium via provability logic","authors":"Mihaly Barasz, Paul Christiano, Benja Fallenstein, Marcello Herreshoff, Patrick Lavictoire, Eliezer Yudkowsky","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Berg et al., 1995] Joyce Berg, John Dickhaut, and Kevin Mc- Cabe. Trust, reciprocity, and social history. Games and economic behavior, 10(1):122-142, 1995.","title":"Trust, reciprocity, and social history","authors":"Joyce Berg, John Dickhaut, Kevin Mc-Cabe","year":"1995","venue":"Games and economic behavior","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Clifton, 2020] Jesse Clifton. Cooperation, conflict, and trans- formative artificial intelligence: A research agenda. Effec- tive Altruism Foundation, March, 4, 2020.","title":"Cooperation, conflict, and transformative artificial intelligence: A research agenda","authors":"Jesse Clifton","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Conitzer and Sandholm, 2006] Vincent Conitzer and Tuo- mas Sandholm. Computing the optimal strategy to commit to. In Proceedings of the 7th ACM conference on Electronic commerce, pages 82-90, 2006.","title":"Computing the optimal strategy to commit to","authors":"Sandholm Conitzer, Vincent Conitzer, Tuomas Sandholm","year":"2006","venue":"Proceedings of the 7th ACM conference on Electronic commerce","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Conitzer and Sandholm, 2008] Vincent Conitzer and Tuo- mas Sandholm. New complexity results about nash equi- libria. Games and Economic Behavior, 63(2):621-641, 2008.","title":"Vincent Conitzer and Tuomas Sandholm. New complexity results about nash equilibria","authors":"Sandholm Conitzer","year":"2008","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Critch et al., 2022] Andrew Critch, Michael Dennis, and Stu- art Russell. Cooperative and uncooperative institution de- signs: Surprises and problems in open-source game theory. arXiv preprint arXiv:2208.07006, 2022.","title":"Cooperative and uncooperative institution designs: Surprises and problems in open-source game theory","authors":"Andrew Critch, Michael Dennis, Stuart Russell","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Critch, 2019] 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.","title":"A parametric, resourcebounded generalization of Löb's theorem, and a robust cooperation criterion for open-source game theory","authors":"Andrew Critch","year":"2019","venue":"Journal of Symbolic Logic","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Fortnow, 2009] Lance Fortnow. Program equilibria and dis- counted computation time. In Proceedings of the 12th Con- ference on Theoretical Aspects of Rationality and Knowl- edge, pages 128-133, 2009.","title":"Lance Fortnow. Program equilibria and discounted computation time","authors":"Fortnow","year":"2009","venue":"Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Halpern and Pass, 2018] Joseph Y Halpern and Rafael Pass. Game theory with translucent players. International Jour- nal of Game Theory, 47(3):949-976, 2018.","title":"Game theory with translucent players","authors":"Y Joseph, Rafael Halpern, Pass","year":"2018","venue":"International Journal of Game Theory","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Halpern and Pass, 2021] Joseph Y Halpern and Rafael Pass. Sequential equilibrium in games of imperfect recall. ACM Transactions on Economics and Computation, 9(4):1-26, 2021.","title":"Sequential equilibrium in games of imperfect recall","authors":"Y Joseph, Rafael Halpern, Pass","year":"2021","venue":"ACM Transactions on Economics and Computation","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Howard, 1988] J. V. Howard. Cooperation in the prisoner's dilemma. Theory and Decision, 24:203-213, 5 1988.","title":"Cooperation in the prisoner's dilemma","authors":"J V Howard","year":"1988","venue":"Theory and Decision","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Korzhyk et al., 2011] Dmytro Korzhyk, Vincent Conitzer, and Ronald Parr. Solving stackelberg games with uncertain observability. In AAMAS, pages 1013-1020, 2011.","title":"Solving stackelberg games with uncertain observability","authors":"Dmytro Korzhyk, Vincent Conitzer, Ronald Parr","year":"2011","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Letchford et al., 2014] Joshua Letchford, Dmytro Korzhyk, and Vincent Conitzer. On the value of commitment. Au- tonomous Agents and Multi-Agent Systems, 28(6):986- 1016, 2014.","title":"On the value of commitment","authors":"Letchford","year":"2014","venue":"Autonomous Agents and Multi-Agent Systems","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[McAfee, 1984] R. Preston McAfee. Effective computabil- ity in economic decisions. https://vita.mc4f.ee/PDF/ EffectiveComputability.pdf, 1984. Accessed: 2022-12-14.","title":"Effective computability in economic decisions","authors":"R, Preston Mcafee","year":"1984","venue":null,"doi":null,"url":"https://vita.mc4f.ee/PDF/EffectiveComputability.pdf","internal_url":null},{"position":16,"raw":"[Oesterheld, 2019] Caspar Oesterheld. Robust program equi- librium. Theory and Decision, 86(1):143-159, 2 2019.","title":"Robust program equilibrium","authors":"Caspar Oesterheld, Oesterheld","year":"2019","venue":"Theory and Decision","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Oesterheld, 2022] Caspar Oesterheld. A note on the compati- bility of different robust program equilibria of the prisoner's dilemma. arXiv preprint arXiv:2211.05057, 2022.","title":"A note on the compatibility of different robust program equilibria of the prisoner's dilemma","authors":"Caspar Oesterheld","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Rubinstein, 1998] Ariel Rubinstein. Modeling Bounded Ra- tionality. Zeuthen Lecture Book Series. The MIT Press, 1998.","title":"Modeling Bounded Rationality","authors":"Ariel Rubinstein","year":"1998","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Rudin, 1987] Walter Rudin. Real and Complex Analysis. Mathematics. McGraw.. HiII, 1987.","title":"Real and Complex Analysis","authors":"Walter Rudin","year":"1987","venue":"Mathematics","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Shoham and Leyton-Brown, 2008] Yoav Shoham and Kevin Leyton-Brown. Multiagent systems: Algorithmic, game- theoretic, and logical foundations. Cambridge University Press, 2008.","title":"Multiagent systems: Algorithmic, gametheoretic, and logical foundations","authors":"Yoav Shoham, Kevin Leyton-Brown","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Smith et al., 2009] Richard H Smith, Caitlin AJ Powell, David JY Combs, and David Ryan Schurtz. Exploring the when and why of Schadenfreude. Social and Personality Psychology Compass, 3(4):530-546, 2009.","title":"Exploring the when and why of Schadenfreude","authors":"H Richard, Caitlin Aj Smith, David Jy Powell, David Ryan Combs, Schurtz","year":"2009","venue":"Social and Personality Psychology Compass","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Tennenholtz, 2004] Moshe Tennenholtz. Program equilib- rium. Games and Economic Behavior, 49(2):363-373, 11 2004.","title":"Moshe Tennenholtz. Program equilibrium","authors":"Tennenholtz","year":"2004","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[von Stackelberg, 1934] Heinrich von Stackelberg. Markt- form und Gleichgewicht. Springer, 1934.","title":"Heinrich von Stackelberg. Marktform und Gleichgewicht","authors":"Von Stackelberg","year":"1934","venue":null,"doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[von Stengel and Zamir, 2010] Bernhard von Stengel and Shmuel Zamir. Leadership games with convex strategy sets. Games and Economic Behavior, 69(2):446-457, 2010.","title":"Leadership games with convex strategy sets","authors":"Von Stengel, ; Zamir, Von Bernhard, Shmuel Stengel, Zamir","year":"2010","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}