Strategic interactions can be represented more concisely, and analyzed and solved more efficiently, if we are aware of the symmetries within that multi-agent system. Symmetries also have conceptual implications, for example for equilibrium selection. We study the computational complexity of identifying and using symmetries. Using the classical framework of normal-form games, we consider game symmetries that can be across some or all players and/or actions. We find a strong connection between game symmetries and graph automorphisms, yielding graph automorphism and graph isomorphism completeness results for characterizing the symmetries present in a game.

Next, we investigate when exactly game symmetries can be successfully leveraged for Nash equilibrium computation. We show that finding a Nash equilibrium that respects a given set of symmetries is PPAD- and CLS-complete in general-sum and team games respectively---that is, exactly as hard as Brouwer fixed point and gradient descent problems. Finally, we present polynomial-time methods for the special cases where we are aware of a vast number of symmetries, or where the game is two-player zero-sum and we do not even know the symmetries.

Computing Game Symmetries and Equilibria That Respect Them

In Tennenholtz’s program equilibrium, players of a game submit programs to play on their behalf. Each program receives the other programs’ source code and outputs an action. This can model interactions involving AI agents, mutually transparent institutions, or commitments. (Tennenholtz 2004) proves a folk theorem for program games, but the equilibria constructed are very brittle. We therefore consider simulation-based programs – i.e., programs that work by running opponents’ programs. These are relatively robust (in particular, two programs that act the same are treated the same) and are more practical than proof-based approaches. Oesterheld’s (2019) $\epsilon$Grounded$\pi$Bot is such an approach. Unfortunately, it is not generally applicable to games of three or more players, and only allows for a limited range of equilibria in two player games. In this paper, we propose a generalisation to Oesterheld’s (2019) $\epsilon$Grounded$\pi$Bot. We prove a folk theorem for our programs in a setting with access to a shared source of randomness. We then characterise their equilibria in a setting without shared randomness. Both with and without shared randomness, we achieve a much wider range of equilibria than Oesterheld’s (2019) $\epsilon$Grounded$\pi$Bot. Finally, we explore the limits of simulation-based program equilibrium, showing that the Tennenholtz folk theorem cannot be attained by simulation-based programs without access to shared randomness.

Characterising Simulation-Based Program Equilibria

AI systems can interact in unexpected ways, sometimes with disastrous consequences. As AI gets to control more of our world, these interactions will become more common and have higher stakes. As AI becomes more advanced, these interactions will become more sophisticated, and game theory will provide the tools for analyzing these interactions. However, AI agents are in some ways unlike the agents traditionally studied in game theory, introducing new challenges as well as opportunities. We propose a research agenda to develop the game theory of highly advanced AI agents, with a focus on achieving cooperation.

Foundations of Cooperative AI

Game Theory 1

technical paper

We are pleased to announce the Thirty-Ninth AAAI Conference on Artificial Intelligence (AAAI-25), which will be held in Philadelphia, Pennsylvania at the Pennsylvania Convention Center from February 25 to March 4, 2025.

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-25 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.

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AAAI 2025

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-25 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.



Game Theory and Social Choice

Senior Member Track Talks 2

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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AAAI 2023

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

Caspar Oesterheld

3

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Computing Game Symmetries and Equilibria That Respect Them

Characterising Simulation-Based Program Equilibria

Foundations of Cooperative AI

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