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Emery Cooper

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2 papers

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AAAI Conference 2025 Conference Paper

Characterising Simulation-Based Program Equilibria

Emery Cooper
Caspar Oesterheld
Vincent Conitzer

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 (https://doi.org/10.1016/j.geb.2004.02.002) 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, https://doi.org/10.1007/s11238-018-9679-3) 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.

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UAI Conference 2023 Conference Paper

Incentivizing honest performative predictions with proper scoring rules

Caspar Oesterheld
Johannes Treutlein
Emery Cooper
Rubi Hudson

Proper scoring rules incentivize experts to accurately report beliefs, assuming predictions cannot influence outcomes. We relax this assumption and investigate incentives when predictions are performative, i. e. , when they can influence the outcome of the prediction, such as when making public predictions about the stock market. We say a prediction is a fixed point if it accurately reflects the expert’s beliefs after that prediction has been made. We show that in this setting, reports maximizing expected score generally do not reflect an expert’s beliefs, and we give bounds on the inaccuracy of such reports. We show that, for binary predictions, if the influence of the expert’s prediction on outcomes is bounded, it is possible to define scoring rules under which optimal reports are arbitrarily close to fixed points. However, this is impossible for predictions over more than two outcomes. We also perform numerical simulations in a toy setting, showing that our bounds are tight in some situations and that prediction error is often substantial (greater than 5-10%). Lastly, we discuss alternative notions of optimality, including performative stability, and show that they incentivize reporting fixed points.

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