Performative Prediction on Games and Mechanism Design

TL;DR

This work studies performative prediction in a networked collective-action setting, where predictions of agents' actions influence their future behavior via a Bayesian trust state $\tau_{t,i}$. The model embeds a Collective Risk Dilemma on graphs with thresholds $T$, group sizes $M_i$, and payoffs $\pi_i(y_i,y_{\mathcal{N}(i)})$, examining how predictions reshape outcomes through a distribution $\mathcal{D}(\theta;\tau)$. A key finding is that maximizing accuracy through Repeated Risk Minimization (RRM) can converge to low-welfare equilibria with high probability, especially on certain topologies, motivating the introduction of welfare-aware mechanism design and learned predictors that balance accuracy and social welfare. The authors demonstrate via theory and simulations that welfare-oriented predictors can improve cooperation and total welfare at the cost of accuracy, and they develop a Pareto-front approach to jointly optimize both goals. Overall, the paper highlights the nontrivial performative effects in interdependent predicted populations and links them to mechanism design and ethics, providing a framework and empirical evidence for welfare-aware prediction in multi-agent systems.

Abstract

Agents often have individual goals which depend on a group's actions. If agents trust a forecast of collective action and adapt strategically, such prediction can influence outcomes non-trivially, resulting in a form of performative prediction. This effect is ubiquitous in scenarios ranging from pandemic predictions to election polls, but existing work has ignored interdependencies among predicted agents. As a first step in this direction, we study a collective risk dilemma where agents dynamically decide whether to trust predictions based on past accuracy. As predictions shape collective outcomes, social welfare arises naturally as a metric of concern. We explore the resulting interplay between accuracy and welfare, and demonstrate that searching for stable accurate predictions can minimize social welfare with high probability in our setting. By assuming knowledge of a Bayesian agent behavior model, we then show how to achieve better trade-offs and use them for mechanism design.

Figures (17)

• Figure 1: Dark nodes have achieved success, and thick arrows are self-fulfilling prophecies. Both a) and c) are self-fulfilling prophecies where accuracy is maximized, therefore an accuracy maximizer is indifferent between them. However, in a) full success is achieved, but in c) all fail. b) also maximizes group success but at the expense of 0% accuracy.
• Figure 2: Dark nodes have achieved success, and thick arrows are self-fulfilling prophecies. Here there is no self-fulfilling prophecy which maximizes group success, forcing a trade-off between accuracy and group success. Only e) maximizes group success, but the center node regrets having cooperated. Note that, with $T=\frac{2}{3}$, groups of size $M_i=2$ require both agents to cooperate.
• Figure 3: Markov chain describing the evolution of a population with $k$ out of $N$ cooperators, $\tau=1$ and $\mathcal{G}_f$ following RRM, for $N>2T-1,T\not=1$. (details in Appendix \ref{['app:low_welfare']})
• Figure 4: Average proportion of time spent below threshold, after convergence, and proportion of cycles. Each point is the average of 5 scale-free $\mathcal{G}$'s, with 10 random $\boldsymbol{\hat{y}}_1$ per $\mathcal{G}$, and $T=0.5$. Shaded areas are standard deviation among $\mathcal{G}$'s. Find histograms for time in each state in Appendix \ref{['app:low_welfare']}.
• Figure 5: Proportion of successful groups with $\tau=0$, for a fully-connected graph (left) and scale-free networks (right) with varying $\alpha$ and population size N. $\frac{c}{r}=\frac{1}{6}$, $T=0.5$ and scale-free's average degree $m=2$.

Theorems & Definitions (10)

• Definition 2.1
• Definition 2.2
• Proposition 2.3
• Proposition 3.2
• Proposition 3.3
• Theorem 3.4
• Lemma C.1
• proof
• Corollary C.2
• proof