Conditional Recall

TL;DR

We address the restrictive perfect-recall assumption in extensive-form games by introducing a memory-modifying device, denoted $X$, which enables conditional forgetting within a single-use, hardware-backed framework built on Trusted Execution Environments ($TEEs$). The paper formalizes a game-transform $\Gamma^X$ that lets an agent forget selected information while preserving time-consistency, and analyzes how this capability yields strict improvements in equilibria across information markets, bargaining, and Coasian dynamics. It links to confidential computing, one-time programs, and commitment-device literature to argue that credible forgetting can reduce inefficiencies caused by information leakage and reputation effects in AI-mediated interactions. The results highlight practical implications for mechanism design, suggesting that hardware-backed forgetting can serve as a cost-effective substitute for traditional legal enforcement while enabling novel coordination opportunities.

Abstract

In the neon-lit nights of 2026, Johnson \& Johnson unveiled X. A pill, not larger than a snowflake, that promised a tempest of change. This miraculous drug didn't just allow people to cherry-pick memories to erase from their minds, it could also leave a reminder of this erasure in the minds of those who ingested it. Amidst the iconic red-bricked walls of Harvard Law, you, with books in one hand and dreams in the other, are on a mission. You are not just another student; you carry the hope of revolutionizing the archaic chambers of the legal world. Each night, as you pore over the tomes of law, you wonder what greatness society can achieve. On a cold evening, your phone buzzes. It's Dex, your old college friend turned underground dealer. His message is simple: ``Got X. Special price for you.'' The temptation swirls around you. Would you trade the lessons of the past for a clearer, yet incomplete future? The decision rests in your hands. We explore the game theoretic implications of a technology (such as TEEs) that allows agents to commit to forget information and discuss several applications.

Figures (5)

• Figure 1: The original game (left): player $1$ chooses between actions A and B and player between actions $a$ and $b$. In the modified game where the second player has access to $X$ (right), the second player can choose to take $X$ which makes him forget whether the first action taken is $A$ or $B$.
• Figure 2: An instantiation of Arrow's information paradox and it's solution with $X$: Nature chooses a state of the world $\omega\in\{\omega_1,\omega_2,\omega_3,\omega_4\}$ and reveals it to player $2.$ Player $1$ needs to take an action A or B. Suppose e.g. if the state of the world is $\omega_1$ then it is optimal for him to choose $A$ and if the state of the world is $\omega_2$ and it is optimal for him to choose $B$. If the state $\omega_3$ or $\omega_4$, it doesn't matter whether he takes action $A$ or $B$. However, knowing whether the state is $\omega_3$ or $\omega_4$ can be relevant to a third party, so that knowing the state has still value (but the same value in either state) for player $2$. In the modified game where the second player has access to $X$, the second player can choose to take $X$ which makes him forget the state that was previously revealed by player $1$ in case that he rejects to buy that information. This introduces the red information set. For appropriate payoffs, the contract has the depicted (highlighted in yellow) subgame perfect equilibrium.
• Figure 3: Continuation of the game tree from the previous page.
• Figure 4: Part of the game tree of a discrete version of the bargaining game: after the initial stages of nature choosing types and of the players making offer and counter-offer (not depicted), Player $1$ can take $X$ (not knowing Player 2's type). Taking $X$ makes him subsequently forget the number of times the concessions game has already been repeated (For readability, information sets of Player $2$ are not depicted).
• Figure 5: The original game (left): the entrant remembers after entrance that he has entered the market. The modified game (right): the entrant can choose to take $X$ after entrance which makes him forget whether he has entered the market.