[Paper Review] Continuation-Performance Decomposition in Dynamic Games with Irreversible Failure

Nicholas H. Kirk|arXiv (Cornell University)|Feb 8, 2026

Game Theory and Applications0 citations

TL;DR

The paper introduces continuation–performance decomposition (CPD) for dynamic games with absorbing failure, showing continuation and performance must be evaluated lexicographically; it proves CPD equivalence to large-penalty payoff limits and discusses viability and bank-run applications.

ABSTRACT

Once failure is irreversible, continuation payoffs cannot be meaningfully aggregated across strategies that differ in their survival properties. Standard scalar evaluation sidesteps this by arbitrarily completing payoffs beyond termination, but such completions are extrinsic to the game form. This paper introduces continuation-performance decomposition (CPD), proving that any evaluation satisfying natural regularity conditions, such as failure-completion invariance, survival locality, and local expected-utility coherence -- must separate continuation from performance lexicographically. Continuation priority thus emerges as a consequence of well-posed evaluation, not as a behavioral assumption. We establish equivalence between CPD and the limit of games with diverging failure penalties, show that viability is a game-form invariant independent of payoffs, and apply the framework to bank runs: preemptive withdrawals reflect rational viability vetoes rather than coordination failure when continuation is distributively asymmetric. CPD resolves a representational problem, not a preference problem.

Motivation & Objective

• Motivate the problem: irreversible failure makes continuation payoffs ill-posed under standard scalar evaluation.
• Propose a representation that separates continuation from performance to restore intrinsic evaluation.
• Characterize the canonical intrinsic evaluation under failure and show its lexicographic structure.
• Demonstrate equivalence to large-penalty payoff limits and discuss viability and bank-run implications.

Proposed method

• Define dynamic game form with absorbing failure and random failure time T.
• Introduce continuation profile C(σ) and conditional continuation payoff Ũi(σ).
• Form CPD as a static normal-form evaluation using (C(σ), Ũi(σ)) with lexicographic ordering.
• Impose intrinsicness constraints: failure-completion invariance, survival locality, and local expected-utility coherence.
• Prove canonical decomposition: CPD arises from these constraints and tail- vs. performance-separation.
• Establish equivalence to large-penalty payoff games and analyze viability and information sensitivity.

Experimental results

Research questions

• RQ1 How can dynamic games with absorbing failure be evaluated intrinsically without extrinsic payoff completion?
• RQ2 Does a canonical continuation–performance decomposition (CPD) exist under natural intrinsicness and locality conditions?
• RQ3 How does CPD relate to limits of games with diverging failure penalties?
• RQ4 What structural properties (viability, information sensitivity) follow from CPD in practical models like bank runs?

Key findings

• An intrinsic evaluation rule under irreversible failure implies a lexicographic separation between continuation (tail) and conditional performance.
• CPD exists and is equivalent to the limit of games with diverging failure penalties (penalty-limit equivalence).
• Viability-preserving strategies are invariant to payoffs and game form, ensuring non-viable outcomes imply termination with failure.
• Unconditional scalar aggregation is non-intrinsic for absorbing failure; CPD avoids this by restricting payoff aggregation to continuation-defined domains.
• Local equivalence shows CPD reduces to standard expected utility on continuation ties.
• Under large penalties, CPD converges to Nash equilibria of the CPD representation (equilibrium correspondence).