Continuation-Performance Decomposition in Dynamic Games with Irreversible Failure

TL;DR

This paper introduces continuation-performance decomposition (CPD) for dynamic games with irreversible failure, clarifying how continuation and performance are evaluated separately under natural conditions.

Contribution

It proves that any natural evaluation must separate continuation from performance, establishing CPD as a fundamental decomposition in such games.

Findings

CPD is equivalent to the limit of games with diverging failure penalties.

Viability is a game-form invariant, independent of payoffs.

Application to bank runs shows preemptive withdrawals reflect rational viability vetoes.

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.