One-shot deviation principle¶

A sequential-game criterion stating that a strategy profile is subgame-perfect when no player can gain by changing one action at one information point and then returning to the prescribed strategy.

Version: v1 · 2026-09-08 · History
Domain-specific #: 5872
Origin domain: dynamic game theory
Subdomain: dynamic game theory

Core Idea¶

The principle holds for finite-horizon games and suitable discounted infinite-horizon games with continuity conditions; it reduces an enormous strategy comparison to local deviations in every subgame. Backward or dynamic consistency means any profitable multi-stage deviation has a last or first profitable local component, so ruling out every one-shot change rules out larger deviations under the theorem's assumptions. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application¶

One-shot deviation principle belongs to dynamic game theory and is useful where the analyst can specify the typed dynamic game theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the extensive-form game, information and perfect-recall assumptions, horizon or discounting conditions, strategy profile, every subgame or information set, one-action deviation and continuation strategy and payoff comparison are explicit. The scope is broad within that domain but bounded by the need for the extensive-form game, information and perfect-recall assumptions, horizon or discounting conditions, strategy profile, every subgame or information set, one-action deviation and continuation strategy and payoff comparison are explicit.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the extensive-form game, information and perfect-recall assumptions, horizon or discounting conditions, strategy profile, every subgame or information set, one-action deviation and continuation strategy and payoff comparison are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to One-shot deviation principle. One-shot deviation principle compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: the typed dynamic game theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the extensive-form game, information and perfect-recall assumptions, horizon or discounting conditions, strategy profile, every subgame or information set, one-action deviation and continuation strategy and payoff comparison are explicit independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of dynamic game theory because they reuse the typed dynamic game theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Backward or dynamic consistency means any profitable multi-stage deviation has a last or first profitable local component, so ruling out every one-shot change rules out larger deviations under the theorem's assumptions., and type the carrier, state every parameter and convention in the definition, test that the extensive-form game, information and perfect-recall assumptions, horizon or discounting conditions, strategy profile, every subgame or information set, one-action deviation and continuation strategy and payoff comparison are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction One-shot deviation principle Domain-specific

Parents (1) — more general patterns this builds on

One-shot deviation principle is a kind of Local Optimum Prime

The proposed strict upward parent is prime:local_optimum.

Hierarchy paths (2) — routes to 2 parentless roots

One-shot deviation principle → Local Optimum → Optimization Landscape

Show alternative path (1)

Neighborhood in Abstraction Space¶

One-shot deviation principle sits in a crowded region of the domain-specific corpus (15^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Unclustered & Miscellaneous (1565 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08