{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T11:40:36Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 21.0, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a0956a-3349-77d2-bfd0-5f953fc8ffad\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: non-cooperative game\nSense to describe: (none recorded)\nDomain code: ACT.ACT\nAlso known as: (none)\n\n\nContext for this batch of 1001 things:\n# Batch 044:", "usd": 0.0, "recall": true }, "codex": { "seconds": 76.5, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a0956a-3339-7fb3-8a59-c910a820ae28\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: non-cooperative game\nRegistry id: vr.tr.non-cooperative-game\nPlane / domain: ACT / ACT.ACT\nRegistry definition: (none recorded)\nNames folded into thi" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T12:00:00Z", "ingestedAt": "2026-10-06T08:41:10+00:00", "fields": [ "agent_conduct", "ethics", "owners" ] }, "gate": { "passed": true, "version": "1.0", "at": "2026-10-07T10:10:26+00:00", "evidence": [ "completeness 1.00", "sense: Wikidata description", "2 live sources", "review by codex: pass" ] } }, "metaModel": { "id": "THING-Q13422573", "registryId": "vr.tr.non-cooperative-game", "name": "non-cooperative game", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "ACT.ACT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q13422573/", "model": { "registry_id": "vr.tr.non-cooperative-game", "name": "non-cooperative game", "purpose": "Enable an agent to recognise a non-cooperative game, assess whether its strategic assumptions and solution claims are justified, and determine which analyses or interventions those assumptions support.", "definition": "A non-cooperative game is a mathematical model of strategic interaction that specifies individual players, their available strategies and preferences over outcomes, with any agreements and their enforcement represented within the game rather than assumed as externally binding coalition commitments.", "scope_statement": "This model owns the representation of strategic interaction through individual players, feasible strategies, information and preferences, with agreements and enforcement represented within the game when relevant; it also owns the assumptions and limits of claims about strategic behaviour.", "in_scope": [ "Players, decision rights, feasible actions and complete contingent strategies", "Move order, information sets, private types, beliefs and chance events", "Outcomes, preferences, utility representations and payoff dependencies", "Communication, commitments and enforcement represented as strategic mechanisms", "Solution concepts, equilibrium claims and their supporting assumptions", "Sensitivity of strategic conclusions to representation and behavioural assumptions" ], "out_of_scope": [ "Cooperative-game primitives such as coalition values and allocations independent of an explicit strategic protocol", "Standalone optimisation problems without strategic interdependence", "Detailed models of the institutions or physical systems in which play occurs", "Mechanism-design objectives and the wider search for desirable game rules", "General theories of cognition, learning or collective action beyond their specified role in play" ], "distinguishing_features": [ "A player's preferred action depends on choices available to other players, distinguishing strategic interaction from a standalone decision problem.", "The representation specifies individual strategies and how their combination determines outcomes, rather than starting solely from coalition values.", "An agreement affects strategic conclusions through specified commitment, enforcement or incentive conditions; its effectiveness cannot be assumed merely because players agree.", "The label does not require hostility, zero-sum payoffs or absence of communication: mutually beneficial cooperation may occur through individually chosen strategies.", "A game remains a non-cooperative game even when no equilibrium has been selected or computed; the interaction and its solution claim are separate records." ], "characteristics": [ { "name": "Player population", "kind": "category", "unit_or_values": "Finite identified players, population classes or an explicitly defined continuum", "why_it_matters": "Determines whose deviations count and which mathematical or computational methods apply." }, { "name": "Strategic representation", "kind": "category", "unit_or_values": "Strategic form, extensive form, Bayesian specification, stochastic game or an explicitly related combination", "why_it_matters": "Determines which timing, information and contingency distinctions are preserved." }, { "name": "Strategic interdependence", "kind": "relation", "unit_or_values": "Dependencies from other players' choices to a player's feasible actions, information or outcome ranking", "why_it_matters": "Identifies the strategic relationships that justify modelling the situation as a game." }, { "name": "Information conditions", "kind": "category", "unit_or_values": "Perfect or imperfect information; complete or incomplete information; specified recall and observability", "why_it_matters": "Separates uncertainty about prior moves from uncertainty about payoff-relevant characteristics." }, { "name": "Payoff representation", "kind": "category", "unit_or_values": "Ordinal rankings, expected-utility values, monetary outcomes with an explicit utility mapping, or another stated criterion", "why_it_matters": "Prevents numerical payoffs from silently introducing unsupported risk preferences or interpersonal comparisons." }, { "name": "Interaction horizon", "kind": "category", "unit_or_values": "One-shot, finite repeated, indefinite repeated or infinite horizon", "why_it_matters": "Changes the opportunities for contingent rewards, punishments and learning." }, { "name": "Commitment and enforcement", "kind": "relation", "unit_or_values": "Links among commitments, feasible deviations, monitoring parties and consequences", "why_it_matters": "Determines whether promises constrain future choices or only influence expectations." }, { "name": "Solution assessment", "kind": "state", "unit_or_values": "Unanalysed, candidate, verified under stated assumptions, refuted or unresolved", "why_it_matters": "Separates a proposed strategic outcome from a supported solution claim." }, { "name": "Maximum unilateral deviation gain", "kind": "measurement", "unit_or_values": "Per-player utility units under a stated strategy profile and solution test", "why_it_matters": "Measures how closely a candidate satisfies a specified unilateral-deviation criterion without assuming utility is comparable across players." } ], "affordances": [ "Construct a strategic or extensive-form representation from an interaction description and expose missing primitives.", "Test candidate strategies for profitable unilateral deviations under stated information and beliefs.", "Compare solution concepts and identify which behavioural or credibility assumptions change the conclusions.", "Evaluate how communication, monitoring or enforcement changes feasible strategies and incentives.", "Analyse sensitivity to payoff estimates, private information, move order and interaction horizon.", "State the observations needed to distinguish competing representations or behavioural predictions." ], "agent_conduct": { "may": [ "Explain non-cooperative games, equilibria and their assumptions, citing game theory sources.", "Build and solve game models for analysis the user has asked for." ], "must_not": [ "Present a model's equilibrium as a prediction of what real people will do without evidence.", "Use game models to design collusion, price fixing or market manipulation.", "Hide the assumptions that drive a model's results.", "Present game theory results as justifying harm to people." ], "requires_human": [ "Using model results in policy, pricing or negotiation decisions that affect people." ] }, "ethics": { "considerations": [ "Models can be used to justify policies that harm people while seeming neutral.", "Strategic models in markets can facilitate collusion." ], "affected_parties": [ "People affected by policies", "Market participants" ] }, "owners": { "steward": "Nobody owns the concept; game theorists study it.", "master_systems": [] }, "what_it_is_for": [ "Non-cooperative games are used in economics, political science and computer science to analyse strategic choices among independently acting participants.", "They support the study of auctions, bargaining, competition and coordination when incentives and agreement enforcement must be represented explicitly." ], "failure_modes_and_hazards": [ "Incorrect assumptions about participants' preferences or information can produce misleading predictions.", "Treating an equilibrium as a guaranteed outcome can support poorly justified decisions.", "Ignoring enforcement, unequal bargaining power or effects on outsiders can conceal harmful consequences." ], "facets_not_applicable": { "interfaces": "No generally applicable standard, law or official classification governs the mathematical concept itself.", "recognition": "A non-cooperative game is an abstract mathematical model without an intrinsic perceptible appearance." } }, "sources": [ { "id": "wikidata", "title": "Wikidata item Q13422573: non-cooperative game", "url": "https://www.wikidata.org/wiki/Q13422573", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" }, { "id": "wikipedia-en", "title": "Wikipedia: Non-cooperative game theory", "url": "https://en.wikipedia.org/wiki/Non-cooperative_game_theory", "url_status": "live", "what_it_supports": "general description of the item", "checked_by": "wikidata-api sitelink" } ], "structure": { "bundles": [ { "id": "non-cooperative-boundary", "name": "Non-cooperative boundary", "description": "Establish what makes the represented interaction a non-cooperative game and what interpretation of that label is being used.", "rationale": "The label is easily confused with antagonistic behaviour or the impossibility of cooperation.", "layers": [ { "id": "definition-and-tradition", "name": "Definition and tradition", "description": "Record the adopted definition and how it treats individual choice and agreements.", "findings": [ { "id": "adopted-non-cooperative-meaning", "name": "Adopted non-cooperative meaning", "description": "Identify whether the account emphasises individual strategic choice, the treatment of binding agreements, or an explicit implementation of cooperative arrangements.", "questions": [ { "text": "Which definition of non-cooperative game is adopted, and which source or theoretical tradition supports it?", "kind": "provenance", "id": "adopted-non-cooperative-meaning-q01" }, { "text": "How does this definition treat agreements that are binding because an enforcement mechanism is represented?", "kind": "boundary", "id": "adopted-non-cooperative-meaning-q02" } ] } ] }, { "id": "strategic-instance-boundary", "name": "Strategic instance boundary", "description": "Identify the interaction being modelled and distinguish its strategic structure from its social interpretation.", "findings": [ { "id": "interdependence-and-cooperation", "name": "Interdependence and cooperation", "description": "Locate dependencies among individual choices and allow aligned interests or cooperative outcomes without changing the game's classification.", "questions": [ { "text": "Whose best choice can change when another player's strategy changes?", "kind": "definition", "id": "interdependence-and-cooperation-q01" }, { "text": "Is cooperation an available behaviour within this game, or is the representation instead built from coalition values and allocation rules?", "kind": "boundary", "id": "interdependence-and-cooperation-q02" } ] } ] } ] }, { "id": "players-strategies-and-outcomes", "name": "Players, strategies and outcomes", "description": "Specify who chooses, what each player can choose and how choices produce consequences.", "rationale": "A strategic claim cannot be assessed without a precise account of feasible choices and outcome dependencies.", "layers": [ { "id": "players-and-decision-rights", "name": "Players and decision rights", "description": "Determine the decision-making units and the scope of their control.", "findings": [ { "id": "player-identification", "name": "Player identification", "description": "Record the justification for treating a person, organisation or other decision-making unit as one player.", "questions": [ { "text": "Which entities are players, and which decisions does each control independently?", "kind": "definition", "id": "player-identification-q01" }, { "text": "If an organisation is represented as one player, which internal conflicts or delegation problems are being abstracted away?", "kind": "boundary", "id": "player-identification-q02" } ] } ] }, { "id": "contingent-choice-and-consequences", "name": "Contingent choice and consequences", "description": "Connect feasible actions and contingent strategies to outcomes and preferences.", "findings": [ { "id": "strategy-payoff-specification", "name": "Strategy and payoff specification", "description": "Distinguish an action at a decision point from a complete contingent strategy and specify the resulting outcome evaluation.", "questions": [ { "text": "What must a strategy specify at every decision point available to its player, including points not reached in the proposed play?", "kind": "definition", "id": "strategy-payoff-specification-q01" }, { "text": "How do strategy profiles and chance events determine outcomes, and how does each player rank those outcomes or lotteries?", "kind": "measurement", "id": "strategy-payoff-specification-q02" }, { "text": "Which constraints are genuine restrictions on feasible actions, and which are merely costly actions encoded in payoffs?", "kind": "boundary", "id": "strategy-payoff-specification-q03" } ] } ] } ] }, { "id": "timing-information-and-beliefs", "name": "Timing, information and beliefs", "description": "Represent the sequence of decisions and the knowledge available when each choice is made.", "rationale": "Apparently identical payoff situations can have different strategic implications when observability, private information or timing changes.", "layers": [ { "id": "move-order-and-observability", "name": "Move order and observability", "description": "Specify decision histories, information sets and recall.", "findings": [ { "id": "decision-information", "name": "Decision information", "description": "Record what a player can distinguish when choosing, rather than inferring knowledge from chronological order alone.", "questions": [ { "text": "Which moves precede each decision, and which of those moves can the deciding player observe?", "kind": "definition", "id": "decision-information-q01" }, { "text": "Which histories belong to the same information set, and does the representation assume players remember their earlier information and choices?", "kind": "definition", "id": "decision-information-q02" } ] } ] }, { "id": "private-types-and-belief-revision", "name": "Private types and belief revision", "description": "Specify uncertainty about payoff-relevant characteristics and beliefs about events or other players.", "findings": [ { "id": "belief-foundations", "name": "Belief foundations", "description": "Distinguish specified distributions, player beliefs and analyst uncertainty, including belief requirements at unreached information sets.", "questions": [ { "text": "Which characteristics are privately known, and what prior distributions or player-specific beliefs are assumed about them?", "kind": "definition", "id": "belief-foundations-q01" }, { "text": "Which observations update beliefs, and what restrictions does the selected solution concept impose after events assigned zero probability?", "kind": "boundary", "id": "belief-foundations-q02" }, { "text": "What evidence supports the information and belief assumptions rather than merely making the analysis tractable?", "kind": "provenance", "id": "belief-foundations-q03" } ] } ] } ] }, { "id": "agreements-commitment-and-repetition", "name": "Agreements, commitment and repetition", "description": "Explain how communication and continuing interaction can support or fail to support coordinated behaviour.", "rationale": "Non-cooperative analysis must account for why players would honour an arrangement and whether its consequences are feasible and credible.", "layers": [ { "id": "communication-and-enforcement", "name": "Communication and enforcement", "description": "Distinguish messages from commitments and model the strategic role of enforcement.", "findings": [ { "id": "agreement-implementation", "name": "Agreement implementation", "description": "Record how an agreement changes information, available actions or consequences, including the role of any enforcing party.", "questions": [ { "text": "Can messages directly alter payoffs or feasible actions, or do they operate only through the information and expectations they convey?", "kind": "definition", "id": "agreement-implementation-q01" }, { "text": "Who detects and penalises a breach, and what makes that enforcement feasible and credible?", "kind": "action", "id": "agreement-implementation-q02" } ] } ] }, { "id": "continuation-and-history", "name": "Continuation and history", "description": "Represent repeated interaction, monitoring and dependence of future actions on past play.", "findings": [ { "id": "intertemporal-incentives", "name": "Intertemporal incentives", "description": "Identify the horizon and continuation incentives needed for proposed rewards, punishments or reputational effects.", "questions": [ { "text": "What horizon, continuation probability or discounting convention governs the value of future outcomes?", "kind": "measurement", "id": "intertemporal-incentives-q01" }, { "text": "Which deviations can players detect, and are the proposed responses optimal when the histories triggering them occur?", "kind": "action", "id": "intertemporal-incentives-q02" } ] } ] } ] }, { "id": "solution-claims-and-validation", "name": "Solution claims and validation", "description": "Assess what a proposed solution establishes and how reliably it applies to the represented interaction.", "rationale": "Equilibrium, prediction and recommendation require different evidence and must not be treated as interchangeable.", "layers": [ { "id": "solution-concept-and-verification", "name": "Solution concept and verification", "description": "Attach each candidate solution to explicit optimality, belief and credibility requirements.", "findings": [ { "id": "candidate-solution-test", "name": "Candidate solution test", "description": "Record the chosen concept, relevant strategy class, verification method and any unresolved multiplicity or existence issue.", "questions": [ { "text": "Which solution concept is claimed, and why is it appropriate to this game's timing and information structure?", "kind": "definition", "id": "candidate-solution-test-q01" }, { "text": "Which unilateral deviations and, where required, continuation and belief conditions have been checked?", "kind": "measurement", "id": "candidate-solution-test-q02" }, { "text": "Does the analysis establish existence, identify one candidate, enumerate solutions or justify a selection among multiple solutions?", "kind": "boundary", "id": "candidate-solution-test-q03" } ] } ] }, { "id": "prediction-robustness-and-use", "name": "Prediction, robustness and use", "description": "Connect formal results to observations and decisions without silently adding behavioural assumptions.", "findings": [ { "id": "supported-strategic-conclusions", "name": "Supported strategic conclusions", "description": "Separate mathematically verified properties from empirical expectations and recommendations sensitive to modelling choices.", "questions": [ { "text": "What observations would support or challenge the proposed behaviour, and can they distinguish it from other equilibria or learning processes?", "kind": "measurement", "id": "supported-strategic-conclusions-q01" }, { "text": "Which conclusions survive plausible changes in payoffs, information, rationality assumptions and equilibrium selection?", "kind": "boundary", "id": "supported-strategic-conclusions-q02" }, { "text": "Which analyses or interventions are supported now, and which require additional information about the players or interaction?", "kind": "action", "id": "supported-strategic-conclusions-q03" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-confidence-notes", "name": "Check these first", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Non-cooperative describes the modelling framework, not necessarily hostile behaviour or an absence of cooperation.", "The listed kinds overlap: representation, information structure and temporal structure are separate classification dimensions.", "Recall-based account; no sources were consulted, and the registry's intended sense was not supplied." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of non-cooperative game this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-kinds", "name": "Kinds and varieties", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Normal-form games", "Extensive-form games", "Complete-information games", "Incomplete-information or Bayesian games", "Repeated games", "Stochastic games" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of non-cooperative game this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-real-world-use", "name": "Real-world use", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Analysing firms' pricing, output and market-entry decisions.", "Designing auctions and mechanisms that account for participants' strategic incentives.", "Studying bargaining, negotiation and international conflict.", "Modelling contributions to public goods and use of shared resources.", "Analysing strategic behaviour in communication networks and multi-agent systems." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of non-cooperative game this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-measurements", "name": "Typical measurements", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "quantity": "Number of players", "typical_range": "Usually two or more; some models use a continuum of players.", "unit": "players" }, { "quantity": "Payoff", "typical_range": "Model-dependent; utility representations need not have comparable scales across players.", "unit": "utility units or a specified outcome unit" }, { "quantity": "Unilateral deviation gain at a strategy profile", "typical_range": "Zero for every player at a Nash equilibrium; at most epsilon for every player at an epsilon-Nash equilibrium.", "unit": "the relevant player's payoff units" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of non-cooperative game this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-failure-modes-and-hazards", "name": "Failure modes and hazards", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Multiple equilibria can leave predictions indeterminate without additional selection assumptions.", "An equilibrium need not be socially efficient, fair or collectively desirable.", "Incorrect assumptions about information, preferences or available actions can undermine conclusions.", "Nash equilibria in dynamic games can depend on non-credible threats unless an appropriate refinement is imposed.", "Equilibrium analysis alone does not establish whether players can learn or compute the predicted behaviour." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of non-cooperative game this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-neighbours", "name": "Neighbouring kinds and how to tell them apart", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "name": "Cooperative game", "difference": "Typically models coalition possibilities and allocations directly; a non-cooperative game specifies individual strategic choices and models enforcement explicitly." }, { "name": "Zero-sum game", "difference": "Requires players' payoffs to sum to zero at every outcome; non-cooperative games also include interactions with shared gains or losses." }, { "name": "Nash equilibrium", "difference": "A solution concept identifying strategy profiles with no profitable unilateral deviation, rather than a game itself." }, { "name": "Decision problem", "difference": "Concerns one decision maker facing circumstances or uncertainty; a strategic game includes other decision makers whose choices affect outcomes." }, { "name": "Mechanism design", "difference": "Chooses rules to induce desired strategic outcomes, whereas a game specifies the interaction to be analysed." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of non-cooperative game this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which reference definition should anchor the registry entry, particularly where accounts differ in their treatment of binding agreements and endogenous enforcement?", "Does an existing Vercy world model already own this concept or the general strategic-game primitives that this entry should reference?", "Should evolutionary and other non-deliberative interpretations be included directly or linked as neighbouring models with different behavioural foundations?", "How should the model distinguish uncertainty about the game itself from private information represented inside a game?", "Which operational standards should govern approximate equilibrium claims when strategy spaces are large or continuous and payoff scales differ across players?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 16, "questions": 30 } }