From Scalar Utility to Profile-State Utility: A Regime-Conditional Upgrade for Market Game Theory
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| Format: | Recurso digital |
| Language: | English |
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Zenodo
2026
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| _version_ | 1866901729934573568 |
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| author | Fathi, Kevin |
| author_facet | Fathi, Kevin |
| contents | <p>Game theory typically represents payoffs with a scalar utility function and compares outcomes<br>by maximizing a single number. In modern markets, however, the outcomes of strategic<br>interaction are often structural : concentration profiles, winner-take-all tails, cross-domain lock-in,<br>and dynamic fragility. Collapsing these features into a scalar invites three failures: (i) the<br>numerology trap (arbitrary cardinal codings of ordinal categories), (ii) regime error (using a<br>universal scalar proxy—such as entropy—when it can invert inequality signals in stabilized<br>multiplicative environments), and (iii) flattening (erasing dependence across dimensions of<br>market power). This paper proposes an upgrade in which the primitive payoff object is a profile<br>distribution p ∈ ∆n−1 induced by actions, evaluated by a regime-conditional structural state<br>vector Ψ(p) = (Regime A score; Regime B scores; dependence; tail stability ). We show how<br>this object switch remains compatible with equilibrium analysis by (i) defining best responses<br>through undominated improvements under partial orders, and (ii) introducing an explicit, declared<br>scalarization only when prediction requires single-valued choices. A worked Bertrand example<br>computes the induced share profile under two competitive regimes and shows how majorization<br>and the regime-conditional coordinates change what is “visible” to the theory.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18237814 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | From Scalar Utility to Profile-State Utility: A Regime-Conditional Upgrade for Market Game Theory Fathi, Kevin game theory ordinal aggregation majorization Lorenz order entropy copula entropy tail risk profile-state utility regime-conditional analysis market concentration restoring-force dominance declared scalarization <p>Game theory typically represents payoffs with a scalar utility function and compares outcomes<br>by maximizing a single number. In modern markets, however, the outcomes of strategic<br>interaction are often structural : concentration profiles, winner-take-all tails, cross-domain lock-in,<br>and dynamic fragility. Collapsing these features into a scalar invites three failures: (i) the<br>numerology trap (arbitrary cardinal codings of ordinal categories), (ii) regime error (using a<br>universal scalar proxy—such as entropy—when it can invert inequality signals in stabilized<br>multiplicative environments), and (iii) flattening (erasing dependence across dimensions of<br>market power). This paper proposes an upgrade in which the primitive payoff object is a profile<br>distribution p ∈ ∆n−1 induced by actions, evaluated by a regime-conditional structural state<br>vector Ψ(p) = (Regime A score; Regime B scores; dependence; tail stability ). We show how<br>this object switch remains compatible with equilibrium analysis by (i) defining best responses<br>through undominated improvements under partial orders, and (ii) introducing an explicit, declared<br>scalarization only when prediction requires single-valued choices. A worked Bertrand example<br>computes the induced share profile under two competitive regimes and shows how majorization<br>and the regime-conditional coordinates change what is “visible” to the theory.</p> |
| title | From Scalar Utility to Profile-State Utility: A Regime-Conditional Upgrade for Market Game Theory |
| topic | game theory ordinal aggregation majorization Lorenz order entropy copula entropy tail risk profile-state utility regime-conditional analysis market concentration restoring-force dominance declared scalarization |
| url | https://doi.org/10.5281/zenodo.18237814 |