arXiv subjects

Thomas Pitz

Publications and source records attributed to Thomas Pitz.

3 recordsLinked to original sources

arXiv2026

Extended Scenario Bundle Analysis: A Formal Framework for Strategic Scenario Modeling

Strategic crisis analysis needs representations that combine qualitative expert judgement, explicit interdependence, and auditable update rules without requiring fully specified payoffs or probabilities. Scenario Bundle Analysis (SBA), developed by Amos Perlmutter and Reinhard Selten, provides such a starting point, but the original formulation leaves several database, topology, and update interfaces implicit. This paper presents a formal refinement and extension of the original SBA framework, introducing a two-layer architecture that separates a static scenario database from a dynamic scenario tree system. The extended framework incorporates a richer attitude vocabulary: beliefs, desires, intentions, fears, and coalitional commitments, with expectations treated as doxastic attitudes. It also adds a domain/modifier layer for contextual framing, a topology on admissible scenario spaces\index{Scenario space}, typed assessment-state updates, and multi-criteria evaluation. Mathematical definitions are stated with sufficient precision to support computational implementation.

econ.TH↗

arXiv2026

Timing, Entry, and Revenue in Clock-Based Platform Markets

On platforms where time-to-contract is itself payoff-relevant--Aalsmeer's flower auctions, ride-hailing dispatch, on-demand-labor matching--the textbook revenue equivalence between Dutch and first-price formats holds the trading outcome fixed. Once participation is endogenous and both sides bear waiting costs, the trading format directly shapes who enters, market thickness, volume, and platform revenue. The platform's ranking of the descending clock against immediate and batched posted-price benchmarks is decided by two estimable primitives on each side of the market: an earnings gap and a timing gap. A bidirectional four-case classification identifies when the descending clock dominates at every level of waiting costs, only above a floor, only below a ceiling, or not at all; the last case is unconditional -- when the descending clock charges no more per trade and contracts no faster than the posted-price benchmark, it cannot win. No format admits a universal ranking. The local verdict propagates through endogenous entry, and cross-side complementarity amplifies shared local advantages into joint dominance. A conditional revenue theorem converts entry and volume gains into a platform-revenue ranking. In calibrated parameterizations the revenue-ranking switching boundary lies near $p_0/\bar v\approx 1$, inside the empirical range for ride-hailing platforms. A measurement protocol provides explicit nonparametric estimators for the six reduced-form objects and a test statistic for the dominance condition, and a Lean~4 formalization audits the algebraic and order-theoretic content. In markets where goods or services cannot wait, the speed of the trading mechanism is a primitive of market design.

econ.TH↗

arXiv2026

Cohesion-Sensitive Power Indices: Representation Results for Banzhaf and Shapley Values

In many applications of cooperative game theory -- from corporate governance and cartel formation to parliamentary voting -- not all winning coalitions are feasible. Ideological distances, institutional constraints, or pre-electoral agreements may render certain coalitions implausible. Classical power indices ignore this and weight all winning coalitions equally. We introduce cohesion structures to quantify coalition feasibility and axiomatically characterize two families of cohesion-sensitive power indices, represented as expected marginal contributions under Luce-type distributions. In the Banzhaf branch, coalition weights are a power transformation of cohesion; in the Shapley branch, additional axioms separate size from cohesion, recovering the classical size weights with cohesion acting within each size class. All results have been mechanically verified in Lean 4 with Mathlib. We illustrate the framework on the German Bundestag and the French Assembl\'ee Nationale, where cordon sanitaire and double cordon scenarios produce sharp, interpretable power shifts.

econ.TH↗