arXiv subjects

Paul S. Koh

Publications and source records attributed to Paul S. Koh.

6 recordsLinked to original sources

arXiv2026

Demand Curvature and Pass-Through in Multiproduct Oligopoly

Economic interventions change firms' pricing incentives, but their effects depend on how those incentives propagate across products and firms. This paper develops tractable characterizations of that propagation under multiproduct Bertrand competition. A decomposition of the pricing system isolates demand curvature, substitution, and ownership, linking the equilibrium response matrix to commonly used empirical demand models. It yields approximations with explicit error bounds and separates individual adjustment from equilibrium feedback. Small-share limits reveal when interactions disappear and when substitution within nests or selection among heterogeneous consumers preserves them. For nested logit, a closed-form response reduces the limiting product-level system to averages within firm--nest groups, exposing the direction of price spillovers. The same framework organizes local responses to changes in costs, demand, and ownership. The results clarify which features of demand support simple incidence predictions and which interactions those predictions must retain.

econ.GN↗

arXiv2026

Estimating Discrete Games of Complete Information: Bringing Logit Back in the Game

Discrete games are central tools for empirical analysis of strategic interaction, but equilibrium multiplicity and partial identification often make them computationally difficult to estimate. This paper develops tractable methods for estimation and inference in complete-information discrete games. The key idea is to construct an outer set by comparing observed frequencies of action profiles with singleton-class generalized likelihoods: model-implied probabilities that those profiles can arise as equilibria. The resulting conditional moment inequalities avoid computationally expensive equilibrium enumeration, numerical simulation, and grid search. Under standard empirical assumptions used in discrete-game models, including logit payoff shocks, these restrictions have closed-form expressions and are convex in a subvector of structural parameters. I develop the approach for both unordered and ordered action spaces. Monte Carlo experiments and empirical applications show that the methods deliver informative outer sets and can reduce computation time by several orders of magnitude relative to existing approaches.

econ.EM↗

arXiv2025

Market Definition: A Sensitivity Analysis

Market definition holds significant importance in antitrust cases, yet achieving consensus on the correct approach remains elusive. As a result, analysts routinely entertain multiple market definitions to ensure the resilience of their conclusions. I propose a simple framework for conducting organized sensitivity analysis with respect to market definition. I model candidate market definitions as partially ordered and use a Hasse diagram, a directed acyclic graph representing a finite partial order, to summarize the sensitivity analysis. I use the Shapley value and the Shapley-Shubik power index to quantify the average marginal contribution of each firm in driving the conclusion. I illustrate the method's usefulness with an application to the Albertsons/Safeway (2015) merger.

econ.GN↗

arXiv2025

Concentration-Based Inference for Evaluating Horizontal Mergers

Antitrust authorities routinely rely on market concentration measures to assess the potential adverse effects of mergers on consumer welfare. Using a first-order approximation argument with logit and CES demand, I derive the relationship between the welfare effect of a merger on consumer surplus and the change in the Herfindahl-Hirschman Index (HHI). My results suggest that merger harm is correlated with the merger-induced change in HHI, and the proportionality coefficient depends on the price responsiveness parameter, market size, and the distribution of market shares within and across the merging firms. I present numerical validation of my formula along with an empirical illustration.

econ.GN↗

arXiv2025

Merger Analysis with Unobserved Prices

Standard empirical tools for merger analysis assume price data, which are often unavailable. I characterize sufficient conditions for identifying the unilateral effects of mergers without price data using the first-order approach and merger simulation. Data on merging firms' revenues, margins, and revenue diversion ratios are sufficient to identify their gross upward pricing pressure indices and compensating marginal cost reductions. Standard discrete-continuous demand assumptions facilitate the identification of revenue diversion ratios as well as the feasibility of merger simulation in terms of percentage change in price. I apply the framework to the Albertsons/Safeway (2015) and Staples/Office Depot (2016) mergers.

econ.EM↗

arXiv2023

Stable Outcomes and Information in Games: An Empirical Framework

Empirically, many strategic settings are characterized by stable outcomes in which players' decisions are publicly observed, yet no player takes the opportunity to deviate. To analyze such situations in the presence of incomplete information, we build an empirical framework by introducing a novel solution concept that we call Bayes stable equilibrium. Our framework allows the researcher to be agnostic about players' information and the equilibrium selection rule. The Bayes stable equilibrium identified set collapses to the complete information pure strategy Nash equilibrium identified set under strong assumptions on players' information. Furthermore, all else equal, it is weakly tighter than the Bayes correlated equilibrium identified set. We also propose computationally tractable approaches for estimation and inference. In an application, we study the strategic entry decisions of McDonald's and Burger King in the US. Our results highlight the identifying power of informational assumptions and show that the Bayes stable equilibrium identified set can be substantially tighter than the Bayes correlated equilibrium identified set. In a counterfactual experiment, we examine the impact of increasing access to healthy food on the market structures in Mississippi food deserts.

econ.EM↗