Paper: arXiv 2611.13841

Authors: Yukun Cao, Jan Palczewski

Abstract

We study a two-player nonzero-sum stochastic exit game with asymmetric information. Each firm chooses the time to exit a duopoly and, conditional on remaining active, when to exit a monopoly. The asymmetry stems from privately observed exit values, while profit flows are driven by a general one-dimensional diffusion. Allowing for exit from monopoly induces singular dynamics of the associated belief process, so we construct it as a limit of regular approximations. The underlying dynamics are not described by a system of SDEs, which requires a new mathematical approach. We construct a symmetric Nash equilibrium in which the duopoly exit is a hitting time of the belief process while the monopoly exit is described through the underlying diffusion. Our equilibrium exhibits novel phenomena: the market may be abandoned by both firms in finite time (market collapse), and firms with heterogeneous exit values may optimally exit simultaneously (clustering). These features are absent when monopoly is always preferred to exit.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper exhibits extremely high mathematical complexity, dealing with singular belief dynamics and non-standard SDEs. However, it is purely theoretical with no empirical validation or backtesting, placing it firmly in the ‘Lab Rats’ quadrant. The novelty is strong due to the new mathematical approach and equilibrium phenomena identified.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Nonzero-Sum Stochastic Exit Games with Singular Belief Dynamics] --> B{Key Methodology: Constructing Belief Process via Limit of Regular Approximations};
    B --> C[Data/Inputs: Private Exit Values, General 1D Profit Flow Diffusion];
    C --> D{Computational Process: Constructing Symmetric Nash Equilibrium};
    D --> E[Key Finding 1: Duopoly Exit as Hitting Time of Belief, Monopoly Exit via Underlying Diffusion];
    E --> F[Key Finding 2: Market Collapse (Both Firms Abandon)];
    E --> G[Key Finding 3: Clustering (Heterogeneous Firms Exit Simultaneously)];