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Dynamic Games among Teams with Delayed Intra-Team Information Sharing

Dengwang Tang, Hamidreza Tavafoghi, Vijay Subramanian, Ashutosh Nayyar, Demosthenis Teneketzis

TL;DR

This work studies stochastic dynamic games among teams with asymmetric information, where intra-team observations are shared with a delay $d$. It develops two layered information-compression frameworks, SPIB and CIB, to identify meaningful Nash equilibria and to enable tractable backward-inductive computation. SPIB-based equilibria always exist, while CIB-based equilibria may fail to exist in general, prompting the backward-decomposition procedure and the identification of conditions (e.g., signaling-neutral or signaling-free settings) under which CIB-CNEs exist. The results illuminate the trade-offs between information compression, equilibrium existence, and computational tractability in dynamic games with asymmetric information, with implications for cyber-physical systems, oligopolies, and team-based coordination under communication constraints.

Abstract

We analyze a class of stochastic dynamic games among teams with asymmetric information, where members of a team share their observations internally with a delay of $d$. Each team is associated with a controlled Markov Chain, whose dynamics are coupled through the players' actions. These games exhibit challenges in both theory and practice due to the presence of signaling and the increasing domain of information over time. We develop a general approach to characterize a subset of Nash Equilibria where the agents can use a compressed version of their information, instead of the full information, to choose their actions. We identify two subclasses of strategies: Sufficient Private Information Based (SPIB) strategies, which only compress private information, and Compressed Information Based (CIB) strategies, which compress both common and private information. We show that while SPIB-strategy-based equilibria always exist, the same is not true for CIB-strategy-based equilibria. We develop a backward inductive sequential procedure, whose solution (if it exists) provides a CIB strategy-based equilibrium. We identify some instances where we can guarantee the existence of a solution to the above procedure. Our results highlight the tension among compression of information, existence of (compression based) equilibria, and backward inductive sequential computation of such equilibria in stochastic dynamic games with asymmetric information.

Dynamic Games among Teams with Delayed Intra-Team Information Sharing

TL;DR

This work studies stochastic dynamic games among teams with asymmetric information, where intra-team observations are shared with a delay . It develops two layered information-compression frameworks, SPIB and CIB, to identify meaningful Nash equilibria and to enable tractable backward-inductive computation. SPIB-based equilibria always exist, while CIB-based equilibria may fail to exist in general, prompting the backward-decomposition procedure and the identification of conditions (e.g., signaling-neutral or signaling-free settings) under which CIB-CNEs exist. The results illuminate the trade-offs between information compression, equilibrium existence, and computational tractability in dynamic games with asymmetric information, with implications for cyber-physical systems, oligopolies, and team-based coordination under communication constraints.

Abstract

We analyze a class of stochastic dynamic games among teams with asymmetric information, where members of a team share their observations internally with a delay of . Each team is associated with a controlled Markov Chain, whose dynamics are coupled through the players' actions. These games exhibit challenges in both theory and practice due to the presence of signaling and the increasing domain of information over time. We develop a general approach to characterize a subset of Nash Equilibria where the agents can use a compressed version of their information, instead of the full information, to choose their actions. We identify two subclasses of strategies: Sufficient Private Information Based (SPIB) strategies, which only compress private information, and Compressed Information Based (CIB) strategies, which compress both common and private information. We show that while SPIB-strategy-based equilibria always exist, the same is not true for CIB-strategy-based equilibria. We develop a backward inductive sequential procedure, whose solution (if it exists) provides a CIB strategy-based equilibrium. We identify some instances where we can guarantee the existence of a solution to the above procedure. Our results highlight the tension among compression of information, existence of (compression based) equilibria, and backward inductive sequential computation of such equilibria in stochastic dynamic games with asymmetric information.

Paper Structure

This paper contains 48 sections, 19 theorems, 152 equations, 1 figure.

Table of Contents

  1. INTRODUCTION
  2. Related Literature
  3. Contribution
  4. Organization
  5. Notation
  6. PROBLEM FORMULATION
  7. System Model and Information Structure
  8. Strategies and Reward Functions
  9. Solution Concept
  10. A Motivating Example
  11. GAME OF COORDINATORS
  12. An Illustrative Example
  13. COMPRESSION OF PRIVATE INFORMATION
  14. A Preliminary Result
  15. Result for $d=1$
  16. ...and 33 more sections

Key Result

Lemma 1

For every pure coordination strategy profile $\nu$, there exists a pure strategy profile $\mu$ that yields the same payoffs for all teams and vice versa.

Figures (1)

  • Figure 1: The pieces (polygons) for which $J^*(p)$ is linear on. The extreme points of the pieces are labeled.

Theorems & Definitions (75)

  • Remark 1
  • Remark 2
  • Definition 1: Team Nash Equilibrium
  • Example 1: Guessing Game
  • Definition 2: Prescription
  • Definition 3: Pure Coordination Strategy
  • Lemma 1
  • proof
  • Definition 4: Behavioral Coordination Strategy
  • Lemma 2
  • ...and 65 more