Zero-Sum Games involving Teams against Teams: Existence of Equilibria, and Comparison and Regularity in Information

TL;DR

This paper establishes the existence of saddle-point equilibria in zero-sum team games, generalizes Blackwell's information ordering to teams, and analyzes the regularity of equilibrium values under information structure variations.

Contribution

It introduces new existence results for equilibria in team-zero-sum games, extends Blackwell's ordering to multi-agent teams, and studies the continuity of equilibrium values in information structures.

Findings

Existence of saddle-point equilibria with common randomness.

Generalization of Blackwell's ordering to n-player teams.

Continuity of equilibrium value under total variation.

Abstract

Many emerging problems involve teams of agents taking part in a game. Such problems require a stochastic analysis with regard to the correlation structures among the agents belonging to a given team. In the context of Standard Borel spaces, this paper makes the following contributions for two teams of finitely many agents taking part in a zero-sum game: (i) An existence result will be presented for saddle-point equilibria in zero-sum games involving teams against teams when common randomness is assumed to be available in each team with an analysis on conditions for compactness of strategic team measures to be presented. (ii) Blackwell's ordering of information structures is generalized to $n$-player teams with standard Borel spaces, where correlated garbling of information structures is introduced as a key attribute; (iii) building on this result Blackwell's ordering of information structures is established for team-against-team zero-sum game problems. (iv) Finally, continuity of the equilibrium value of team-against-team zero-sum game problems in the space of information structures under total variation is established.