The Investment Management Game: Extending the Scope of the Notion of Core

TL;DR

This paper extends the concept of the core from cooperative game theory to an investment management game against nature, characterizing its core on perfect graphs using total dual integrality.

Contribution

It introduces a novel application of the core in a non-cooperative, single-agent investment game and characterizes its core on perfect graphs via total dual integrality.

Findings

Core characterized on perfect graphs

Polynomial-time solution for maximum stable set

Novel use of total dual integrality in core characterization

Abstract

The core is a dominant solution concept in economics and cooperative game theory; it is predominantly used for profit, equivalently cost or utility, sharing. This paper demonstrates the versatility of this notion by proposing a completely different use: in a so-called investment management game, which is a game against nature rather than a cooperative game. This game has only one agent whose strategy set is all possible ways of distributing her money among investment firms. The agent wants to pick a strategy such that in each of exponentially many future scenarios, sufficient money is available in the right firms so she can buy an optimal investment for that scenario. Such a strategy constitutes a core imputation under a broad interpretation, though traditional formal framework, of the core. Our game is defined on perfect graphs, since the maximum stable set problem can be solved in polynomial time for such graphs. We completely characterize the core of this game, analogous to Shapley and Shubik characterization of the core of the assignment game. A key difference is the following technical novelty: whereas their characterization follows from total unimodularity, ours follows from total dual integrality