[Paper Review] A model of coopetitive game and the Greek crisis

David Carfì, Daniele Schilirò|arXiv (Cornell University)|Jun 17, 2011

Business Strategy and Innovation3 citations

TL;DR

This paper proposes a coopetitive game model to resolve the Greek debt crisis by enabling Germany and Greece to achieve win-win outcomes through coordinated investment and trade expansion. Using transferable utility and Kalai-Smorodinsky bargaining on a convexified payoff space, it identifies a win-win solution where Germany increases imports from Greece and both countries achieve growth via cooperative strategy implementation, with Germany gaining even under fair distribution.

ABSTRACT

In the present work we propose an original analytical model of coopetitive game. We try to apply this analytical model of coopetition - based on game theory and conceived at a macro level - to the Greek crisis, suggesting feasible solutions in a cooperative perspective for the divergent interests which drive the economic policies in the euro area.

Motivation & Objective

• To address the persistent economic imbalances and crisis in Greece through a normative coopetitive game model.
• To explore feasible, mutually beneficial strategies for Greece and Germany that ensure growth and stability in the Eurozone.
• To develop a transferable utility framework that enables fair and efficient distribution of gains from coopetition.
• To identify a win-win solution that rebalances trade and investment while improving the collective payoff for both countries.
• To provide a policy-relevant analytical tool for Eurozone countries to transition from competitive austerity to cooperative growth.

Proposed method

• The model uses normal form game theory with two strategic variables: investment levels and trade volume in a coopetitive framework.
• It constructs a payoff space as the convex hull of the image of the base game and its translation by a vector representing external gains, forming a hexagonal payoff set.
• The Pareto maximal boundary is defined as a line segment [P′, Q′], where P′ = f(1,1) and Q′ = P′ + v(1), representing the optimal cooperative frontier.
• A Kalai-Smorodinsky bargaining solution is applied on the segment [P′, Q′], using the infimum and supremum of the Pareto boundary as reference points.
• A transferable utility solution is derived by identifying the point Q′ = (1/2, 2 + m + n) as the maximum collective gain on the Pareto boundary.
• A new compromise solution K is determined as the intersection of two segments: one defining the feasible gain range for Greece, and another representing the Kalai-Smorodinsky optimal path.

Experimental results

Research questions

• RQ1 Can a coopetitive game model generate win-win outcomes for Greece and Germany despite divergent economic interests in the Eurozone?
• RQ2 What level of increased German demand for Greek exports would lead to a sustainable and mutually beneficial economic rebalancing?
• RQ3 How can transferable utility and bargaining theory be applied to a non-constant sum game to ensure fairness and growth in a crisis context?
• RQ4 What is the optimal investment and trade strategy that maximizes collective payoff while ensuring both countries benefit?
• RQ5 Can a coopetitive solution be implemented through a sequence of cooperative and non-cooperative moves, such as Nash equilibrium followed by contract-based sharing?

Key findings

• The model identifies a win-win solution K on the transferable utility Pareto boundary that exceeds the initial supremum payoff of (3/2, 1) for Greece and Germany.
• The optimal compromise solution K is achieved by intersecting the feasible gain segment for Greece with the Kalai-Smorodinsky bargaining segment, ensuring fairness and efficiency.
• Germany achieves a gain under the final solution, contradicting the assumption that cooperation would only benefit Greece, thus validating the win-win nature of the outcome.
• The collective payoff f₁ + f₂ is not constant along the Pareto boundary, indicating that the game supports global growth, not just redistribution.
• The solution is implementable via a three-step process: agreement on a common cooperative strategy, implementation of Nash equilibrium (1,1), and contract-based sharing of the total gain (5/2 + n).
• The model demonstrates that a win-win outcome is possible even when one country (Germany) is initially in a strong position, provided strategic cooperation and fair distribution are ensured.