Semicooperation under curved strategy spacetime

ABSTRACT

Mutually beneficial cooperation is a common part of economic systems as firms in partial cooperation with others can often make a higher sustainable profit. Though cooperative games were popular in 1950s, recent interest in noncooperative games is prevalent despite the fact that cooperative bargaining seems to be more useful in economic and political applications. In this paper we assume that the strategy space and time are inseparable with respect to a contract. Furthermore, it is assumed that each firm’s strategy polygon is a geodesic polygon which changes its shape every point of time with the stubbornness strategy surface of firm’s executive board follow a Gaussian free field. This gives us more flexibility to deal with generalized geodesic cooperative games which is the main contribution of this paper. Under this environment we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry fails to give a proper feedback Nash equilibrium. Cooperation occurs when two firms’ strategies fall into each other’s influence curvature in this strategy spacetime. Small firms in an economy dominated by large firms are subject to the influence of large firms. We determine an optimal feedback semicooperation of the small firm in this case using a Liouville-Feynman path integral method.

KEYWORDS:

• Curvature tensor
• curved strategy spacetime
• econophysics
• liouville-feynman-like
• path integral
• quantum control
• semicooperative games

Acknowledgments

The authors are grateful to the Editor, Zack W. Almquist, and two reviewers for their constructive comments and suggestions which led to the improvement of an earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The authors declare that no data have been used in this paper.

Additional information

Funding

The authors declare that they did not use any funding to write this paper.