Semicooperation under curved strategy spacetime

Abstract

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.