Transforming Strategic Games into Biform Games: Applications in Allocation Mechanisms and Green Technology Investment

TL;DR

The paper introduces a biform game framework that integrates cooperative and non-cooperative decision-making in strategic settings by defining a coalition-valued function $v_f(S,x)=u_f(S,x)+ abla(S,x)$ and a cooperation set ${X^C}$. It analyzes how different distribution rules—egalitarian, marginalist, and Shapley-based allocations—shape the equilibrium outcomes, showing that egalitarian sharing can promote cooperation and Pareto efficiency, while marginalist sharing tends to preserve non-cooperative outcomes. The framework is illustrated through two domains: (i) public regulation with multiple departments facing the anti-commons tragedy, where proper cooperation and allocation circumvent deadlock and yield Pareto-optimal results; and (ii) green technology investment in market competition, with Bertrand and Cournot-style models demonstrating that cost-sharing cooperations raise both green investment and total profits, with egalitarian allocations typically outperforming marginalist ones. The results provide a principled method for designing incentive mechanisms that harmonize competition and cooperation in economic and regulatory contexts, guiding policy and organizational design toward higher efficiency and sustainability.

Abstract

As Aumann stated, cooperation and non-cooperation are different ways of viewing the same game, with the main difference being whether players can reach a binding cooperative agreement. In the real world, many games often coexist competition and cooperation. Based on the above reasons, we propose a method to transform strategic games into a biform game model, which retains the characteristics of cooperative games while considering the ultimate goal of players to maximize their own interests. Furthermore, based on this biform game model, we analyze the impact of two different distribution methods, namely marginalism and egalitarianism, on the game results. As an application, we analyze how food producers seek maximum profits through cooperative pricing.