We develop generalized game theoretic analytical models involving a manufacturer, a supplier, and a retailer entity considering both collaboration and leadership-based paradigms of decision-making within a supply chain (SC) considering pricing and profitability as two key economic dimensions. Both centralized and Stackelberg game-based structures are developed considering green technology investments by both the supplier and the manufacturer with an aim to reduce accompanying carbon emissions. The evolved analytical models also integrate uncertainties associated with customer demand (sensitive to carbon emission) represented as fuzzy variable. In such settings, we ascertain the optimal pricing, profitabilities, carbon emissions levels etc. for the pertinent SC entities for both the centralized and decentralized supply chain structures. To investigate the influence of green technology investment and carbon emission sensitivity on economic objectives such as profitability of individual entities and entire supply chain, we also carry out sensitivity analysis. We also examine both the individual and cross effects under both centralized and decentralized SC structures. The study augments extant supply chain literature in terms of comprehensive pricing-profitability models under both decentralized and centralized supply chain structures considering three-tiered SC structure. Novel findings are also reported based on the numerical and sensitivity analysis. For instance, though retailer dominant SC is most environmentally supportive and price friendly for the customer amongst decentralized scenarios, increase in fuzziness associated with emissions leads to jump in net emissions only marginally, but significant surge in retail price. Counterintuitively, from an emission reduction point of view, retailer dominant SC is identified as best scenario for the manufacturer.