A gradient-based distributed algorithm for triopoly advertising competition game over interconnected market systems

This paper investigates a triopoly advertising competition problem over interconnected market systems using a noncooperative game framework that effectively captures the strategic interactions and conflicting objectives among the three firms. By taking both the targeted advertising efforts of the firms and the continuous co-evolution of consumer opinions across market systems via social network interactions into consideration, we build a noncooperative game model with nonlinear cost functions to analyze the optimal advertising strategy of each firm. To address the challenge of limited information exchange among firms, we design an estimation mechanism for each firm to estimate the current strategy profile and propose a gradient-based distributed algorithm to seek the Nash equilibrium of the game. Finally, numerical simulations are provided for verifying the developed results.