A Fisher market is an economic model of buyer and seller interactions in which each buyer's utility depends only on the bundle of goods she obtains. Many people's interests, however, are affected by their social interactions with others. In this paper, we introduce a generalization of Fisher markets, namely influence Fisher markets, which captures the impact of social influence on buyers' utilities. We show that competitive equilibria in influence Fisher markets correspond to generalized Nash equilibria in an associated pseudo-game, which implies the existence of competitive equilibria in all influence Fisher markets with continuous and concave utility functions. We then construct a monotone pseudo-game, whose variational equilibria and their duals together characterize competitive equilibria in influence Fisher markets with continuous, jointly concave, and homogeneous utility functions. This observation implies that competitive equilibria in these markets can be computed in polynomial time under standard smoothness assumptions on the utility functions. The dual of this second pseudo-game enables us to interpret the competitive equilibria of influence CCH Fisher markets as the solutions to a system of simultaneous Stackelberg games. Finally, we derive a novel first-order method that solves this Stackelberg system in polynomial time, prove that it is equivalent to computing competitive equilibrium prices via t\^{a}tonnement, and run experiments that confirm our theoretical results.

翻译：Fisher市场是一种描述买卖双方互动的经济模型，其中每个买方的效用仅取决于其获得的商品组合。然而，许多人的兴趣会受到与他人社会互动的影响。本文引入Fisher市场的一种推广形式，即影响力Fisher市场，以捕捉社会影响对买方效用的作用。我们证明在影响力Fisher市场中，竞争均衡对应于相关伪博弈中的广义纳什均衡，这意味着所有具有连续凹效用函数的影响力Fisher市场均存在竞争均衡。随后，我们构建了一个单调伪博弈，其变分均衡及其对偶共同刻画了具有连续、联合凹及齐次效用函数的影响力Fisher市场的竞争均衡。这一发现表明，在效用函数满足标准光滑性假设的前提下，这些市场的竞争均衡可在多项式时间内计算。该第二个伪博弈的对偶使我们能够将影响力CCH Fisher市场的竞争均衡解释为同步Stackelberg博弈系统的解。最后，我们推导出一种新颖的一阶方法，可在多项式时间内求解该Stackelberg系统，证明其等价于通过试错法计算竞争均衡价格，并通过实验验证了我们的理论结果。