Autonomous agents can adopt socially-aware behaviors to reduce social costs, mimicking the way animals interact in nature and humans in society. We present a new approach to model socially-aware decision-making that includes two key elements: bounded rationality and inter-agent relationships. We capture the interagent relationships by introducing a novel model called a relationship game and encode agents' bounded rationality using quantal response equilibria. For each relationship game, we define a social cost function and formulate a mechanism design problem to optimize weights for relationships that minimize social cost at the equilibrium. We address the multiplicity of equilibria by presenting the problem in two forms: Min-Max and Min-Min, aimed respectively at minimization of the highest and lowest social costs in the equilibria. We compute the quantal response equilibrium by solving a least-squares problem defined with its Karush-Kuhn-Tucker conditions, and propose two projected gradient descent algorithms to solve the mechanism design problems. Numerical results, including two-lane congestion and congestion with an ambulance, confirm that these algorithms consistently reach the equilibrium with the intended social costs.

翻译：自主智能体可以采取具有社会意识的行为来降低社会成本，模仿动物在自然界和人类在社会中互动的方式。我们提出了一种新的方法来建模具有社会意识的决策，该方法包含两个关键要素：有限理性和智能体间关系。我们通过引入一种称为关系博弈的新模型来捕捉智能体间关系，并利用量化响应均衡对智能体的有限理性进行编码。对于每个关系博弈，我们定义了一个社会成本函数，并构建了一个机制设计问题来优化关系的权重，从而在均衡状态下最小化社会成本。我们通过以两种形式呈现该问题来处理均衡的多重性：最小-最大化（Min-Max）和最小-最小化（Min-Min），分别旨在最小化均衡中的最高社会成本和最低社会成本。我们通过求解基于其卡罗需-库恩-塔克条件定义的最小二乘问题来计算量化响应均衡，并提出了两种投影梯度下降算法来解决机制设计问题。数值结果（包括双车道拥堵和带救护车的拥堵情景）证实，这些算法能够持续达到具有预期社会成本的均衡状态。