论文标题
静态游戏中社会意识行为的关系设计
Relationship Design for Socially-Aware Behavior in Static Games
论文作者
论文摘要
自主代理可以采用社会意识的行为来减少社会成本，模仿动物在自然界中与人类互动的方式。我们提出了一种新的方法来建模具有社会意识的决策，其中包括两个关键要素：有限的合理性和跨性别关系。我们通过引入一种称为“关系游戏”的新型模型来捕获跨关系，并使用量子响应平衡编码代理的有限合理性。对于每个关系游戏，我们定义一个社会成本功能，并制定一个机制设计问题，以优化关系的权重，以最大程度地减少平衡的社会成本。我们通过以两种形式提出该问题来解决平衡的多样性：最小和最小值，分别针对平衡中最高和最低的社会成本的最小化。我们通过解决使用Karush-kuhn-tucker条件定义的最小二乘问题来计算量子响应平衡，并提出了两种预测的梯度下降算法来解决机制设计问题。数值结果，包括两车道的交通拥堵和救护车的交通拥堵，证实这些算法始终达到预期的社会成本。
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.
