The cross-fertilization of AI and economic concepts has led to the advanced development of novel computational ideas. These ideas include models and approaches for analyzing multi-agent interaction (via game-theoretic models and solution concepts) in strategic environments and designing strategic environments (via mechanism design) to address principal decision-making problems involving multi-agent within various social contexts. In what follows, we will discuss our works on these two main topics. For analyzing multi-agent interaction, we will discuss several computational game-theoretic models to capture various agent characteristics and social (e.g., self-organization) domains. For designing strategic environments, we will discuss principal decision-making mechanism design settings in various social (e.g., facility location) contexts where the principal has to design mechanisms that elicit agent preferences over social outcomes and implement the principal's desirable social outcomes.