This is a survey of recent developments in the intersection of economics, finance, theoretical computer science and artificial intelligence. We study various problems related to computation and quality of solution concepts in multi-agent environments. Such concepts include Nash equilibria, voting mechanisms, fair division of divisible and indivisible items, and optimal adaptation to financial competition. We present our extensive contribution to these fields both from a theoretical and an applied perspective. Our findings can be utilized in a multitude of applications spanning across a wide range of economic environments: auction design, online advertisement, design of supply chains, centralised/distributed security systems, voting settings, fair split of inheritance, design of optimal routing networks, portfolio management in financial markets, financial trading, and many more.