Social choice and game theory : Recent results with a topological approach

This chapter presents a summary of recent results obtained in game and social choice theories, and highlights the application and the development of tools in algebraic topology . The purpose is expository : no attempt is made to provide complete proofs, for which references are given, nor to review the previous work in this area, which covers a significant subset of the economic literature . The aim is to provide an oriented guide to recent results, through economic examples with geometric interpretations, and to indicate possibly fruitful avenues of research . The use of topological tools has a long tradition in economic analysis, which goes back to the work of Von Neumann on balanced economic growth of 1937 and 1945 . He proved a generalization of Brouwer's fixed point theorem that was the basis of Kakutani's theorem . In game theory and in general equilibrium market analysis, fixed point methods are the topological methods most frequently utilized to show existence of solutions . As a matter of fact, fixed point theorems are the largest part of applications of topology to economics as a whole . Instead of topological methods, social choice theory has traditionally been formulated in a