Configuration spaces in cooperative game theory and the topology of embeddings into Euclidean spaces

There is an interesting connection between the configuration spaces arising in cooperative game theory with the complexes arising as obstructions for embedding (mapping) spaces into higher dimensional Euclidean spaces without double (multiple) points. It turns out that objects like threshold complexes and ‘simple games’ (von Neumann and Morgenstern) are naturally linked with Kuratowski graphs, Tverberg-Van Kampen-Flores obstructions, r-unavoidable complexes, etc.
The connection opens a new possibility of using ideas from linear programming and polyhedral combinatorics which will be illustrated by examples, including a proof of a general ‘balanced Van Kampren-Flores theorem’ (D.Jojic, S.Vrecica, R.Zivaljevic, J. Algebraic Combin., 2017).