Optimism and Pessimism in Games

This paper considers the impact of ambiguity in strategic situations. It extends the earlier literature by allowing for optimistic responses to ambiguity. Ambiguity is modelled by CEU preferences. We propose a new solution concept for players who may express ambiguity- preference. Then we study comparative statics of changes in ambiguity-attitude in games with strategic complements. This gives a precise statement of the impact of ambiguity on economic behaviour.Ambiguity in games, support, strategic complementarity, optimism, multiple equilibria.

On the homotopy Lie algebra of an arrangement

Let A be a graded-commutative, connected k-algebra generated in degree 1. The homotopy Lie algebra g_A is defined to be the Lie algebra of primitives of the Yoneda algebra, Ext_A(k,k). Under certain homological assumptions on A and its quadratic closure, we express g_A as a semi-direct product of the well-understood holonomy Lie algebra h_A with a certain h_A-module. This allows us to compute the homotopy Lie algebra associated to the cohomology ring of the complement of a complex hyperplane arrangement, provided some combinatorial assumptions are satisfied. As an application, we give examples of hyperplane arrangements whose complements have the same Poincar\'e polynomial, the same fundamental group, and the same holonomy Lie algebra, yet different homotopy Lie algebras.Comment: 20 pages; accepted for publication by the Michigan Math. Journa