| Abstract: |
The structural Quantal Response Equilibrium (QRE) generalizes the Nash
equilibrium by augmenting payoffs with random elements that are not removed in
some limit. This approach has been widely used both as a theoretical framework
to study comparative statics of games and as an econometric framework to
analyze experimental and field data. The framework of structural QRE is
flexible: it can be applied to arbitrary finite games and incorporate very
general error structures. Restrictions on the error structure are needed,
however, to place testable restrictions on the data (Haile et al., 2004). This
paper proposes a reduced-form approach, based on quantal response functions
that replace the best-response functions underlying the Nash equilibrium. We
define a {\em regular} QRE as a fixed point of quantal response functions that
satisfies four axioms: continuity, interiority, responsiveness, and
monotonicity. We show that these conditions are not vacuous and demonstrate
with an example that they imply economically sensible restrictions on data
consistent with laboratory observations. The reduced-form approach allows for
a richer set of regular quantal response functions, which has proven useful
for estimation purposes. |