In multi-agent systems where sets of joint actions (JAs) are generated, metrics are needed to evaluate these sets and efficiently allocate resources for the many JAs. For the case where a JA set can
be represented by multiple solutions to a DCOP, we introduce koptimality as a metric that captures desirable properties of diversity
and relative quality, and apply results from coding theory to obtain
upper bounds on cardinalities of k-optimal JA sets. These bounds
can help choose the appropriate level of k-optimality for settings
with fixed resources and help determine appropriate resource allocation for settings where a fixed level of k-optimality is desired.