  A classic model to study strategic decision making in multi-agent systems is
the normal-form game. This model can be generalised to allow for an infinite
number of pure strategies leading to continuous games. Multi-objective
normal-form games are another generalisation that model settings where players
receive separate payoffs in more than one objective. We bridge the gap between
the two models by providing a theoretical guarantee that a game from one
setting can always be transformed to a game in the other. We extend the
theoretical results to include guaranteed equivalence of Nash equilibria. The
mapping makes it possible to apply algorithms from one field to the other. We
demonstrate this by introducing a fictitious play algorithm for multi-objective
games and subsequently applying it to two well-known continuous games. We
believe the equivalence relation will lend itself to new insights by
translating the theoretical guarantees from one formalism to another. Moreover,
it may lead to new computational approaches for continuous games when a problem
is more naturally solved in the succinct format of multi-objective games.
