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.

翻译：经典的研究多智能体系统中战略决策的模型是标准式博弈。该模型可泛化为允许无限数量的纯策略，从而形成连续博弈。多目标标准式博弈是另一种泛化，它建模了玩家在多个目标中获得独立收益的场景。我们通过提供理论保证，证明一种场景下的博弈总能转化为另一种场景下的博弈，从而连接了这两种模型。我们将理论结果扩展至包括纳什均衡的等价性保证。这种映射使得可以将一个领域的算法应用于另一个领域。我们通过引入一种用于多目标博弈的虚拟博弈算法，并将其应用于两个著名的连续博弈来展示这一点。我们相信，这种等价关系将通过将一种形式体系的理论保证转化为另一种形式体系，从而带来新的见解。此外，当问题在多目标博弈的简洁格式中更容易求解时，它可能为连续博弈提供新的计算方法。