We study new classes of games, called zero-sum equivalent games and zero-sum
equivalent potential games, and prove decomposition theorems involving these
classes of games. We say that two games are "strategically equivalent" if, for
every player, the payoff differences between two strategies (holding other
players' strategies fixed) are identical. A zero-sum equivalent game is a game
that is strategically equivalent to a zero-sum game; a zero-sum equivalent
potential game is a zero-sum equivalent game that is strategically equivalent
to a common interest game. We also call a game "normalized" if the sum of one
player's payoffs, given the other players' strategies, is always zero. We show
that any normal form game can be uniquely decomposed into either (i) a zero-sum
equivalent game and a normalized common interest game, or (ii) a zero-sum
equivalent potential game, a normalized zero-sum game, and a normalized common
interest game, each with distinctive equilibrium properties. For example, we
show that two-player zero-sum equivalent games with finite strategy sets
generically have a unique Nash equilibrium and that two-player zero-sum
equivalent potential games with finite strategy sets generically have a
strictly dominant Nash equilibrium.

该研究证明了零和等价游戏和零和等价潜在游戏的分解定理，其中规范化游戏可以分解成零和等价游戏和规范化共同利益游戏或者分解成零和等价潜在游戏、规范化零和游戏和规范化共同利益游戏，每个游戏具有独特的平衡性质。

正态式博弈的策略分解：零和博弈与潜在博弈

Strategic Decompositions of Normal Form Games: Zero-sum Games and  Potential Games

The 2-spin Ising model in statistical mechanics and the 2x2 normal form game
in game theory are compared. All configurations allowed by the second are
recovered by the first when the only concern is about Nash equilibria. But it
holds no longer when Pareto optimum condiderations are introduced like in the
prisoner's dilemma. This gap can nevertheless be filled by adding a new
coupling term to the Ising model, even if that term has up to now no physical
meaning. An individual complete bilinear objective function is thus found to be
sufficient to reproduce all possible configurations of a 2x2 game. Using this
one-to-one mapping, new perspectives for future research in both fields can be
envisioned.

通过比较统计力学中的 2 自旋伊辛模型和博弈论中的 2x2 标准形式博弈，发现只考虑 Nash 均衡时两者有相同表现，但在考虑 Pareto 最优解时则不然。但是通过在伊辛模型中添加新的耦合项，可以弥补这个差距。因此发现，单个完整双线性客观函数足以模拟 2x2 标准形式博弈的所有可能情况。使用这种一一映射，可以展望未来在两个领域中的新研究方向。