payoff of each agent also depends on the actions of her neighbors, and is differentiated on two objectives ${{\mathcal{D}}}=\{1,2\}$ that it would hardly make sence to aggregate, for instance: sales revenue (to buy their daily lives) and the remaining natural resources (so that, in the future, their children could also live). (Here, the payoffs are random integers.)

In the subjective theory of value, every individual evaluates her endowment $(u_{1}^{i},\ldots,u_{d}^{i})$ however she wants based on an utility function $v^{i}:{\mathbb{R}^d}\rightarrow{\mathbb{R}}$. The theory of multi-objective games [@blackwell1956analog; @shapley1959equilibrium] aims at allowing for individuals that behave according to several unknown, uncertain, or inconsistent utility functions. These utility functions are reduced to their common denominator: the Pareto-dominance, as defined below. That vector $\bm{y}\in{\mathbb{R}^d}$ weakly-Pareto-dominates and respectively *Pareto-dominates* vector $\bm{x}\in{\mathbb{R}^d}$ is denoted and defined by: $$\begin{aligned}
\bm{y}{\succsim}\bm{x} & \Leftrightarrow & \forall k\in{{\mathcal{D}}},\quad  y_k\geq x_k,\\ 
\bm{y}{\succ}\bm{x} &\Leftrightarrow & \forall k\in{{\mathcal{D}}},\quad y_k\geq x_k\mbox{~~and~~}\exists k\in{{\mathcal{D}}}, y_k> x_k.\end{aligned}$$ For the preferences of individuals, given an adversary action-profile$\bm{a}^{-i}=(a^j\mid j\neq i)$, this defines a partial rationality on set$\bm{u}^{i}(A^{i},\bm{a}^{-i})=\{\bm{u}^{i}(b^{i},\bm{a}^{-i})\mid b^i\in A^i\}$, which is less assumptive than complete orders, since it does not presume any individual utility function $v^{i}:{\mathbb{R}}^{d}\rightarrow{\mathbb{R}}$. Formally, given a finite set of vectors $X\subseteq{\mathbb{R}^d}$, the set of *Pareto-efficient* vectors is defined 