Summary: As agent-based systems are increasingly used to model real-life applications such as the internet, electronic markets or disaster management scenarios, it is important to study the computational complexity of such usually combinatorial systems with respect to some desirable properties. The purpose of this paper is to consider two computational models: graphical games encoding the interactions between rational and selfish agents; and weighted directed acyclic graphs (DAG) for evaluating derivatives of numerical functions. The author studies the complexity of a certain number of search problems in both models. The author’s approach is essentially theoretical, studying the problem of verifying game-theoretic properties for graphical games representing interactions between self-motivated and rational agents, as well as the problem of searching for an optimal elimination ordering in a weighted DAG for evaluating derivatives of functions represented by computer programs. A certain class of games is identified for which Nash or Bayesian Nash equilibria can be verified in polynomial time; then, it is shown that verifying a dominant strategy equilibrium is non-deterministic polynomial (NP)-complete even for normal form games. Finally, it is shown that the optimal vertex elimination ordering for weighted DAGs is NP-complete. The paper presents a general framework for graphical games. The presented results are novel and illustrate how modeling real-life scenarios involving intelligent agents can lead to computationally hard problems while showing interesting cases that are tractable.