Empirical Game-Theoretic Analysis: A Survey

TL;DR

The paper surveys empirical game-theoretic analysis (EGTA), a methodology that induces empirical game models from agent-based simulations to enable equilibrium-based reasoning in complex, intractable environments. It organizes EGTA around the core workflow: restrict strategy sets with heuristic players, build empirical payoff models (often via heuristic payoff tables), solve for equilibria, and iteratively extend the model through learning and strategy exploration (notably PSRO). The survey highlights evolutionary dynamics, incomplete model handling, statistical reasoning (variance reduction, bootstrapping, sampling bounds), and automated strategy generation as key components, with wide applications in recreational games, economics/finance, and security. It also discusses empirical mechanism design and future directions, including richer representations (extensive form, mean-field, team settings) and improved reliability of conclusions under sampling noise.

Abstract

In the empirical approach to game-theoretic analysis (EGTA), the model of the game comes not from declarative representation, but is derived by interrogation of a procedural description of the game environment. The motivation for developing this approach was to enable game-theoretic reasoning about strategic situations too complex for analytic specification and solution. Since its introduction over twenty years ago, EGTA has been applied to a wide range of multiagent domains, from auctions and markets to recreational games to cyber-security. We survey the extensive methodology developed for EGTA over the years, organized by the elemental subproblems comprising the EGTA process. We describe key EGTA concepts and techniques, and the questions at the frontier of EGTA research. Recent advances in machine learning have accelerated progress in EGTA, and promise to significantly expand our capacities for reasoning about complex game situations.

Figures (16)

• Figure 1: EGTA: A high-level view. The underlying game is represented by an agent-based simulator, depicted in the top row, center. Proceeding clockwise, data from the simulation is used to induce an empirical game model. The green-box modules show how we develop the empirical game and ultimately obtain results, through a repeated process of game model analysis, extension, and refinement. Section references indicate where key issues and techniques are surveyed herein.
• Figure 2: General payoff $(A, B)$ for a two-action bimatrix game.
• Figure 3: Payoff matrix for the BoS game. Strategies $B$ and $S$ correspond to attending concerts of Bach or Stravinsky music, respectively.
• Figure 4: Contour deviation graph for the sequential auction game model of Table \ref{['tab:sec-auc3']}. Nodes are strategy profiles, and edges denote most beneficial one-player deviations. The dashed ellipses in orange delimit increasing levels of regret ($\epsilon$) as one moves outward in the plot.
• Figure 5: Payoff matrix (left) and directional field plot (right) for the Prisoners' Dilemma game. Strategies $D$ and $C$ represent Defect and Cooperate. Flows point towards full probability on the unique Nash equilibrium, $(D,D)$, which is a strong attractor.