Efficiently characterizing games consistent with perturbed equilibrium observations

Ziani, 2017

Category: Econometrics

Overall Rating

2.1/5 (15/35 pts)

this thesis offers a specific technical contribution: a computationally efficient framework using convex optimization to characterize the entire set of consistent games under set-based uncertainty for perturbations.
The potential novelty lies in porting this methodology—characterizing the consistent set via tractable convex programs given observations of system stable states under bounded, unknown disturbances—to other structured inverse problems, provided the system structure allows for such formulations (LP, SOCP, SDP).
While limited by the requirement for tractable convex formulations, this approach offers a distinct alternative to probabilistic methods by providing guaranteed set membership under weaker distributional assumptions.
its practical applicability seems confined to very specific, structured inverse problems where the necessary tractable convex formulations are feasible, limiting its potential for widespread impact without significant theoretical extensions or identification of highly specific target domains.

this thesis offers a computationally efficient framework for characterizing the entire set of consistent games (the "sharp identification region") using convex optimization and robust optimization concepts (set-based uncertainty for perturbations).
The general methodology – using convex optimization to characterize the set of underlying models consistent with observations generated by a perturbed equilibrium/stable-state process under set-based uncertainty – has strong potential to be ported to other domains dealing with similar inverse problems.
The core methodology can be highly valuable for inverse problems in fields where observed data represents "equilibrium" or stable states of a system under unknown, bounded perturbations, and the underlying system parameters need to be inferred.
Applying the efficiency techniques developed here (e.g., formulating constraints based on the system's structure leading to tractable convex forms) to inverse problems in complex, large-scale biological or physical models could enable rigorous uncertainty quantification and model validation that is currently intractable or relies on strong, potentially unwarranted, statistical assumptions.

The core relevance of this work hinges on the specific assumptions of observed correlated equilibria from perturbed versions of a single underlying game, where perturbations belong to a known convex set.
Despite claims of efficiency relative to prior work, the computational approach relies on representing the consistent set using a quadratic number of variables and constraints in the number of actions (m1*m2).
The framework for handling observations without partial payoff/shifter information (Section 5) requires games to have strict equilibria for non-degenerate recovery.
Misspecification in any of these aspects could lead to a "consistent set" that is empty or irrelevant, without clear mechanisms within the framework to diagnose such issues robustly.

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