Last-iterate Convergence to Trembling-hand Perfect Equilibria
Martino Bernasconi, Alberto Marchesi, Francesco Trov\`o

TL;DR
This paper introduces a scalable, last-iterate algorithm for computing trembling-hand perfect equilibria in two-player zero-sum sequential games with imperfect information, improving robustness to mistakes.
Contribution
It presents the first efficient last-iterate method that converges to EFPE, leveraging regularized-perturbed games and tailored convergence procedures.
Findings
Algorithm converges to EFPE in two-player zero-sum games.
Strategies produced are more robust to player mistakes.
Method is more scalable than linear programming approaches.
Abstract
Designing efficient algorithms to find Nash equilibrium (NE) refinements in sequential games is of paramount importance in practice. Indeed, it is well known that the NE has several weaknesses, since it may prescribe to play sub-optimal actions in those parts of the game that are never reached at the equilibrium. NE refinements, such as the extensive-form perfect equilibrium (EFPE), amend such weaknesses by accounting for the possibility of players' mistakes. This is crucial in real-world applications, where bounded rationality players are usually involved, and it turns out being useful also in boosting the performances of superhuman agents for recreational games like Poker. Nevertheless, only few works addressed the problem of computing NE refinements. Most of them propose algorithms finding exact NE refinements by means of linear programming, and, thus, these do not have the potential…
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Taxonomy
TopicsGambling Behavior and Treatments · Sports Analytics and Performance · Experimental Behavioral Economics Studies
