Protecting against adversarial attacks is a common multiagent problem. Attackers in the real world are predominantly human actors, and the protection methods often incorporate opponent models to improve the performance when facing humans. Previous results show that modeling human behavior can significantly improve the performance of the algorithms. However, modeling humans correctly is a complex problem, and the models are often simplified and assume humans make mistakes according to some distribution or train parameters for the whole population from which they sample. In this work, we use data gathered by psychologists who identified personality types that increase the likelihood of performing malicious acts. However, in the previous work, the tests on a handmade game could not show strategic differences between the models. We created a novel model that links its parameters to psychological traits. We optimized over parametrized games and created games in which the differences are profound. Our work can help with automatic game generation when we need a game in which some models will behave differently and to identify situations in which the models do not align.

We study reinforcement learning (RL) for learning a Quantal Stackelberg Equilibrium (QSE) in an episodic Markov game with a leader-follower structure. In specific, at the outset of the game, the leader announces her policy to the follower and commits to it. The follower observes the leader's policy and, in turn, adopts a quantal response policy by solving an entropy-regularized policy optimization problem induced by leader's policy. The goal of the leader is to find her optimal policy, which yields the optimal expected total return, by interacting with the follower and learning from data. A key challenge of this problem is that the leader cannot observe the follower's reward, and needs to infer the follower's quantal response model from his actions against leader's policies. We propose sample-efficient algorithms for both the online and offline settings, in the context of function approximation. Our algorithms are based on (i) learning the quantal response model via maximum likelihood estimation and (ii) model-free or model-based RL for solving the leader's decision making problem, and we show that they achieve sublinear regret upper bounds. Moreover, we quantify the uncertainty of these estimators and leverage the uncertainty to implement optimistic and pessimistic algorithms for online and offline settings. Besides, when specialized to the linear and myopic setting, our algorithms are also computationally efficient. Our theoretical analysis features a novel performance-difference lemma which incorporates the error of quantal response model, which might be of independent interest.

Solution concepts of traditional game theory assume entirely rational players; therefore, their ability to exploit subrational opponents is limited. One type of subrationality that describes human behavior well is the quantal response. While there exist algorithms for computing solutions against quantal opponents, they either do not scale or may provide strategies that are even worse than the entirely-rational Nash strategies. This paper aims to analyze and propose scalable algorithms for computing effective and robust strategies against a quantal opponent in normal-form and extensive-form games. Our contributions are: (1) we define two different solution concepts related to exploiting quantal opponents and analyze their properties; (2) we prove that computing these solutions is computationally hard; (3) therefore, we evaluate several heuristic approximations based on scalable counterfactual regret minimization (CFR); and (4) we identify a CFR variant that exploits the bounded opponents better than the previously used variants while being less exploitable by the worst-case perfectly-rational opponent.

With the rapid development of robot and other intelligent and autonomous agents, how a human could be influenced by a robot's expressed mood when making decisions becomes a crucial question in human-robot interaction. In this pilot study, we investigate (1) in what way a robot can express a certain mood to influence a human's decision making behavioral model; (2) how and to what extent the human will be influenced in a game theoretic setting. More specifically, we create an NLP model to generate sentences that adhere to a specific affective expression profile. We use these sentences for a humanoid robot as it plays a Stackelberg security game against a human. We investigate the behavioral model of the human player.

Frequently, it is advantageous for an agent to model other agents in order to predict their behavior during an interaction. Modeling others as rational has a long tradition in AI and game theory, but modeling other agents’ departures from rationality is difficult and controversial. This paper proposes that bounded rationality be modeled as errors the agent being modeled is making while deciding on its action. We are motivated by the work on quantal response equilibria in behavioral game theory which uses Nash equilibria as the solution concept. In contrast, we use decision-theoretic maximization of expected utility. Quantal response assumes that a decision maker is rational, i.e., is maximizing his expected utility, but only approximately so, with an error rate characterized by a single error parameter. Another agent’s error rate may be unknown and needs to be estimated during an interaction. We show that the error rate of the quantal response can be estimated using Bayesian update of a suitable conjugate prior, and that it has a finitely dimensional sufficient statistic under strong simplifying assumptions. However, if the simplifying assumptions are relaxed, the quantal response does not admit a finite sufficient statistic and a more complex update is needed. This confirms the difficulty of using simple models of bounded rationality in general settings.