Level-0 Models for Predicting Human Behavior in Games

Wright, James R.; Leyton‐Brown, Kevin

doi:10.1613/jair.1.11361

Cited by 16 publications

(11 citation statements)

References 32 publications

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“…In most work in the literature, the issue does not come up; level-0 behavior is defined simply as uniform randomization. However, we showed in recent work that model performance can be substantially improved by allowing for richer level-0 specifications [32,16,34]. This raises the question of how rich these specifications should be allowed to become, before level-0 stops being plausible as a description of nonstrategic behavior.…”

Section: Introductionmentioning

confidence: 94%

“…To demonstrate the generality of elementary behavioral models, we show how to encode each of the candidate level-0 behavioral models that we proposed in our past work [32,34]. (Thus, although that work only appealed to intuition, we can now conclude that these behavioral models are all nonstrategic.…”

Section: Examples Of Elementary Behavioral Modelsmentioning

confidence: 99%

“…We now consider behavioral models that are constructed by drawing together the predictions of multiple elementary models. For example, we might build a behavioral model from some convex combination of the predictions of the elementary behavioral models defined in Section 5.2 (as, indeed, we did in our past work [32,34]). Our key result in this section is that the class of such models is strictly larger than the class of elementary behavioral models.…”

Section: Finite Aggregations Of Elementary Modelsmentioning

confidence: 99%

See 2 more Smart Citations

A Formal Separation Between Strategic and Nonstrategic Behavior

Wright¹,

Leyton‐Brown²

2018

Preprint

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It is common to make a distinction between "strategic" behavior and other forms of intentional but "nonstrategic" behavior: typically, that strategic agents model other agents while nonstrategic agents do not.However, a crisp boundary between these concepts has proven elusive. This problem is pervasive throughout the game theoretic literature on bounded rationality. It is particularly critical in parts of the behavioral game theory literature that make an explicit distinction between the behavior of "nonstrategic" level-0 agents and "strategic" higher-level agents (e.g., the level-k and cognitive hierarchy models). The literature gives no clear guidance on how the rationality of nonstrategic agents must be bounded, instead typically just singling out specific decision rules and informally asserting them to be nonstrategic (e.g., truthfully revealing private information; randomizing uniformly). In this work, we propose a new, formal characterization of nonstrategic behavior. Our main contribution is to show that it satisfies two properties: (1) it is general enough to capture all purportedly "nonstrategic" decision rules of which we are aware; (2) behavior that obeys our characterization is distinct from strategic behavior in a precise sense.

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Section: Introductionmentioning

confidence: 94%

Section: Examples Of Elementary Behavioral Modelsmentioning

confidence: 99%

Section: Finite Aggregations Of Elementary Modelsmentioning

confidence: 99%

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A Formal Separation Between Strategic and Nonstrategic Behavior

Wright¹,

Leyton‐Brown²

2018

Preprint

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“…Players at level 0 are not assumed to perform any information processing, and simply choose uniformly over actions (i.e. a Laplacian assumption due to the principle of insufficient reason), although alternate level-0 configurations can be considered (Wright and Leyton-Brown, 2019). Level-1 players then exploit these level-0 players and act based on this.…”

Section: Mutual Consistencymentioning

confidence: 99%

Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making

Evans¹,

Prokopenko²

2021

Preprint

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While game theory has been transformative for decision-making, the assumptions made can be overly restrictive in certain instances. In this work we focus on some of the assumptions underlying rationality such as mutual consistency and best-response, and consider ways to relax these assumptions using concepts from level-k reasoning and quantal response equilibrium (QRE) respectively. Specifically, we provide an informationtheoretic two-parameter model that can relax both mutual consistency and best-response, but can recover approximations of level-k, QRE, or typical Nash equilibrium behaviour in the limiting cases. The proposed approach is based on a recursive form of the variational free energy principle, representing self-referential games as (pseudo) sequential decisions. Bounds in player processing abilities are captured as information costs, where future chains of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources.

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“…Level-0 agents are nonstrategic (NS) agents who choose their actions uniformly at random, whereas Level-1 agents are strategic (S) agents who believe that the population consists solely of Level-0 agents, and their response is a QBR response to Level-0 agents' actions. In the original QLk model, level-0 agents follow an uniform distribution mixed strategy; however, in our case we use an expanded definition of level-0 agents presented in (Wright and Leyton-Brown 2014), where instead of an uniform distribution, the level-0 agents' strategies follow more intuitive yet non-strategic response, such as best response (BR) or maxmin (MM) response. We believe that the expanded definition of the level-0 agents suit our situation much better, since it is unrealistic to expect a driver to choose actions purely at random from their available actions.…”

Section: Solution Conceptsmentioning

confidence: 99%

Solution Concepts in Hierarchical Games under Bounded Rationality with Applications to Autonomous Driving

Sarkar¹,

Czarnecki²

2020

Preprint

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With autonomous vehicles (AV) set to integrate further into regular human traffic, there is an increasing consensus of treating AV motion planning as a multi-agent problem. However, the traditional game theoretic assumption of complete rationality is too strong for the purpose of human driving, and there is a need for understanding human driving as a bounded rational activity through a behavioral game theoretic lens. To that end, we adapt three metamodels of bounded rational behavior; two based on Quantal level-k and one based on Nash equilibrium with quantal errors. We formalize the different solution concepts that can be applied in the context of hierarchical games, a framework used in multi-agent motion planning, for the purpose of creating game theoretic models of driving behavior. Furthermore, based on a contributed dataset of human driving at a busy urban intersection with a total of ~4k agents and ~44k decision points, we evaluate the behavior models on the basis of model fit to naturalistic data, as well as their predictive capacity. Our results suggest that among the behavior models evaluated, modeling driving behavior as pure strategy NE with quantal errors at the level of maneuvers with bounds sampling of actions at the level of trajectories provides the best fit to naturalistic driving behavior.

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Level-0 Models for Predicting Human Behavior in Games

Cited by 16 publications

References 32 publications

A Formal Separation Between Strategic and Nonstrategic Behavior

A Formal Separation Between Strategic and Nonstrategic Behavior

Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making

Solution Concepts in Hierarchical Games under Bounded Rationality with Applications to Autonomous Driving

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