Rewards

The reward of a human agent is the negative of its travel time. The reward of an autonomous vehicle (AV) varies with its configured behavior.

Defining Automated Vehicles Behavior Through Reward Formulations

As described in the paper, the reward function enforces a selected behavior on the agent. For an agent k with behavioral parameters φₖ ∈ ℝ⁴, the reward is defined as:

\[ r_k = \varphi_{k1} \cdot T_{\text{own}, k} + \varphi_{k2} \cdot T_{\text{group}, k} + \varphi_{k3} \cdot T_{\text{other}, k} + \varphi_{k4} \cdot T_{\text{all}, k} \]

where Tₖ is a vector of travel time statistics provided to agent k, containing:

  • Own Travel Time (\(T_{\text{own}, k}\)): The amount of time the agent has spent in traffic.

  • Group Travel Time (\(T_{\text{group}, k}\)): The average travel time of agents in the same group (e.g., AVs for an AV agent).

  • Other Group Travel Time (\(T_{\text{other}, k}\)): The average travel time of agents in other groups (e.g., humans for an AV agent).

  • System-wide Travel Time (\(T_{\text{all}, k}\)): The average travel time of all agents in the traffic network.


Behavioral Strategies & Objective Weightings

Behavior

φ₁

φ₂

φ₃

φ₄

Interpretation

Altruistic

0

0

0

-1

Minimize delay for everyone

Collaborative

-0.5

-0.5

0

0

Minimize delay for oneself and one’s own group

Collectivist

-0.1

-0.9

0

0

Primarily minimize delay for one’s own group

Competitive

-2

0

1

0

Minimize self-delay and maximize delay for others

Cooperative

0

-1

0

0

Minimize delay for one’s own group

Malicious

0

0

1

0

Maximize delay for the other group

Militant

0

-2

1

0

Minimize group delay and maximize delay for others

Selfish

-1

0

0

0

Minimize delay for oneself

Social

-0.5

0

0

-0.5

Minimize delay for oneself and everyone