For clarity, \(u_{i}\) is short for \( u_{i}(a_{i,F/Y},a_{i^{\prime},Y/F})\). In the table, \(u_1^{\prime}\) and \(u_2^{\prime}\) refers to the more aggressive player's cost if she or he chooses to fight, which are supposed to be much smaller than \(u_{i}\), because aggressive road-users tend to assume that there would be no collision. For simplification, we define that \(u_1^{\prime}(a_{1,F},a_{2,Y})= u_1(a_{1,F},a_{2,Y})\)and \(u_2^{\prime}(a_{1,F},a_{2,Y})= u_2(a_{1,F},a_{2,Y})\). Meanwhile, if Player One chooses to yield, Player Two's choice (to yield or to fight) makes no difference to player one's cost, and vice versa. This means that \(u_1(a_{1,Y},a_{2,F})= u_1(a_{1,Y},a_{2,Y})\), \(u_2(a_{1,Y},a_{2,Y})= u_2(a_{1,F},a_{2,Y})\). To find the Bayesian Nash equilibrium, we have to extend the table using Note S3, Supporting Information. Let