The game of "chicken" is played by two macho teens who speed toward each other on a single-lane road. The first to veer off is branded the chicken, whereas the one who doesn't turn gains peer group esteem. Of course, if neither veers, both die in the resulting crash. Payoffs to the chicken game are provided in the following table. a. Does this game have a Nash equilibrium? b. Is a threat by either not to chicken-out a credible one? c. Would the ability of one player to firmly commit to a not-chicken strategy (by, for example, throwing away the steering wheel) be desirable for that player?

Let's represent the payoff matrix of the game. Let C stand for "Chicken-out" and N for "Not-chicken". The matrix will look like this: ``` Player 2 ----------------------- | N | C | Player 1 ----------------------- | N(-10,-10) | N(1,0) | ----------------------- | C(0,1) | C(-1,-1)| ----------------------- ``` The entries represent the payoffs for each scenario (Player 1, Player 2).

A Nash Equilibrium occurs when no player has an incentive to change their strategy given the strategies of the other players. Let's examine each cell of the matrix and compare each player's payoff considering the other player's strategy. (N,N): Both players die in a crash. If either player switches to C, they would avoid the crash and gain a positive payoff. (C,N): Player 1 chickens-out while Player 2 doesn't. Player 1 cannot improve their payoff by changing to N because they would die in a crash. If Player 2 switches to C, they'd get a lower payoff so they wouldn't switch their strategy. (N,C): Same as (C,N), but with the roles reversed. (C,C): Both players chicken-out. If either player switches to N, they would gain a higher payoff. There are two Nash Equilibria in this game: (C,N) and (N,C).

A threat by either player not to chicken-out may seem like a good strategy to gain an advantage. However, in this game both players have the same available strategies and neither of them wants to end in the (N,N) situation due to the fatal consequences. Additionally, if both claim not to chicken-out, the most rational response would be not believing the other's threat because of their own desire to survive. Thus, neither player has a credible threat in this context.

If one player could commit to a not-chicken strategy, it would force the other player to choose between a chicken-out strategy or risking the (N,N) scenario. In a rational game, the other player would choose to avoid crashing and chicken-out. Therefore, committing to a not-chicken strategy would be advantageous for one player since it forces the other player to chicken-out, leading to a higher payoff for the not-chicken player. In conclusion: a. The game has two Nash Equilibria: (C,N) and (N,C). b. A threat by either player not to chicken-out is not credible in the context of this game. c. The ability to commit to a not-chicken strategy would be advantageous for one player, as it forces the other player to chicken-out.