Question

Bonnie and Jessie are both workers on a team. At the same time both workers can choose to work on the risky project (R) or the safe project (S). If both choose to work on the R project the payoffs are 10 to Bonnie and 15 to Jessie. If both work on the S project the payoffs are 8 each. If Bonnie works on R and Jessie on S, the payoffs are (4, 6) to Bonnie and Jessie respectively. Finally, if Bonnie plays S and Jessie plays R, the payoffs are (6, 4).

a. What are the Nash equilibria of the game? Interpret your equilibria in terms of a firm using teams.

b. Now assume that Bonnie can move first and choose which project to work on. Jessie observes Bonnie’s choice before making her choice of either R or S. What are the subgame perfect equilibria of the game? Interpret this sequential game in terms of communication and leadership in organisations.

Answer 1

Answer:

a. The payoff table is as follows:

  

	Jessie
Bonnie		Risky	Safe
	Risky	10, 15	4, 6
	Safe	6, 4	8, 8

Nash equilibria: There are two Nash equilibria in this game. Risky - Risky and Safe- Safe.

Explanation of the choice of strategy:They choose at the same time. Bonnie reasons out Jessie's strategy and his options with payoffs. If Jessie were to select Risky, then Bonnie can choose Risky (payoff 10) or Safe (payoff 6). So he is better off if he selects Risky. Ont he other hand, if Jessie were to choose Safe, Bonnie would choose Safe too with a higher payoff (8) than Risky (4).

Similarly, Jessie weighs out her options. If Bonnie chooses Risky, she has the option to choose Risky (payoff 15) of Safe (payoff 6). She would consider Risky for Bonnie's Risky. If Bonnie goes for Safe, she can choose Risky (payoff 4) or Safe (payoff 8). So she goes Safe for Bonnie's Safe.

This makes sense. Bonnie and Jessie are a team. It is only right that they both select the same project. If one benefits from going risky and the other by going safe, they would not be best suited to be on the same team. So, these Nash equilibria confirm that the firm has chosen the right team.

b. In a sequential game, where Bonnie makes the first move, the game tree would look like this:

R 10, is R 6,4

Bonnie makes the first move. Jessie observes his move. For Bonnie going risky or safe depends on the final outcome. That is, for Bonnie, it is more beneficial if Jessie goes Risky ultimately (RR). It would give him the highest a payoff, 10. Also, he is sure that Jessie will be forced to go for Risky if he goes Risky as her payoff is also better (15) than if she were to go Safe(6) in response. So Bonnie initiates the move by going Risky.

When Jessie sees that Bonnie has gone Risky, she knows that Risky is better payoff for her too. So she also goes Risky.

In the case of sub game perfect equilibria, Risky, Risky is the best response for both the players.

From the firm's perspective, Bonnie and Jessie make a perfect team. Bonnie's choice is reciprocated by Jessie which resonates support for her leader. Their collective choice of Risky-Risky is the best outcome for the firm as it has the highest payoff. Bonnie makes a good leader too, as he is the one who leads Jessie to this outcome.