Question

Consider a simple game theory exercise between two coworkers (A and B) that are working together in a group. Each coworker has two possible actions: “work selfishly” or “be a team player.” If both workers work as team players, then the project is a success and they both earn 10 utility. If both workers work selfishly, then the project fails and they both earn 0 utility. If worker A is selfish and worker B works as a team player, then worker A gets all the credit and worker B looks like a slacker so that worker A earns a utility of 15 and worker B earns a utility of -5. Similarly, if worker B is selfish and worker A works as a team player, then worker B gets all the credit and worker A looks like a slacker so that worker A earns a utility of -5 and worker B earns a utility of 15.

a. (20 points) Are there any dominant strategies? If so, then identify them.
b. (20 points) What is the Nash Equilibrium of this game? That is, what actions are played by each player and what are each player’s equilibrium utilities?

Answer 1

On the basis of the above information, we can create a payoff matrix for the game as follows.

		B
		Work Selfishly	Team Player
A	Work Selfishly	(0,0)	(15,-5)
Team Player	(-5,15)	(10,10)

The first number represents the payoff of Player A, and the second of Player B.

a) Clearly, if A works selfishly, he will recieve a greater utility, irrespective of what B chooses to do. Similarly if B works selfishly, he will recieve a greater utility, irrespective of what A chooses to do. Working Selfishly is the dominant strategy of both players A & B.

b) A nash equilibrium is determined where neither player has any incentive to change the strategy they are playing. In this scenario, since both have dominant strategies, each player will choose to 'Work Selfishly'. Both of them will receive a payoff of 0 at the equilibrium.