CMSC 477/677 - Spring 2007

Discussion Questions for Class #14, March 15

Reading: Wooldridge (Appendix A) and Chapter 6.

• A rational agent's utility function will satisfy the properties (p. 107) of reflexivity, transitivity, and comparability. Do you think all agents (e.g., humans) actually have utility functions that satisfy these properties? If they do not, how would that affect the ways in which we design our agents to interact with them?
• Figure 6.2 (p. 108) shows the relationship between money and utility graphically. Do you think this relationship is constant across (human) agents? If not, how would that affect their interactions?
• What is the difference between strong dominance and weak dominance?
• Why do some interaction scenarios not have any Nash equilibrium? Can you give some real-world examples?
• Why do some interaction scenarios have more than one Nash equilibrium? Can you give some real-world examples?
• Can you think of a (real-world or contrived) example of an interaction scenario that is strictly competitive but not zero-sum?
• The payoff matrix for the Prisoner's Dilemma is designed to create a "everybody defects" Nash equilibrium. How could you change the payoff matrix to move or eliminate the Nash equilibrium? How sensitive is the equilibrium to the specific numbers that are chosen (e.g., if you change the payoff of 3 to 3.2, would that matter)?
• Why is the iterated prisoner's dilemma a different game from the PD? Is there a Nash equilibrium for the IPD?