Week 8 – Chapter 6 Game theory – Homework

Chp 6. Exercise 1. – Say whether the following claim is true or false, and provide a brief (1-3 sentence) explanation for your answer.

Claim: If player A in a two-person game has a dominant strategy , then there is a pure strategy Nash equilibrium in which player A plays and player B plays a best response to .

Chp 6. Exercise 3 – Find all pure strategy Nash equilibria in the game below. In the payoff matrix below the rows correspond to player A’s strategies and the columns correspond to player B’s strategies. The first entry in each box is player A’s payoff and the second entry is player B’s payoff

Chp 6. Exercise 4 – Consider the two-player game with players, strategies and payoffs described in the following game matrix.

(a) Does either player have a dominant strategy? Explain briefly (1-3 sentences).

(b) Find all pure strategy Nash equilibria for this game.

Chp 6. Exercise 5 – Consider the following two-player game in which each player has three strategies.

Find all the (pure strategy) Nash equilibria for this game.

**NetLogo Assignment**

**Download Netlogo First**

- For this assignment we will investigate a prisoner dilemma model in net logo
- One of the most prominently studied phenomena in Game Theory is the “Prisoner’s Dilemma.” The Prisoner’s Dilemma, which was formulated by Melvin Drescher and Merrill Flood and named by Albert W. Tucker, is an example of a class of games called non-zero-sum games.
- In zero-sum games, total benefit to all players add up to zero, or in other words, each player can only benefit at the expense of other players (e.g. chess, football, poker — one person can only win when the opponent loses). On the other hand, in non-zero-games, each person’s benefit does not necessarily come at the expense of someone else. In many non-zero-sum situations, a person can benefit only when others benefit as well. Non-zero-sum situations exist where the supply of a resource is not fixed or limited in any way (e.g. knowledge, artwork, and trade). Prisoner’s Dilemma, as a non-zero-sum game, demonstrates a conflict between rational individual behavior and the benefits of cooperation in certain situations.
- As in the Exam-or-Presentation Game, we can consider how one of the suspects — say Suspect 1 — should reason about his options.
- If Suspect 2 were going to confess, then Suspect 1 would receive a payoff of −4 by confessing and a payoff of −10 by not confessing. So in this case, Suspect 1 should confess.
- If Suspect 2 were not going to confess, then Suspect 1 would receive a payoff of 0 by confessing and a payoff of −1 by not confessing. So in this case too, Suspect 1 should confess.

- Assignment – For this assignment. Adjust the defection-award and run the model. What happens when you increase defection award?
- and what happens when you decrease the defection-award?
- Please take a screenshot of your model