This next group is about finding equilibrium points using the arrow diagram technique. In each case, find the equilibrium point or points, or say there is no equilibrium based on the arrows. Be sure to label the arrows clearly AND label the cells where you find equilibria with an asterisk, *. Assume payoffs are measured in dollars. More money is preferred to less. The games are expressed as parameterized 2 x 2 games analogous to the Lion-Lamb games in the lecture notes. There are 4 Parts --- note the differential point values. Setup for Parts A and B H V-C VC H 2 2 VO The parameterized game is shown in the right-hand payoff matrix. Here, V and C are the parameters that defined a particular game. That is, once you pick values for V and C you've defined a game. Assume V>0. In the following questions you should work with the qualitative information. For instance, JUST USE V>C>O in Part A --- don't put specific numbers in the payoff table. D ov | K Continued: Basic Possible Game Classes 2 H H D V-C V50 H Different combinations of V and C may give rise to games with the strategic structure of one of the following 2 x 2 games. Prisoner's Dilemma Cooperation Stag Hunt or Game of Assurance Chicken (also known as Hawk- Dove) 0,V NK S NK Part A (10 points] V >> 1 H V-C V-c VELV Ivo H Assume that V>C>0. What is the game's particular strategic structure? Choose one from the list and use arrows in the game in the right panel to find the equilibrium point or points in case of multiple equilibria. Remember: We only consider equilibria in the pure strategies as there are no mixed strategies yet. D ovka Part B: [10 points] C>V>0 V.C Ke a Evac Ivo H Suppose now C>V> 0. What is the game's particular strategic structure? Choose one from the list and use arrows in the game in the right panel to find the equilibrium point or points in case of multiple equilibria. Remember: We only consider equilibria in the pure strategies as there are no mixed strategies yet. D vr 232 2 Part C [10 points] A Variant Payoff Matrix H . Consider the variant of the parameterized payoff matrix shown in the right-hand panel. Assume that V>C> 0. What is the game's particular strategic structure? Choose one from the list and use arrows in the game in the right panel to find the equilibrium point or points in case of multiple equilibria. Remember: We only consider equilibria in the pure strategies as there are no mixed strategies yet. 4 keer oo D ojo 2 2 Part D (5 points] H H Use the game in Part C to determine which (if any) equilibrium point(s) is (are) COST-BENEFIT EFFICIENT. Use the table in the right-hand panel to show the total surplus in each payoff cell. Label the cost-benefit efficient cell(s) with a DOLLAR sign, $. This next group is about finding equilibrium points using the arrow diagram technique. In each case, find the equilibrium point or points, or say there is no equilibrium based on the arrows. Be sure to label the arrows clearly AND label the cells where you find equilibria with an asterisk, *. Assume payoffs are measured in dollars. More money is preferred to less. The games are expressed as parameterized 2 x 2 games analogous to the Lion-Lamb games in the lecture notes. There are 4 Parts --- note the differential point values. Setup for Parts A and B H V-C VC H 2 2 VO The parameterized game is shown in the right-hand payoff matrix. Here, V and C are the parameters that defined a particular game. That is, once you pick values for V and C you've defined a game. Assume V>0. In the following questions you should work with the qualitative information. For instance, JUST USE V>C>O in Part A --- don't put specific numbers in the payoff table. D ov | K Continued: Basic Possible Game Classes 2 H H D V-C V50 H Different combinations of V and C may give rise to games with the strategic structure of one of the following 2 x 2 games. Prisoner's Dilemma Cooperation Stag Hunt or Game of Assurance Chicken (also known as Hawk- Dove) 0,V NK S NK Part A (10 points] V >> 1 H V-C V-c VELV Ivo H Assume that V>C>0. What is the game's particular strategic structure? Choose one from the list and use arrows in the game in the right panel to find the equilibrium point or points in case of multiple equilibria. Remember: We only consider equilibria in the pure strategies as there are no mixed strategies yet. D ovka Part B: [10 points] C>V>0 V.C Ke a Evac Ivo H Suppose now C>V> 0. What is the game's particular strategic structure? Choose one from the list and use arrows in the game in the right panel to find the equilibrium point or points in case of multiple equilibria. Remember: We only consider equilibria in the pure strategies as there are no mixed strategies yet. D vr 232 2 Part C [10 points] A Variant Payoff Matrix H . Consider the variant of the parameterized payoff matrix shown in the right-hand panel. Assume that V>C> 0. What is the game's particular strategic structure? Choose one from the list and use arrows in the game in the right panel to find the equilibrium point or points in case of multiple equilibria. Remember: We only consider equilibria in the pure strategies as there are no mixed strategies yet. 4 keer oo D ojo 2 2 Part D (5 points] H H Use the game in Part C to determine which (if any) equilibrium point(s) is (are) COST-BENEFIT EFFICIENT. Use the table in the right-hand panel to show the total surplus in each payoff cell. Label the cost-benefit efficient cell(s) with a DOLLAR sign, $