Game Theory: Please show your work and explain the answers to help me understand
ID: 1149299 • Letter: G
Question
Game Theory: Please show your work and explain the answers to help me understand the process
3. Consider the following normal form game between A and B. Use IEDS to solve game. R1 R2 R3 C1 5, 10 6, 5 7, 8 C2 3,8 0, 2 2,8 C3 0, 11 4, 5 5, 7 (a.) If A eliminates first, list each elimination in order, and find solution (b.) If B eliminates first, list each elimination in order, and find solution. Firm A and B produce good x and the firms are in a normal form game of price competition. Demand for good x is given as x - 8- P, where P is equilibrium price. Each firm can pick either $2, 4 or 6 for his price If prices match, they split demand and if prices don't match, then firm with lowest price meets entire demand at his price. Payoffs are in terms of revenue. (All costs are zero!) (a.) Draw the 3 X 3 normal form game and list all payoffs (b.) Starting with firm A apply IEDS to solve the game (c.) For each elimination round, have A and B simultaneously eliminate any dominated strategies. In this 4. case, what is the outcome?Explanation / Answer
Answer for 3/a
If A eliminates first
A has Action Profile (R1,R2,R3) out of these actions R3 dominates R2 because if we compare both these actions
In Given payoffs first number is payoff for Player A and second number is payoff for Player B
If we compare R3 to R2 then 7>6; 2>0; 5>4
Hence R3 strictly dominates R2 (Strictly dominannce becasue each payoff from R3 is strictly higher than payoff from R2)
Now R3 and R1 remains.
Now Player B whi has action profile (C1,C2,C3)
C1 weakly dominates C3. 10>8 ; 8=8
Hence no payoff matrix shrniks to 2x2 matrix which is as below
C1 C3
R1 (5,10) (0,11)
R3 (7,8) (5,7)
In this payoff matrix it is simply observed (R3,C1) is Nash Equillibrium if A plays first
Answer for 3/b
If Player B eliminates first
As discussed above C1 weakely dominates C2 hence C2 is eliminated
Now R3 strictly dominates R1 and R2
Hence remaining matrix is
C1 C3
R3 (7,8) (5,7)
Again (R3,C1) is Nash Equillibria
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