Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / Consider the situation described in Figure 1 below
Consider the situation described in Figure 1 below. R |? 1,3 L R 1 R' 2,1 0,0 0,2 0,1 1. Represent the strategic form of the game.[1 point] 2. Determine all Nash equilibria in pure strategies of the game.[1 point] 3. Determine the subgame-perfect equilibria in pure strategies of the game.[1 point] 4. Is it plausible or credible to have the situation (RR) as an equilibrium in this game? Explain. [1 point] 5. Assume that player 2 believes that history L occurred with probability p, and history M occurred with probability 1-p. a. Given player 2's belief, calculate player 2's expected payoff from playing R' and player 2's expected payoff from playing 2': [1 point] b. Given the belief, what action should player 2 choose between R' and L? Explain. [1 point] C. Requiring that each player has a belief and acts optimally given this belief, would any change occur in the subgame-perfect equilibria found in question 3.7 [1 point]
1. Player 1 can choose L, R and M while player 2 has two choices L' and R', So his strategies are
L' following L and R' following M, L'R'
R' following L and L' following M, R'L'
R' following L and R' following M, R'R'
L' following L and L' following M, L'L'
so strategic form of game is given by
| Player1\player2 | L'R' | R'L' | R'R' | L'L' |
| L | 2,1 | 0,0 | 0,0 | 2,1 |
| R | 1,3 | 1,3 | 1,3 | 1,3 |
| M | 0,1 | 0,2 | 0,1 | 0,2 |
2.Nash Equilibrium in pure strategy: If player 1 plays L, Player 2 plays L' (as it gives more payoff). Also if player 2 plays L' player 1 gets maximum payoff from L, so LL' is Nash equilibrium
If player 1 plays M, player 2 gets maximum payoff by playing L'. But if player 2 plays L' player 1 gets more payoff by playing L, so ML' is not nash.
Only 1 nash equilibrium exists, LL' giving (2,1) payoff respectively to player 1 and 2.
3. Here player 2 has dominant strategy to play L' (as it always gives more payoff than chosing R'). And given this, it is in best interest for player 1 to play L (as it gives maximum payoff). Thus nash equilibrium LL' is also the subgame perfect equilibrium in pure strategy.
4. RR' is not credible as player 1 knows that player 2 will always get maximum by this and he has a chance of getting higher payoff by chosing L. So he will not choose R that will give a definitely higher payoff to player 2.
5 a) Player 2 expected payoff if he plays L' is p/2+(1-p)*(2/2) = p/2+1-p = 1+p/2
and if he plays R' it is 0+(1-p)*(1/2) =1/2-p/2
b) Since 1+p/2>1/2-p/2, he should play L'.
c) No it will not change the subgame perfect equilibrium in this case as player 2 has dominant strategy of playing L' in this game. And player 1 knows that so will choose L.
