Consider a game between a tax collector (player 1) and a tax payer (player 2). Player2 has an income of 200 and may either report his income truthfully or lie. If he reports truthfully, he pays 100 to player 1 and keeps the rest. If player 2 lies and player 1 does not audit, then player 2 keeps all his income. If player 2 lies and player 1 audits then player 2 gives all his income to player 1. The cost to player 1 of conducting an audit is 20. Suppose that both parties move simultaneously (i.e. player 1 must decide whether to audit before he knows player 2’s reported income). Find the mixed-strategy Nash equilibrium for this game and the equilibrium payoffs to each player. Explain in your own words the meaning of these results.
Consider a game between a tax collector (player 1) and a tax payer (player 2). Player2 has an income of 200 and may eit...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0, 0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0,0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players get...
Consider a game in which, simultaneously, player 1 selects a number x and player 2 select a number y, where x and y must be greater than or equal to 0. Player 1's payoff is U1 = 8x - 2xy - x2 and player 2's payoff is U2 = 4by + 2xy - y? The parameter b is privately known to player 2. Player 1 knows only that b = O with probability 1/2 and b = 4 with probability...
3. Player 1 and Player 2 are going to play the following stage
game twice:
Player 2
Left
Middle
Right
Player 1
Top
4, 3
0, 0
1, 4
Bottom
0, 0
2, 1
0, 0
There is no discounting in this problem and so a player’s payoff
in this repeated game is the sum of her payoffs in the two plays of
the stage game.
(a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
. Player 1 and Player 2 are going to play the following stage game twice: Player 2 Left Middle Right Player 1 Top 4, 3 0, 0 1, 4 Bottom 0, 0 2, 1 0, 0 There is no discounting in this problem and so a player’s payoff in this repeated game is the sum of her payoffs in the two plays of the stage game. (a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
4. Consider a game where Player 2 has two possible types. Player 2 knows her own type but Player 1 believes that the probability of Player 2 being type 1 is p. Identify the Bayesian Nash equilibrium of this game Type 1 C N C 0,0 7-2 N -2,75,5 Type 2: C N C -2,0 5,2 N | 0,5 | 7,7 |
Question 1 (15 polnts) Consider the following simultaneous-move game Player 2 ILIR T15. 2 | 2,0 B 3,30, 5 A. Find the pure-strategy Nash equilibrium of this game. Player M B. Can player 2 help himself by employing a simple unconditional strategie move? If so, what action will player 2 choose to commit to? What are the players' new payoffs? C. Answer the following question only if your were not able to find an unconditional strategic move. Can player 2...