Question

In: Statistics and Probability

Consider a game between a tax collector (player 1) and a tax payer (player 2).  Player2 has...

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.

Solutions

Expert Solution


Related Solutions

Coin taking game This game is played between 2 players, player 1 and player 2. There...
Coin taking game This game is played between 2 players, player 1 and player 2. There are two piles of coins. The values of a coin can be any integer. Both players know the values of all coins in both piles. Player 1 makes the first move, and play alternates between the players. A move consists of taking a coin from the top of either of the piles (either player can take from either pile). The game ends when both...
Consider the following two-player game, in which Player 1 is the IMF, and Player 2 is...
Consider the following two-player game, in which Player 1 is the IMF, and Player 2 is a debtor country. Reform Waste Aid 3, 2 -2, 3 No Aid -2, 1 0, 0 a) Compute all (pure and mixed) Nash equilibria. b) Do you think that the above game is the case of a resource curse? Interpret the game with a story of a resource curse.
Consider the following game. Player 1’s payoffs are listed first:                        Player 2 X Y Player...
Consider the following game. Player 1’s payoffs are listed first:                        Player 2 X Y Player 1 A 90 , 1 10 , 0 B 10 , 0 50 , 1 C 100 , 0 80 , 1 Imagine that player 1 makes a decision first and Player 2 makes a decision after observing player 1’s choice. What is the subgame-perfect equilibrium of this game? Imagine that player 2 makes a decision first and Player 1 makes a decision after...
Consider a game in which, simultaneously, player 1 selects any real number x and player 2...
Consider a game in which, simultaneously, player 1 selects any real number x and player 2 selects any real number y. The payoffs are given by: u1 (x, y) = 2x − x2 + 2xy u2 (x, y) = 10y − 2xy − y2. (a) Calculate and graph each player’s best-response function as a function of the opposing player’s pure strategy. (b) Find and report the Nash equilibria of the game. (c) Determine the rationalizable strategy profiles for this game.
Question 4: Jar Game Consider the following game: Players: 2 - We designate player #1 to...
Question 4: Jar Game Consider the following game: Players: 2 - We designate player #1 to be the one that starts with the jar. Actions: - Each round at the same time both players deposit between 1 to 4 pennies into the jar. - Then both players are able to count the pennies in the jar. - If there are 21 or more pennies, the person with the jar is the winner. - If there are 20 or less pennies,...
Below is a game between player A and player B. Each player has two possible strategies:...
Below is a game between player A and player B. Each player has two possible strategies: 1 or 2. The payoffs for each combination of strategies between A and B are in the bracket. For example, if A plays 1 and B plays 1, the payoff for A is -3, and the payoff for B is -2. Player B Strategy 1 Strategy 2 Player A Strategy 1 (-3,-2) (10,0) Strategy 2 (0,8) (0,0) How many pure strategy Nash equilibria does...
Below is a game between player A and player B. Each player has two possible strategies:...
Below is a game between player A and player B. Each player has two possible strategies: 1 or 2. The payoffs for each combination of strategies between A and B are in the bracket. For example, if A plays 1 and B plays 1, the payoff for A is 1, and the payoff for B is 0. Player B Strategy 1 Strategy 2 Player A Strategy 1 (1,0) (0,1) Strategy 2 (0,1) (1,0) How many pure strategy Nash equilibria does...
Consider the game in normal form given in the followingtable. Player 1 is the “row” player...
Consider the game in normal form given in the followingtable. Player 1 is the “row” player with strategiesA,BandCandplayer 2 is the “column” player with strategiesL,CandR. The gameis given in the following table: L C R A 0,0 2,-2 -2,3 B -2,2 0,0 2,-1 C 3,1 -1,2 0,1 (a) Find whether there is a mixed strategy Nash equilibrium (M.S.N.E) where player 1 mixes between A and C and player 2 mixes between L,C and R with positive probability. (b) Find whether...
Consider the following game that has two players. Player A has three actions, and player B...
Consider the following game that has two players. Player A has three actions, and player B has three actions. Player A can either play Top, Middle or Bottom, whereas player B can play Left, Middle or Right. The payoffs are shown in the following matrix. Notice that a payoff to player A has been omitted (denoted by x). Player B    Left Middle Right Top (-1,1) (0,3) (1,10) Middle (2,0) (-2,-2) (-1,-1) Bottom (x,-1) (1,2) (3,2) (player A) Both players...
Consider the following strategic-form simultaneous game. Player 1’s payoffs are listed first, in bold Player 2...
Consider the following strategic-form simultaneous game. Player 1’s payoffs are listed first, in bold Player 2 W X Y Z Player 1 A 2 , 500 30 , 400 200 , 200 4 , 4 B 5 , 50 20 , 40   10 , 20 4 , 4 C 1 ,   0 1 ,   4 3 ,   2 4 , 4 Does either player have any weakly dominant strategies? If yes, list them. Briefly explain. Does either player have any...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT