5. Consider the game given in the adjoining (Figure 1). Player l's actions in the initial...
Consider the infinitely repeated version of the symmetric two-player stage game in figure PR 13.2. The first number in a cell is player 1's single-period payoff. Assume that past actions are common knowledge. Each player's payoff is the present value of the stream of single-period payoffs where the discount factor is d. (a) Derive the conditions whereby the following strategy profile is a subgame perfect Nash Equilibrium: 2 Consider the infinitely repeated version of the symmetric two-player stage game in...
In the above figure of a game between player 1 and 2 choosing between shaking (S) and pushing (P). What are their payoffs in a backward induction solution to the game?
or 5. 1. Consider the following game tree. In this tree, a player, say Player 3, has an information set with three nodes, I, II, and III in it. Explain whether each of the following is true or false. (a) Node I is Player 3's decision node, but node II is Player 2's decision node. (b) Player 3 has three actions at node III and two at node I (c) Player 3 has exactly two actions at node III, labeled...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1 moves twice: Player 1 chooses Enter or Erit, and if she chooses Exit the game ends with payoffs of 2 to player 2 and 0 to player 1. • Player 2 observes player l's choice and will have a choice between Fight or Help if player 1 chose Enter. Choosing Help ends the game with payoffs of 1 to both players. • Finally, player...
1. Consider a gaine where the row player moves first, choosing between T and B. The column player observes the row player's action and must choose between L and R. In the payoff table given in (a), solve for the unique backward induction strategy profile, and compare it to the Nash equilibrium when actions are chosen simultaneously. In the payoff table (b); solve for all pure strategy Nash equilibria. Optional question: Are there any inixed strategy equilibria in (b)? DLR...
2. Consider the extensive form game shown in the figure below. The top payoff at a terminal node is for player 1. Find all subgame perfect Nash equilibria P1 P2 P2 P1 P1 0 10 4 4 4 2. Consider the extensive form game shown in the figure below. The top payoff at a terminal node is for player 1. Find all subgame perfect Nash equilibria P1 P2 P2 P1 P1 0 10 4 4 4
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...
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...
Consider the following game: Player 1 announces an integer p in the interval (1.201. Player 2 then announces an integer g in the interval (21.40) . Ifp-1, then the game is a tie (each player gets a payoff of zero). . If q is prime, then Player 1 wins (the payoffs are (1,-1). . If pand q have a common factor greater than 1, then Player 1 wins (the payoffs are (1,-1). If pand qare relatively prime (but g is...