The payoff matrix shows the payoffs to Player 1 and Player 2 given the various strategies they might select. The players' goal is to get the biggest payoff possible (i.e. bigger numbers are better than smaller numbers in the payoff matrix). Solve the payoff matrix to determine the Nash equilibrium(s) of the game? a b С d Selected answer will be automatically saved. For keyboard navigation, press up/down arrow keys to select an answer. (Bottom, Right) Player 1 (Top, Left) Top Bottom (Top, Left) and (Bottom, Right) Player 2 (Top, Left) and (Bottom, Left); Left 5,3 4, 2 Right 2, 2 3,6

There are three players who must each choose an “effort” level from 1 to 7, that is, Si = {1, 2, 3, ..., 7}. The payoff for each player i is ui(si, s−i) = 10 max{s1, s2, s3} − si. How many pure- strategy Nash equilibria are there?   Select one: a.2 b.4 c.none of the other answers d.3 e.1

on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.

Two players bargain over $20. Player 1 first proposes a split of(n, 20 - n), where n is an integer in {0, 1, ..., 20}. Player 2 can either accept or reject this proposal. If player accepts it, player 1 obtains $n and player 2 obtains $(20 - n). If player 2 rejects it, the money is taken away from them and both players will get $0. Question: Find two subgame perfect Nash equilibria of this game and state clearly each player's equilibrium strategies (recall that in a dynamic game, a player's strategy is a complete-contingent plan). Explain why the strategy profiles form a subgame perfect equilibrium.