Game Theory

In this lab you will play a game against the computer and try to develop a winning strategy.ccollins@math.utk.eduBefore You Get StartedHere are some cool sights for getting a new name or nickname for you or your friends: Hobbit Name Prof. Poopy-Pants Name Anagrams Tough Name Pokemon NameFor you RISK fanatics:Here's the table of probabilities I got for up to 10 Attackers vs. 8 Defenders: risk2.outGamebotSave this MATLAB function gamebot.m in the MATLAB work folder. To play a game using Gamebot, you just typegamebotand then it will ask you for a payoff matrix and a strategy vector for Player 2. You will play as Player 1. Then you get to play the game repeatedly, and Gamebot keeps track of the payoffs and other statistics. Use 0 as your choice to end the game.Examplegamebot Enter payout matrix: [2 -2;-2 4] Strategy vector for Player 2: [1/2 1/2] Enter 0 for your choice to end the game. Your choice: 1 Computer chooses 1 for a payout of 2. Number of games: 1 Avg. Payout: 2 . . Your choice: 2 Computer chooses 1 for a payout of -2. Number of games: 50 Avg. Payout: -0.16 Your choice: 0 Strategy used by Player 1: 0.7 0.3Note the strategy reported is the probability for me choosing each choice, i.e. my strategy vectorMoraFor Mora the payout matrix is [2 -2;-2 4] The plays for Player 1 and for Player 2 are: 1 or 2 Play against the gamebot, with Player 2 having the strategy: (a) [1/2, 1/2] (b) [3/4, 1/4] (c) [3/5, 2/5] Play at least 20 games against each strategy and try to develop a winning strategy for Player 1. E-mail me your best strategy in each case. ccollins@math.utk.eduMountain City SiegeFor Mountain City Siege the payout matrix is [3 1 0 -1;0 2 -1 -2; -3 1 1 -3; -2 -1 2 0; -1 0 1 3] The plays for Player 1 are: 1=(4,0), 2=(3,1), 3=(2,2), 4=(1,3), 5=(0,4) and for Player 2: 1=(3,0), 2=(2,1), 3=(1,2), 4=(0,3) Play against the gamebot, with Player 2 having the strategy: (a) [1/4 1/4 1/4 1/4] (b) [1/18, 4/9, 4/9, 1/18] Play at least 20 games against each strategy and try to develop a winning strategy for Player 1. E-mail me your best strategy in each case. ccollins@math.utk.eduChallengeWrite a MATLAB program which accepts the payout matrix and the strategy vectors for Players 1 and 2 and determines the average payoff (called thevalue).