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Solve the game with the given payoff matrix

Solution for Solve the game with the given payoff matrix. P = -6 0 1 -9 0 0 0 -1 -2 a) Find the optimal row player strategy b) Find the optimal colum Solve the game with the given payoff matrix. Hint [See Example 3.] Optimal row player strategy 1/10 0 3/10 Optimal column player strategy 2/15 0 1/5 Expected value of the game 1/ Solve the game with the given payoff matrix. [3 7 6 6 P-1 0-3 46 4 0-34 Reduce the payoff matrix by dominance. LIO Find the optimal row strategy Find the optimal column strategy Find the expected value of the game in the event that each player uses his or her optimal strategy Solve the game whose pay-off matrix is given below : A). 1: B). 2: C). 3: D). 4-- View Answer. 6). Consider a game G with the following pay-off matrix, determine the value of game. A). 2: B). 3: C). 4: D). None of these-- View Answer: 7). The range of p and q that will make the pay-off element \( \Large a_{22}\) a saddle point for the game.

Answered: Solve the game with the given payoff bartleb

  1. Calculating the Solution of a Matrix Game. If you want to solve a matrix game, you've surfed to the right web page. Here you are able to enter an arbitrary matrix. It will be considered as a matrix of a matrix game where Player I chooses a row and simultaneously Player II chooses a column. The matrix entry of the jointly selected row and column.
  2. us the second, then top
  3. In game theory, a payoff matrix is a table in which strategies of one player are listed in rows and those of the other player in columns and the cells show payoffs to each player such that the payoff of the row player is listed first.. Payoff of a game is incremental gain/benefit or loss/cost that accrue to a player by executing its strategy given the strategy of the other player
  4. Textbook solution for Finite Mathematics and Applied Calculus (MindTap Course 7th Edition Stefan Waner Chapter 6 Problem 25RE. We have step-by-step solutions for your textbooks written by Bartleby experts

Advanced Math Q&A Library Solve the game with the given payoff matrix. -3 P = -10 0 -1 -2 Find the optimal row player strategy. Find the optimal column player strategy. Find the expected value of the game This learning video will show you how to identify the solution of game theory by payoff matrix. In this tutorial we will find the solution of the game to the..

Solve the game whose pay-off matrix is given below : A). 1: B). 2: C). 3: D). 4-- View Answer: 7). Consider a game G with the following pay-off matrix, determine the value of game. A). 2: B). 3: C). 4: D). None of these-- View Answer: 8). The range of p and q that will make the pay-off element \( \Large a_{22}\) a saddle point for the game. Solve the game with the given payoff matrix. -1 1 2 P = 5 -1 -2 3 2 Optimal row player strategy Optimal column player strategy Expected value of the game. close. Start your trial now! First week only $4.99! arrow_forward. Question. help_outline. Image Transcriptionclose Solve the game with the given payoff matrix. P =-6. 0. 1-9. 0. 0. 0-1-2. a) Find the optimal row player strategy b) Find the optimal column player strategy c) Find the expected value of the game. Feb 08 2021 04:55 AM. Expert's Answer. Solution.pdf Next Previous. GAME THEORY Q. Obtain the optimal strategies for both the players and the value of the game whose payoff matrix is as follows : Player-B Player-A B1 B2 A1 1 -3 A2 3 5 A3 -1 6 A4 4 -1 A5 2 2 A6 -5 0 • Solution : The given problem does not possess any saddle point Solve the following game using the graphical method: Payoff matrix Player Player B's Strategies A's Strategies B1 B2 A1 -7 6 A2 7 -4 A3 -4 -2 A4 8 -6 Let B play the strategies B1 and B2 with respective probabilities q1 and 1- q1, the expected pay-off for which, when A chooses to play A1, shall be -7 q1 + 6(1- q1) or -13 q1 + 6.

Example 4 • Using the dominance probability, obtain the optimal strategies for both the players and determine the value of the game. The payoff matrix for player A is given Player B Player A I II III IV V I 2 4 3 8 4 II 5 6 3 7 8 III 6 7 9 8 7 IV 4 2 8 4 3 26. Graphic Method (mX2 or 2Xn) Example 5 Consider the 2-player game given in Fig 1, which will be played by 2 players- Player A and Player B. Each player has 2 strategies each- Player A can play Top or Bottom and Player B can play Left or right. The matrix above is called the payoff matrix. Player A is also called row player and Player B column player Solving the Prisoner' s Dilemma Abstract We will follow the usual convention of representing a game as a payoff matrix. Here is an example of the notation we will use for two-player games: The first player, to whom we will generally refer as I, selects a move labeling one of the dehne therestricted game given by 1. Intuitively,. A saddle point is a position in payoff matrix where the maximum of row minima coincides with the minimum of column maxima. The payoff at the saddle point is called the value of the game. 1. Solve the game whose pay off matrix is given by. 2. Determine which of the following two people zero sum games are strictly determinable and fair Determine the optimal strategies for the players and value of the game from the following payoff matrix. Player B Player A B1 B2 A1 4 -4 A2-4 4 Solution: The given problem does not have a saddle point. Therefore, the method of saddle point is not sufficient to determine optimal strategies. Let the payoff matrix is given by B's strategie

Determine the optimal strategy for both the manufacturers & value of the Game. Ans : Value of Game = 3/2, p1=1/2, 1-p1=1/2, q1=1/10, 1-q2=9/10. Q16. Two competitors are competing for the market share of the similar product. The pay off matrix in terms of their advertising plan is show below 1. Method & Example-1. This method can only be used in games with no saddle point, and having a pay-off matrix of type n × 2 or 2 × n. The example is used to explain the procedure. 1. Saddle point testing. We apply the maximin (minimax) principle to analyze the game. ∴ This game has no saddle point. First, we draw two parallel lines 1 unit.

13) is the payoff matrix of a strictly determined game. Find a saddle point. A) 9. B) 2. C) 3. D) 8. E) none of these. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The given matrix is the payoff matrix for a strictly determined game. Find a saddle point. Determine optimum pure strategies for. This video summarizes how we can look at a payoff matrix for a game such as the Prisoner's Dilemma. The video covers basic game theory techniques how to read.. {Given the non-strictly determined matrix game M, free of recessive rows and columns, {to find and v {proceed as follows: {1. If M is not a positive matrix, add a suitable positive constant k to each element of M to get a new matrix M 1 {If v1 is the value of game M1 , then the value of the original game M is given by v = v 1 -

Solved: Solve The Game With The Given Payoff Matrix

Solve The Game With The Given Payoff Matrix

  1. $\begingroup$ The given answer in the book is (3/5,2/5) for player 1 and for player 2 it is (0,1,0).I understand how the 1/2<probability<2/3 is obtained and that's what I got when I did it graphically but that's not the given answer.I am trying to do this problem graphically as found in the last example of this:link.With this method how can I calculate player 2's probabilities.Sorry I don't.
  2. The set of feasible payoff profiles of a strategic games is the set of all weighted averages of payoff profiles in the game.The set of feasible payoff pairs in a two player strategic game can be represented graphically. The set of weighted averages of the points (x 1,x 2) and (y 1,y 2). Represent the feasible payoff profiles of Prisoner's.
  3. ated by the j th row and can be deleted from the matrix. Do
  4. negative of the negative of the maximum value i.e.,k>2,let k=3,then the given pay-off matrix becomes: Company B 6 -1 5Company A 4 0 -4 1 7 10 Step 2: let the strategy of company A bedesignated by p1 and p2 and that of company B byq1 q2 and q3 respectively, such that p1+p2+p3 = 1 and q1+q2+q3=1 If the value of the game is v, then for companyA.
  5. The payoff matrix for this game is given in Figure 11.6 Payoff Matrix for the Prisoners' Dilemma. The two rows represent Frankie's strategic choices; she may confess or not confess. The two columns represent Johnny's strategic choices; he may confess or not confess. There are four possible outcomes: Frankie and Johnny both confess.

Table 1.2.1. A game matrix showing the strategies for each player Definition 1.2.2.. A payoff is the amount a player receives for given outcome of the game.. Now we can fill in the matrix with each player's payoff. Since the payoffs to each player are different, we will use ordered pairs where the first number is Player 1's payoff and the second number is Player 2's payoff However, many games do not have a dominant strategy for each player. Let us examine the payoff matrix given in the table below, which is the same as the above matrix, except for the bottom right-hand corner, if neither firm advertises, Firm B will again earn a profit of 2, but Firm A will earn a profit of 20. Now Firm A has no dominant strategy Such games are known as two-person zero-sum games because a gain by one player signifies an equal loss to the other. It suffices, then, to summarize the game in terms of the payoff to one player. Designating the two players as A and B with m and n strategies, respectively, the game is usually represented by the payoff matrix to player A as B1. The simplest type of game is one where the best strategies for both players are pure strategies. This is the case if and only if, the pay-off matrix contains a saddle point. To illustrate, consider the following pay-off matrix concerning zero sum two person game. Example Player B Player A I II III IV V I -2 0 0 5 3 I

Solve the game whose pay off matrix is given by table

  1. point and for a m x2 matrix problem we have to find a
  2. =3.
  3. The most basic tool of game theory is the payoff matrix. Typically, matrices are used to describe 2-player, simultaneous games. Seen in the template below, the two-player choices line up perpendicular to each other on the outer borders of our matrix— one stems across the top (left-to-right), & one spans down the left-side (top-to-bottom)
  4. Return to the game given by the payoff matrix in Problem. Two classmates A and B are assigned an extra credit group project. Each student can choose to Shirk or Work. If one or more players choose Work, the project is completed and provides each with extra credit valued at 4 payoff units each
  5. Example: 4 Solve the game whose payoff matrix is given below B 1 B 2 B 3 B 4 Row Minimum A 1 3 2 4 0 0 A 2 3 4 2 4 A 3 4 2 4 0 0 A 4 0 4 0 8 0 Column maximum Minimax elements Example 5. Two breakfast food manufacturers, ABC and XYZ are competing for an increased market share. The payoff matrix, shown in the following table,.

Interval matrix game is the interval generation of classical matrix games. Because of uncertainty in real-world applications, payoffs of a matrix game may not be a fixed number. Since the payoffs may vary within a range for fixed strategies, an interval-valued matrix can be used to model such uncertainties Algebraic Method Example 1: Game Theory. Consider the game of matching coins. Two players, A & B, put down a coin. If coins match (i.e., both are heads or both are tails) A gets rewarded, otherwise B. However, matching on heads gives a double premium. Obtain the best strategies for both players and the value of the game The payoff matrix for the 2-person 0-sum game of Union in negotiation with Management for annual percentage pay raise is given below: M1 M2 M3 M4 U1 2 4 2 3 U2 3 3 5 2 U3 4 3 2 3 U4 4 4 1 4 Required: a. Eliminate all dominated strategies to obtain the irreducible matrix. b. Identify and solve all sub-games. c. Summarize the solution of the game Solve the following games by using maxmin (minimax) principle whose payoff matrix are given below: Include in your answer - (i) strategy selection for each player, (ii) the value of the game to each player If you need help to solve larger games feel free to contact me at rahul dot savani at liverpool.ac.uk Enter dimension of game e.g. 2 3 for 2x3 matrices (max 15x15) Enter payoff matrix A for player 1 , e.g

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optimization - Solving a 3x3 payoff matrix - Mathematics

Now that we have created a complete payoff matrix we can start to solve the game! Step 5: Look For Dominant Strategies. This is where game theory gets really interesting. The first step in this analysis is to determine if any of the choices (or strategies) for either player are dominant over the other choices. Dominant Strategie Solve the game with the given payoff matrix. Hint [See Example 3.] Optimal row player strategy 1/10 0 3/10 Optimal column player strategy 2/15 0 1/5 Expected value of the game ½ Posted 4 days ago. Refer to the matrix game: 1. Solve M. 2. Write the two linear programming problems corresponding to.. Use the relation of dominance to solve the rectangular game whose payoff matrix to A is given in the following table. written 5.1 years ago by sayalibagwe ♦ 7.5k modified 7 months ago by ninadsail ♦ 1

Payoff Matrix Definition Presentation Exampl

Free matrix calculator - solve matrix operations and functions step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy PAYOFF MATRIX The payoff (a quantitative measure of satisfaction that a player gets at the end of the play) in terms of gains and losses, when player select their particular strategies, can be represented in the form of a matrix, called the payoff matrix. 24 36 8 32 20 16 PLAYER Y Y1 Y2 Y3 X1 X2 In this pay-off matrix, positive pay-off is the. Therefore the given game has no saddle point. It is a mixed game. Let us convert the given game into a LPP. Problem formulation Let V denote the value of the game. Let the probability that the player B will use his first strategy be r and second strategy be s. Let V denote the value of the game (427) to show, step by step, how to use this linear programming package to solve a two person zero sum game. Call our players, player 1 and player 2. Suppose player 1 has r strategies and player 2 has s strategies. Let A(i, j) be the payoff if player 1 chooses strategy i and player 2 chooses strategy j. The matrix A is called the payoff matrix Solve the problem. 12) A game has payoff matrix . Suppose R plays strategy [0.2 0.8]. (a) Determine C's best counterstrategy. (b) If C uses the best counterstrategy, what is the expected value of the game? 13) A game has payoff matrix . (a) Determine the optimal strategy for R. (b) Determine the optimal strategy for C. 14) The payoff matrix for.

Let's start with the first cell, and see if row player wants to switch choices. Since 1>-2, row player doesn't want to switch, so we can circle that payoff (in blue). The same method for column player shows that they would not want to switch as well so we can circle their payoff (in red). We can do the same analysis with each choice, to see where all of the circles should go Payoff Matrix Let's assume that the incremental profits that accrue to Coca-Cola and Pepsi are as follows: If both keep prices high, profits for each company increase by $500 million (because of. Problem 4 Easy Difficulty. Given the following payoff matrix for building at possible sites $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ under varying environmental conditions $\{\# 1, \# 2, \# 3\}$, set up and then solve the games for the builder and environmental conditions Matrix Game . A matrix game, which is short for finite two-person zero-sum game, allows a game to be represented in matrix form as its name implies. This is a direct consequence of the fact that two opponents with exactly opposite interests play a game under a finite number of strategies, independently of his or her opponent's action

In Exercises 23-26, solve the game with the given payoff

Game 1: The call lines Game. a. The Game Set-up. First things first, I present a simple game based on calling lines during an ultimate frisbee game. Ultimate is played with two teams. Each team needs to put 7 people on the line to play any given point Equation. The problem is modeled with a payoff matrix R ij in which the row index i describes a choice that must be made by the player, while the column index j describes a random variable that the player does not yet have knowledge of, that has probability p j of being in state j.If the player is to choose i without knowing the value of j, the best choice is the one that maximizes the. 1. Solve the game whose pay-off matrix is given below by the method of dominance

Maximim for A=Max(Minimum in each Row) =Max(-7,-5,3) =3. Minimax of B=Min(Maximum in each column) =Min(4,7,9,8) =4. Maximum for A is called the lower value of the game and denoted by V and minimax of B is called the upper value of the game and denoted by . So here V =3 & =4. If V is the value of the game then always satisfies the inequalit Solve the game whose pay-off matrix is given by. Answer: Please or signup to continue, It's FREE! Repeated: 2012 . Report Marks: 5 . 7. For the game with payoff matrix: Player B: Player A: B1: B2: B3: A1-1: 2-2: A2: 6: 4-6: Determine the optimal strategies for players A and B. Also determine the values of game

  1. I am absolutely new to decision theory . I came across this following payoff matrix in the book.(Math. Stats : John E Freund). Player A I II Player B 1 7 -4 2 8 10 The value of the game is given as 8 units.However i . have a question . I agree the optimal strategy for Play B is 2
  2. - Payoff matrix • For example, if the batter looks for a fastball and the pitcher actually pitches a fastball, then player I has probability 0.30 of getting a hit. - This is a constant sum game because player II's payoff and player I's payoff actually add up to 1. Wenson Chang @ NCK
  3. Payoff Matrix for Nash Equilibrium. Nash equilibrium refers to the level of outcome where change of strategic would not provide extra benefits to a player if other players do not change their strategies. Nash equilibrium can occur multiple times in a game. It is invented by John Nash and can be applied in many fields, such as ecology and economics
  4. (
  5. The given payoff matrix better demonstrates this: In this game, if player one chooses to play heads, player two would obviously respond with tails. Again if player two chose tails, player one would be interested to play tails in order to win and these choices would repeat themselves in a cyclic manner

Operation Research game theory by payoff matrix solution

  1. The proposed model and its solution represent a new method for solving rough matrix games, where the payoff matrix contains rough variables. We developed an optimal strategy and game for the players using rough constraints, by applying a GA to the trust measure with a confidence level (chosen by the decision maker)
  2. 3 Simplex Method 2x2, mx2, 2xn and mxn games 21.1.1 Analytical Method A 2 x 2 payoff matrix where there is no saddle point can be solved by analytical method. Given the matrix Value of the game is With the coordinates Alternative procedure to solve the strategy Lecture 21 Game Theory : Games with Mixed Strategies ( analytic and graphic methods )
  3. e the pay off matrix, the optimal strategies for both the players
  4. Based on the sets of strategies of players and linguistic variables for payoff assessment given above, the payoff matrix can be constructed for this game. Because the game is zero-sum, it only needs to give the payoff matrix of either player ALPHA or BETA. Here, the payoff matrix of ALPHA is given as shown in Table 1. It is worth noting that.
  5. A payoff matrix is a visual representation of the possible outcomes of a strategic decision. A payoff matrix includes data for opponents, strategies, and outcomes. A payoff matrix can be used to.
  6. The Game Theory Solver: Solve Any 2×2 Matrix Game Automatically. As ever, you can view more videos on math and game theory on my YouTube channel. The Prisoner's Dilemma. We'll start out with the most famous problem in game theory. Although this game is logically counter-intuitive, it is mathematically one of the easiest examples to solve
  7. The payoff matrix for companies A and B is shown (figures represent profit in millions of dollars). The dictator game is closely related to the ultimatum game, in which Player A is given a set.

The pay off matrix of a game is given below : Find the

The payoff matrix of a 2 * N game consists of 2 rows and N columns.This article will discuss how to solve a 2 * N game by graphical method. Consider the below 2 * 5 game: Solution: First check the saddle point of the game. This game has no saddle point. Step 1: Reduce the size of the payoff matrix by applying dominance property, if it exists.This step is not compulsory The above payoff table can also be depicted by the following payoff matrix, , where the columns represent the defensive team's actions and the rows represent the offensive team's actions. = [] In order to determine their optimal strategy, the offense must solve the below linear program Consider the below 2 * 5 game: Solution: First check the saddle point of The graphical method is used to solve the games whose payoff matrix has Two rows and n columns (2 x n) m rows and two columns (m x 2 A game may be represented as a set of matrices, one for each player, that specify the payoff to that player given the strategies of all players Example 1. (Solving a 2 2 Game) Consider the payo matrix P = 2 0 3 1 : (a) Find the optimal strategy for the row player. (b) Find the optimal strategy for the column player. (c) Find the expected payo of the game assuming both players use their optimal strategies. Finding the expected payo , and hence the expected winner, of a game unde That is basically the whole process of solving payoff matrices. Many times, you pretend that all but one player have made their strategy decision, and you find what the last player would do in that situation, given all their options. That's the same thing as defining p-1 indexes for a p-player game and sticking a colon in the empty space

This post is going to go over how to create a payoff matrix, associated with the game theory side of economics. The question associated with this is: Write out a pay off matrix when two players are offered $100 bills. If one bids $2 and the other bids $1 they pay $3, and the higher bidder gets the money leaving him with net gain of $98 while the other with a net loss of $1 The payoff matrix shows the gain (positive or negative) for player 1 that would result from each combination of strategies for the two players. Note that the matrix for player 2 is the negative of the matrix for player 1 in a zero-sum game. The entries in the payoff matrix can be in any units as long as they represent the utility (or value) to. 2. Obtain the optimal strategies for both-persons and the value of the game for zero-sum two person game whose payoff matrix is as follows : 1 3 3 5 1 6 4 1 2 2 5 0 Sol. Clearly, the given problem does not possess any saddle point. So, let the player B play the mixed strategy 1 2 1 2 B B B S q q with q q 2 1 1 against player A 2. Normal Form and Extensive Form Games: Normal form games refer to the description of game in the form of matrix. In other words, when the payoff and strategies of a game are represented in a tabular form, it is termed as normal form games. Normal form games help in identifying the dominated strategies and Nash equilibrium

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Then form a 2 x 2 payoff matrix from the original problem by retaining only the columns corresponding to those two lines which are having opposite slopes. 8. Solve the 2x2 game using oddments and find the strategies for Players A and B and also the value of the game. Consider the payoff matrix of Player A and solve it optimally using graphical. The simplest game is called a matrix payoff game with two players. In a matrix payoff game Game in which all actions are chosen simultaneously., all actions are chosen simultaneously. It is conventional to describe a matrix payoff game as played by a row player and a column player. The row player chooses a row in a matrix; the column player. is called the value of the matrix game with payoff matrix ij m n G g ~ and denoted by v(G) or simply v. 1) Definition 3.2: Thus if , is an equilibrium situation in mixed strategies of the game S S E m n, then *, * are the optimal strategies for the players A and B respectively in the matrix game with fuzzy payoff matrix . Hence * In this book the fundamental theorem of such games is states as: Theorem: Given... Stack Exchange Network Stack Exchange network consists of 177 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers

In our last lecture you learned to solve zero sum games having mixed strategies. But... Did you observe one thing that it was applicable to only 2 x 2 payoff Given the payoff matrix for player A, obtain the optimum strategies for both the players and determine the value of the game. Player B Player A 6 -3 7 -3 0 4. Algorithm for solving 2 x n matrix games. Make two vertical axes 1 unit apart. The two lines are as follows x 1 = 0, x 1 = 1; Get the points of the I st row in the payoff matrix on the vertical line x 1 = 1 and the points of the II nd row in the payoff matrix on the vertical line x 1 = 0

Game Theory concepts with application in Python using

When the rules of the game treat both players exactly the same, the game is called symmetric, which may be a little confusing because it corresponds to the payoff matrix being anti-symmetric, which simply means \(A = -A^{\top}\), i.e., the payoff matrix from the point of view of player two is the same as the one from the point of view of player. The most basic of games is the simultaneous, single play game. We can represent such a game with a payoff matrix: a table that lists the players of the game, their strategies and the payoffs associated with every possible strategy combination. We call games that can be represented with a payoff matrix, normal-form games In the game of tennis, each point is a zero-sum game with two players (one being the server S, and the other being the returner R). In this scenario, assume each player has two strategies (forehand F, and backhand B). Observe the following hypothetical in the payoff matrix A mixed strategy is the Nash equilibrium point of the game if and only if is the optimal solution to the following optimization problem, and the optimal value is 0: Especially, for the two-player matrix game, it can be seen from Theorem 1 that finding the Nash equilibrium of the game is equivalent: where and are payoff matrices of players, is. More than 2 choices for a player and matrix cannot be reduced by dominance (cannot use yesterday's formulas) Solving a Zero Sum Game 1. Set up the payoff matrix. 2. Remove any dominated rows or columns. (Section 11.1, Day 1) 3. Check for a saddle point. (Section 11.1, Day 2) If the saddle point exists, value of the game = saddle poin

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solving the game. Simultaneous move matrix games describe. Coordination problems between firms because firms must choose a strategy without observing the other firm's choice. dominant strategy. A strategy that will result in the highest payoff Section 2.1 Introduction to Two-Person Zero-Sum Games. In all of the examples from the last section, whatever one player won, the other player lost. Definition 2.1.1.. A two player game is called a zero-sum game if the sum of the payoffs to each player is constant for all possible outcomes of the game. More specifically, the terms (or coordinates) in each payoff vector must add up to the same. Thisgood has market demand given by the inverse demand function p(y) = 10 2y, wherep is price, and y = y1 + y2 is the... Posted 4 months ago Suppose A is a game matrix and Y0 is a given strategy for player II Y. To find the Nash equilibria, we examine each action profile in turn. ( X, X ) Firm 2 can increase its payoff from 1 to 2 by choosing the action Y rather than the action X. Thus this action profile is not a Nash equilibrium. ( X, Y ) Firm 1 can increase its payoff from 1 to 2 by choosing the action Y rather than the action X 246 SUMMARY OF METHODS FOR SOLVING GAMES The following steps can be used for from OPM 101 at Ms Ramaiah Institute Of Technolog

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