# Topic: Would you pls me? you! For the generalization, think of (1) real-life scenario where you can apply game theory. You must have: Two (2)

Topic: Would you pls me? you! For the generalization, think of (1) real-life scenario where you can apply game theory. You must have:

Two (2) players

Two (2) choices/strategies

Two (2) payoffs for each choice

Assume that the two (2) players cannot collaborate or communicate with each other.

Construct the payoff matrix for their situation. Clearly identify the dominant strategy in your payoff

matrix. You must also justify your choice/s by identifying the maximax and maximin strategies in the

situation. Hayes, A. (2021, April 28). How game theory works. Investopedia. https://www.investopedia.com/terms/g/gametheory.asp For the generalization. think of one [1] real-life scenario where you can apply game theory. You

must haye: Two [2] players Two l2] choicesfsh’ategies Two [2} payoffs for each choice Assume that the two [2} players cannot collaborate or communicate with each other. Clearly identify the dominant strategy in your payoff matrix. You must also justify your choicel’s

by identifying the maximax and maximin strategies in the situation. Coin Matching Game. Roger and Colleen play a game. Each one has a coin. They

will both show a side of their coin simultaneously. If both show heads, no money

will be exchanged. If Roger shows heads and Colleen shows tails then Colleen will

give Roger 40. If Roger shows tails and Colleen shows heads. then Roger will pay Colleen 40. if both show tails. then Colleen will giye Roger

ED. This is a Two person game. the players are Roger and Colleen. It is also a zero-sum

game. This means that Roger’s gain is Colleen’s loss. We can use a 2 x 2 array or matrix to show all four situations and the results as

follows: Colleen Roger Roger pays Roger gets 0 40 Colleen pays Colleen pays 40 This is called a two-person. . Roger pays Roger gets

zero-sum game because the 4:0 80

amount won by each player CDIIEBII gets Colleen pays is

equal to the negative of the 40 30

amount won by the opponent for any given situation. The amount won by either player in any given

situation is called the pay-off for that player. A negative pay—off denotes a loss of that amount for the player. Since it is a zero~sum game. we can deduce the payhoff of one

player from that of the other. thus we can deduce all of the ahoye information from

the pay-off matrix shown below. The pay-off matrix for a game shows only the pay-

off for the row player for each scenario. cm… R

It: ll-I

Cl

EH

3. A player’s plan of action against the opponent is called a strategy. in the aboye

example. each player has two possible strategies; H and T. We will try to

determine each player’s best strategy assuming both piayers want to maximize

their pay-off. Sometimes our conclusions will make most sense when we consider players who are repeatedly playing the same game. In the general situation for a two-player. zero sum game. we will call the two

players Rifor row] and leor column]. For each such game, we can represent all of

the information about the game in a matrix. This matrix is called the Pay—off

matrix for R. It is a matrix with a list of R’s strategies as labels for the rows and a

list of [‘5 strategies as labels for the columns. The entries in the pay-off matrix are

what R gains for each combination of strategies. If this is a negatiye number than

it represents a loss for R. Minimax strategy: minimizing one’s own maximum loss

Maximin strategy: maximize one’s own minimum gain

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