Assignment:

$1)$ What is the difference between a cooperative and a noncooperative game? Give an example of each.

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$2)$ Suppose the following game of $$Matching Pennies.$$ In this game, each player chooses heads or tails and the two players reveal their coins at the same time. If the coins match $($i$.$e$.,$ both are heads or both are tails$),$ Player A wins and receives a dollar from Player B$.$ If the coins do not match, Player B wins and receives a dollar from Player A$.$ The payoff matrix is shown in the next table

Player B

Heads Tails

Player A Heads $1,-1-1,1$

Tails $-1,11,-1$

Check that there is no Nash Equilibrium in pure strategies. Explain the Nash Equilibrium in mixed strategies for this game.