Q. 2. Consider the game of voters participation. Two candidates A (with two suporters) and B (with remaining three voters supporting him) compete. Voters have the option of voting for the preferred candidate or abstain. If a voter decides to vote then her payoffs are 2-e, 1- c and - c if her preferred candidate wins, ties or loose respectively. Her payoffs are 2, 1 and 0 for the above outcomes if she abstains. Show that there is a mixed strategy Nash equilibrium in which both supporters of A votes with probability p (0

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Q. 2. Consider the game of voters participation. Two candidates A
(with two suporters) and B (with remaining three voters supporting
him) compete.
Voters have the option of voting for the preferred candidate or
abstain. If a voter decides to vote then her payoffs are 2-e, 1- c and - c
if her preferred candidate wins, ties or loose respectively. Her payoffs
are 2, i and 0 for the above outcomes if she abstains.
Show that there is a mixed strategy Nash equilibrium in which both
supporters of A votes with probability p (0 <p<1), two of the supporters
of B votes with certainty while the other one abstain.
Transcribed Image Text:Q. 2. Consider the game of voters participation. Two candidates A (with two suporters) and B (with remaining three voters supporting him) compete. Voters have the option of voting for the preferred candidate or abstain. If a voter decides to vote then her payoffs are 2-e, 1- c and - c if her preferred candidate wins, ties or loose respectively. Her payoffs are 2, i and 0 for the above outcomes if she abstains. Show that there is a mixed strategy Nash equilibrium in which both supporters of A votes with probability p (0 <p<1), two of the supporters of B votes with certainty while the other one abstain.
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