Another homework question. I'm not understanding the lesson. Can I ask that I see the work done?Thank you! Sure! Here's a transcription and explanation suitable for an educational website:---### Voting Game Theory Exercise**Problem 2: Election Dynamics and Bayesian Games**In a simple voting game, the election of candidate 1 or candidate 2 depends on the votes of two citizens. The economic environment can be in one of two possible states, A or B. Both citizens agree:- Candidate 1 is preferable if the economy is in state A.- Candidate 2 is preferable if the economy is in state B.#### Payoff StructureEach citizen's preference is characterized by the expected value of a Bernoulli payoff function:- **Payoff of 1**: If the chosen candidate, deemed best for the state, wins.- **Payoff of 0**: If the other candidate wins.- **Payoff of 0.5**: If there is a tie.Citizen 1 has certain knowledge that the state is A. Citizen 2 believes:- The probability that the state is A is 0.9.- The probability that the state is B is 0.1.#### Voting OptionsEach citizen can make one of three decisions:1. Vote for candidate 1.2. Vote for candidate 2.3. Abstain from voting.#### Questionsa. **Formulation as a Bayesian Game** Define this setup as a Bayesian game, identifying the set of players, the potential states, and the signals available to each player.b. **Identification of Nash Equilibria** Demonstrate that the game possesses exactly two pure Nash equilibria: - In the first equilibrium, citizen 2 chooses not to vote. - In the second equilibrium, citizen 2 votes for candidate 1.c. **Dominance of Strategies** Show how one of the player's strategies in the second equilibrium is weakly dominated.d. **The "Swing Voter's Curse"** Analyze why the term "swing voter's curse" aptly describes citizen 2's choice in the second equilibrium.---This exercise provides a foundational understanding of strategic decision-making in uncertain environments and demonstrates the application of Bayesian and Nash equilibrium concepts in game theory.

Given information There are 2 candidates: 1 and 2 There are 2 states: A and B In state, A player 1 is the best candidate and in state B candidate 2 is the best. If the best wins then get payoff=1, if the tie gets pay off=1/2 and neither win gets pay off=0 Player 1 knows his state but player 2 does not know the state. So for player 1 probability of state A=0.9 and for state B =0.1 Part a) Pay off matrix will be: Player 1 is the Row player and player 2 is the column player. State A State B P=0.9 P=0.1 A B N A B N A 1,1 0.5,0.5 1,1 0,0 0.5,0.5 0,0 B 0.5,0.5 0,0 0,0 0.5,0.5 1,1 1,1 N 1,1 0,0 0.5,0.5 0,0 1,1 0.5,0.5 Part b) Expected payoff for player 1 AA AB AN BA BB BN NA NB NN A 0.9 0.95 0.9 0.45 0.5 0.45 0.9 0.95 0.9 B 0.5 0.55 0.55 0.05 0.1 0.1 0.05 0.1 0.1 N 0.9 1 0.95 0 0.1 0.05 0.45 0.55 0.45Now expected pay off for the player B Final expected pay-off matrix for both the player Player 1 is the row player and player 2 is the Column player. When player 1 choose A the player 2 chooses AB and NB When player 1 choose B the player 2 chooses AB and AN When player 1 choose N the player 2 chooses AB When player 2 choose AA the player 1 chooses A and N When player 2 choose AB the player 1 chooses N When player 2 choose AN the player 1 N When player 2 choose BA the player 1 chooses A When player 2 choose BB the player 1 chooses A When player 2 choose BN the player 1 chooses A When player 2 choose NA the player 1 chooses A When player 2 choose NB the player 1 chooses A When player 2 choose NN the player 1 chooses A Therefore There are 2 pure Nash equilibrium: {N,AB} and A, NB} Here in the Nash equilibrium {A,NB} only 1 citizen vote and he wins. In Nash equilibrium {N, AB} 2nd citizen votes. Part c) In Nash equilibrium {A, NB} NB is weekly dominated for the player 2 (0.95=0.95,0.1<0.55,0.55<1)--- It shows that NB is weekly dominated over the AB strategy. Part d) Swing voters curse refers to the situation where one of the voters is uncertain about the realization of the state. In this case, it affects the overall utility. So in this case less informed voter remains indifferent and restrain themselves to vote rather than voting for either candidate. Hers for the second Nash equilibrium where voter 2 is less informed about the state. So he restrains to vote for either of the candidates.