?? EXERCISE 213.1 (Electoral competition with strategic voters) Consider the variant of the game in this section in which (i) the set of possible positions is the set of

numbers x with 0 ≤ x ≤ 1, (ii) the favorite position of at least one citizen is 0

and the favorite position of at least one citizen is 1, and (iii) each citizen’s pref- erences are represented by a payoff function that assigns to each terminal history the distance from the citizen’s favorite position to the position of the candidate in the set of winners whose position is furthest from her favorite position. Under the other assumptions of the previous exercise, show that in every subgame perfect equilibrium in which no citizen’s action is weakly dominated, the position chosen by every candidate who enters is the median of the citizens’ favorite positions. To do so, first show that in any equilibrium each candidate that enters is in the set   of winners. Then show that in any Nash equilibrium of any voting subgame in which there are more than two candidates and not all candidates’ positions are the same, some candidate loses. (Argue that if all candidates tie for first place, some citizen can increase her payoff by changing her vote.) Finally, show that in any subgame perfect equilibrium in which either only two candidates enter, or all can- didates who enter choose the same position, every entering candidates chooses the median of the citizens’ favorite positions.

The one-stage deviation principle for subgame perfect equilibria Recall that ui(σ | x) is the payoff to player i when the players implement the strategy vector σ, given that the play of the game has arrived at the vertex x. Prove that a strategy vector σ∗ = ()i∈N in an extensive-form game with perfect information is a subgame perfect equilibrium if and only if for each player i ∈ N, every decision vertex x, and every strategy  of player i that is identical to  at every one of his decision vertices except for x,

Guidance: To prove that σ ∗ is a subgame perfect equilibrium if the condition above obtains, one needs to prove that the condition ui(σ∗ | x) ≥ ui((σi, σ ∗ −i) | x) holds for every vertex x, every player i, and every strategy σi. This can be accomplished by induction on the number of vertices in the game tree as follows. Suppose that this condition does not hold. Among all the triples (x, i, σi) for which it does not hold, choose a triple such that the number of vertices where σi differs from σ∗i is minimal. Denote by X the set of all vertices such that σi differs from σ∗ i. By assumption, |X| ≥ 1. From the vertices in X, choose a “highest” vertex, i.e., a vertex such that every path from the root to it does not pass through any other vertex in X. Apply the inductive hypothesis to all the subgames beginning at the other vertices in X .

This paper is focusing on how you can make best use of your personality traits as a leader in Human Resources. Which leadership style(s) would best fit your personality. And what would likely be the most challenging adjustments for you to make in your leadership style when a situation requires a different style, given your particular personality traits?

Attached is the rubic, please read it carefully before you start to write. Thanks.

Explain how cookies can show that a user has visited a site if that user’s history has been deleted.

Optional: install Windows Historian and see the sites visited by a particular user.

Write in 300-400 words, in APA format.

Discuss at least two ways that you can help to control what information is readily available about you to anyone, including employers on the internet. 100-150 words.