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Consider the electoral competition game presented in Lecture 6. In this game there are two candidates who simultaneously choose policies from the real line. There is a distribution of voters with median m and the candidate whose policy is closest to the median wins the election and the winning candidate's policy is implemented. If the two candidates are an equal distance from the median, then the average of the two policies is implemented. For this problem we suppose that both candidates care about both the implemented policy and winning the election. That is, the payo to each candidate has two parts. The first part is the utility from the implemented policy a*. That is, each candidate has utility u(a* ; xi), where xi is the ideal policy of candidate i and utility decreases to the left and right of xi. We suppose that xi < m < xj . The second part is the value of winning office, which we denote wi > 0 for candidate i. Putting these two parts together, we de ne the payoff to candidate i by
Find all Nash equilibria to this game.
In any game, payoffs are numbers that represent the motivations of players. Payoffs might represent profit, quantity, "utility," or different continuous measures (cardinal payoffs)
A participant in a very game who selects from among her methods randomly, primarily based on some predetermined chance distribution, instead of strategically, primarily based on pa
Find the pure-strategy Nash equilibrium Alice is on vacation in Wonderland and considers trying a special mushroom sold by the caterpillar. She cannot tell upfront if the mush
Rollback (often referred to as backward induction) is an iterative method for solving finite in depth kind or sequential games. First, one determines the optimal strategy of the pl
. A bid is an sign by a potential buyer of the price the buyer is ready to pay for the object being auctioned. In a Procurement Auction, the bid is an sign of the price a seller is
"Assurance game" is a general name for the game more commonly known as "Stag Hunt." The French philosopher, Jean Jacques Rousseau, presented the subsequent circumstances. Two hunte
A pure strategy defines a selected move or action that a player can follow in each potential attainable state of affairs in a very game. Such moves might not be random, or drawn fr
The Cournot adjustment model, initial proposed by Augustin Cournot within the context of a duopoly, has players choose methods sequentially. In every amount, a firm selects the act
Assurance game Scenario "Assurance game" may be a generic name for the sport a lot of commonly called "Stag Hunt." The French thinker, Jean Jacques Rousseau, presented the subse
Find Pure Nash Equilibria 1. Consider a two-player game in which player 1 chooses the strategy x 1 from the closed interval [-1, 1] while player 2 chooses the strategy x 2 fr
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