(A) Explain, using examples, the following concepts from game theory:
(i) a strategy, (ii) a strategy profile, (iii) dominant strategy equilibrium, (iv) pure strategy Nash equilibrium, (v) mixed strategy Nash equilibrium, (vi) a reaction function.
(i) A strategy: A strategy refers to a move or action a player can make in any given game, where the outcome will depend on the players actions and the actions of others. A strategy determines what move/action a player will make at any given stage during a game. For example, a dominant strategy is a strategy which dominates all others i.e. a player will always be better off choosing A over B, regardless of the choices of the other players. In the Prisoner’s Dilemma, the best thing Clyde can do in …show more content…
A game that cannot have regret has a pure Nash equilibrium, and a game that cannot have no regret has no pure Nash equilibrium. For example, in the Prisoners Dilemma game the responses (-10, -10) and (-10, -10) are both pure strategy Nash equilibria, as neither player would wish to change their strategy once they seen the outcome. They both chose the best response available to the opponent’s …show more content…
• That all political views up for election are placed along a one-dimensional policy spectrum.
The effect of the median voter theorem on political parties is explained using the following examples. Let’s say a Democratic political party and a Republican political party are running for election in a majority-rule, single-peaked, two-party system. For either of the parties to get the majority vote from voters along the one-dimensional policy spectrum, they will need to get at least one vote more than 50%.
The Democratic party, being on the far left (Fig. 1), will presumably receive the votes of those on the far left side of the one-dimensional voting spectrum, as they will have similar political views. As the spectrum moves right, the democratic views become less extreme and more mainstream, so while they may not be a guarantee, the party can presume they will still get the majority of votes from those within that section. However, as we move towards the middle of the spectrum, political views become less extreme and more independent, possibly even quite different from democratic views, but the party will need these votes to guarantee a vote of over
(i) a strategy, (ii) a strategy profile, (iii) dominant strategy equilibrium, (iv) pure strategy Nash equilibrium, (v) mixed strategy Nash equilibrium, (vi) a reaction function.
(i) A strategy: A strategy refers to a move or action a player can make in any given game, where the outcome will depend on the players actions and the actions of others. A strategy determines what move/action a player will make at any given stage during a game. For example, a dominant strategy is a strategy which dominates all others i.e. a player will always be better off choosing A over B, regardless of the choices of the other players. In the Prisoner’s Dilemma, the best thing Clyde can do in …show more content…
A game that cannot have regret has a pure Nash equilibrium, and a game that cannot have no regret has no pure Nash equilibrium. For example, in the Prisoners Dilemma game the responses (-10, -10) and (-10, -10) are both pure strategy Nash equilibria, as neither player would wish to change their strategy once they seen the outcome. They both chose the best response available to the opponent’s …show more content…
• That all political views up for election are placed along a one-dimensional policy spectrum.
The effect of the median voter theorem on political parties is explained using the following examples. Let’s say a Democratic political party and a Republican political party are running for election in a majority-rule, single-peaked, two-party system. For either of the parties to get the majority vote from voters along the one-dimensional policy spectrum, they will need to get at least one vote more than 50%.
The Democratic party, being on the far left (Fig. 1), will presumably receive the votes of those on the far left side of the one-dimensional voting spectrum, as they will have similar political views. As the spectrum moves right, the democratic views become less extreme and more mainstream, so while they may not be a guarantee, the party can presume they will still get the majority of votes from those within that section. However, as we move towards the middle of the spectrum, political views become less extreme and more independent, possibly even quite different from democratic views, but the party will need these votes to guarantee a vote of over