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Additional resources for Introduction to Game Theory
The game contains the two threat points -- d1 = 2000 -- d2 = 4000 • Let the sought after apportionments of the profits be u1 for Rene and u2 Jenny. • The constraint u1 + u2 = 10,000 applies, that is, the complete sum must be apportioned. To determine the solution we apply the so-called Nash solution, which maximises the term (u1 – d1) • (u2 – d2) under the above-mentioned constraint. We thus obtain the maximisation problem max (u1 – d1) • (u2 – d2) under the constraint p – u1 – u2 = 0 The constraint is (as already done here) to be reformed so that there is a zero on the right-hand side.
According to the rules of game theory, the player should be indifferent between the two urns, because the probability of forecasting the right colour is 50 percent in each case. However, in reality, the experimental subjects mainly choose urn 1. 1 The ultimatum game In the ultimatum game $100 are to be divided between two players. First of all, player 1 (proposer) makes a suggestion as to how the amount is to be divided. Player 2 (responder) can accept this proposal – and the amount is then split accordingly – or reject it.
Sequential games are also known as games in extensive form. While simultaneous games are illustrated by means of matrices, sequential games are shown by means of a decision tree: Player 2 Player 1 X2 (A1, A 2) Y2 X1 (A1, A 2) X2 Y1 (A1, A 2) Y2 (A1, A 2) In this game, player 1 makes a decision first; he has the choice between X1 and Y1. Player 2 then makes his choice between X2 and Y2. Depending on what the choice of player 1 is, player 2 makes his decision in another node. Because the game’s information is known to the players, player 2 can already consider from the start how he will decide in which case.