Example 43 Application of the SCG algorithm

There are five students, A, B, C, D, and E, and five rooms, V, W, X, Y, and Z. Three of the rooms are presently occupied W by student B, X by student C, and Y by student D. All five students will participate in the allocation scheme because all three tenants are guaranteed rooms that are at least as attractive as the ones they currently occupy. Assume that the priority ordering is ABCDE. A partial list of the students's preferences is presented in Table 9.21. We have given only a partial...

Relation to the Gibbard Satterthwaite Theorem

Truthful revelation is a dominant strategy for each individual when the pivotal mechanism is used to select a public project. Why does that not contradict the Gibbard-Satterthwaite Theorem of Chapter 7 (Section 2) That theorem establishes that there does not exist a nondictatorial incentive scheme for inducing truthful revelation when there are more than two possible outcomes. The pivotal mechanism is even invulnerable to manipulation when there is a continuum of possible outcomes. And the...

Example 51 Extensive form twoperson game

The game is represented as Figure 1.5 . At the first stage player A has a choice of moving left or right. If A moves left the game is over, and A's payoff is 1 and B's payoff is 5. If player A moves right at the first stage then player B has the next move and can go up or down. If B chooses up then each gets a payoff of 3, but if B moves down then A's payoff is 0 and B's payoff is 2. Consider the normal form representation of the same game displayed as Table 1.13. R U represents the strategy B...