Some practice questions

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Presentation transcript:

Some practice questions Vincent Conitzer conitzer@cs.duke.edu

Matching pennies to decide who is player 1 In the poker game discussed in class, it matters who is player 1. Suppose two players first play a round of “matching pennies” to determine who gets to be player 1, and then play the game. Model the whole game as an extensive-form game and solve for subgame-perfect equilibrium.

Many equilibria Can you create an n x n game that has 2n-1 Nash equilibria?

Correlated beats unique pure Nash Can you create a game that has a unique Nash equilibrium, which is a pure-strategy equilibrium, and another correlated equilibrium that is better for both players

Confusing profiles of votes For an arbitrary number n of alternatives, can you come up with a profile of votes such that… The Borda ranking is the opposite of the plurality ranking? The Copeland ranking is the opposite of the plurality ranking? Etc.

Generous Groves For a combinatorial auction, can you create a Groves mechanism so that every bidder always receives a nonnegative payment?

False-name bidding Suppose there are three bids already: ({A,B}, 1) ({A,C}, 1) ({C,D}, 1) The auction mechanism is the GVA. Can you win everything for free with only two bids? Now suppose there are four bids ({A,B}, 1) ({A,C}, 1) ({A,D}, 1) ({C,D}, 1)

Mixing necessary to get commitment benefit Can you create a game where committing to a pure strategy hurts (is strictly worse than the simultaneous-move solution), but committing to a mixed strategy helps (is strictly better than the simultaneous-move solution)?