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CPS 296.1 Some practice questions

This set of practice questions explores various concepts in game theory, including extensive-form games, subgame-perfect equilibria, correlated equilibria, commitment benefits, voting profiles, Groves mechanisms, and false-name bidding.

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CPS 296.1 Some practice questions

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  1. CPS 296.1Some practice questions Vincent Conitzer conitzer@cs.duke.edu

  2. 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.

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

  4. 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

  5. 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)?

  6. 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.

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

  8. 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) • Can you win everything for free with only two bids?

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